Can P -> P ?

[HereLiesTheBible]

Just need a quick reminder regarding symbolic logic.

is it valid to say p implies p?

[kennethamy]

Just need a quick reminder regarding symbolic logic.

is it valid to say p implies p?

No, but it's true.

Every proposition implies itself since it is impossible for the antecedent to be true and the consequent false, and if an implication is such that is is impossible for the antecedent to be true, and for the consequent to be true, then that implication is true.

("P implies P" is a statement, and only arguments are valid or invalid. Only statement are true or false).

[Antiplastic]

No, but it's true.

Every proposition implies itself since it is impossible for the antecedent to be true and the consequent false, and if an implication is such that is is impossible for the antecedent to be true, and for the consequent to be true, then that implication is true.

("P implies P" is a statement, and only arguments are valid or invalid. Only statement are true or false).

Actually, schemata are truth-functionally valid or not valid. A schema (like 'p->p') is truth-functionally valid iff for all assignments of variables, it returns a value of True. So 'p->p' is truth-functionally valid.

[kennethamy]

Actually, schemata are truth-functionally valid or not valid. A schema (like 'p->p') is truth-functionally valid iff for all assignments of variables, it returns a value of True. So 'p->p' is truth-functionally valid.

Arguments are valid. If that statement were reconstructed as an argument, the resulting argument would be valid. Why mix up truth and validity? (I know that some logician like to say that tautologies are "valid statements" to point out that they are tautologies. I think that just confuses matters).

[HereLiesTheBible]

even if P does keep causing P over and over again, it can't be the initial cause of itself right?

[kennethamy]

even if P does keep causing P over and over again, it can't be the initial cause of itself right?

Implication is not a causal relation. It is a logical relation.

[HereLiesTheBible]

Let me just give the context that I'm talking about for clarification.

Suppose the botched suicide scenario:

You are very depressed. You are suicidally depressed. You have a gun. But
you do not quite have the courage to point the gun at yourself and kill
yourself in this way. If only someone else would kill you, that would be a
good thing. But you can't really ask someone to kill you. That wouldn't be
fair. You decide that if you remain this depressed and you find a time
machine, you will travel back in time to just about now, and kill your earlier
self. That would be good. In that way you even would get rid of the
depressing time you will spend between now and when you would get into
that time machine. You start to muse about the coherence of this idea, when
something amazing happens.

Out of nowhere you suddenly see someone coming towards you with a gun
pointed at you. In fact he looks very much like you, except that he is
bleeding badly from his left eye, and can barely stand up straight. You are at
peace. You look straight at him, calmly. He shoots. You feel a searing pain
in your left eye.

Your mind is in chaos. You stagger around and accidentally enter a strange
looking cubicle. You drift off into unconsciousness. After a while, you can
not tell how long, you drift back into consciousness and stagger out of the
cubicle. You see someone in the distance looking at you calmly and
fixedly. You realize that it is your younger self. He looks straight at you. You
are in terrible pain. You have to end this, you have to kill him, really kill
him once and for all. You shoot him, but your eyesight is so bad that your
aim is off. You do not kill him, you merely damage his left eye. He
staggers off. You fall to the ground in agony, and decide to study the
paradoxes of time travel more seriously.

Obviously there is a loop occuring here, but what causes the first loop?

[kennethamy]

Let me just give the context that I'm talking about for clarification.

Suppose the botched suicide scenario:

You are very depressed. You are suicidally depressed. You have a gun. But
you do not quite have the courage to point the gun at yourself and kill
yourself in this way. If only someone else would kill you, that would be a
good thing. But you can't really ask someone to kill you. That wouldn't be
fair. You decide that if you remain this depressed and you find a time
machine, you will travel back in time to just about now, and kill your earlier
self. That would be good. In that way you even would get rid of the
depressing time you will spend between now and when you would get into
that time machine. You start to muse about the coherence of this idea, when
something amazing happens.

Out of nowhere you suddenly see someone coming towards you with a gun
pointed at you. In fact he looks very much like you, except that he is
bleeding badly from his left eye, and can barely stand up straight. You are at
peace. You look straight at him, calmly. He shoots. You feel a searing pain
in your left eye.

Your mind is in chaos. You stagger around and accidentally enter a strange
looking cubicle. You drift off into unconsciousness. After a while, you can
not tell how long, you drift back into consciousness and stagger out of the
cubicle. You see someone in the distance looking at you calmly and
fixedly. You realize that it is your younger self. He looks straight at you. You
are in terrible pain. You have to end this, you have to kill him, really kill
him once and for all. You shoot him, but your eyesight is so bad that your
aim is off. You do not kill him, you merely damage his left eye. He
staggers off. You fall to the ground in agony, and decide to study the
paradoxes of time travel more seriously.

Obviously there is a loop occuring here, but what causes the first loop?

I don't see what this had to do with your original question about logic. However, you are pointing out the paradox of killing yourself in the past, when you are alive now. I suppose that the answer is that it is impossible for you do do that, since that would imply a contradiction (you would be both alive and not alive) and whatever implies a contradiction is a contradiction, and therefore, as I just said, impossible. There is a better known variation on this non-paradox. It is your going into the past, and killing your own grandfather. For the same reason, that is also impossible. Therefore, either you cannot go back into the past, or else, you can, but you cannot kill yourself or your grandfather.

[HereLiesTheBible]

If you read more carefully you will see that while it was intent of yourself to kill yourself you failed, and created this loop in time in which you continually going back in time to only injure yourself and do it again.

[comiezapr]

i think what ken and bible are saying is this ...

when you use the symbol " -> " do you mean to use it as:

1) a truth functional connective (it is part of sentences)
2) a symbol of proof theory indicating deductive consequence (it connects sentences together)

To make this clearer ill use the symbol " -> " in both manners.

1)

I have a sentence that says "if birds fly then birds fly" and transcribe this into logical symbols. The transcription would read "P -> P". I have use " -> " as a truth functional connective.

2)

I have an argument that says "from the sentence 'birds fly' i can deduce 'birds fly'". In order to make this more readable i use symbols: P -> P. I have used " -> " to join two sentences within a deduction.

In your first post you should have been clearer about how you were using the symbol " -> ". But practically speaking it doesnt matter; its a wonderful result of proof theory that if B is deducible from A then the sentence "if A then B" is truth functionally valid.

And yes, "P -> P" is valid, and P can be derived from P!

[Antiplastic]

Arguments are valid. If that statement were reconstructed as an argument, the resulting argument would be valid.

I am not talking about reconstructing the statement as an argument. I am talking about the truth-functional schema it instantiates. And the schema it instantiates is valid. You can do the truth table yourself if you don't believe me.

Why mix up truth and validity?

I wouldn't know. That sounds like a terrible idea.

[kennethamy]

I am not talking about reconstructing the statement as an argument. I am talking about the truth-functional schema it instantiates. And the schema it instantiates is valid. You can do the truth table yourself if you don't believe me.



I wouldn't know. That sounds like a terrible idea.

I know, it is a tautology. I suppose I don't mind you introducing the technical term, "schema" and ascribing validity to it. Of course, technically, p implies p is not a statement at all, it is a statement form, and if statement forms are schemata, and schemata can be valid, then that statement form is valid. So I have to withdraw my former assertion that p implies p is a statement. That was sloppy. It is a statement form (or "schema") and if schema are valid, it is valid. An irenic compromise, and I had to eat only a little bit of crow.

[rob117]

I don't see what this had to do with your original question about logic. However, you are pointing out the paradox of killing yourself in the past, when you are alive now. I suppose that the answer is that it is impossible for you do do that, since that would imply a contradiction (you would be both alive and not alive) and whatever implies a contradiction is a contradiction, and therefore, as I just said, impossible. There is a better known variation on this non-paradox. It is your going into the past, and killing your own grandfather. For the same reason, that is also impossible. Therefore, either you cannot go back into the past, or else, you can, but you cannot kill yourself or your grandfather.

Or, in killing your grandfather, you generate an alternate and parallel reality that does not replace the one you came from. Therefore there is no paradox.

[comiezapr]

I don't see what this had to do with your original question about logic. However, you are pointing out the paradox of killing yourself in the past, when you are alive now. I suppose that the answer is that it is impossible for you do do that, since that would imply a contradiction (you would be both alive and not alive) and whatever implies a contradiction is a contradiction, and therefore, as I just said, impossible. There is a better known variation on this non-paradox. It is your going into the past, and killing your own grandfather. For the same reason, that is also impossible. Therefore, either you cannot go back into the past, or else, you can, but you cannot kill yourself or your grandfather.

It is definetly logically possible to go back in time and kill your gradnfather. I dont think you would disagree. I would also argue it is metaphysically possible to go back in time and kill your grandfather. It is, however, not physically possible to go back in time and kill your grandfather; though this is true because you cant physically go back in time.

The counterfactual conditional "if i were to go back in time, i couldnt kill my grandfather" is questionable to me and is probably a case of the vagueness of counterfactual conditionals ... i wouldnt be to vehement about the truth or falsity of this counterfactual. On the one hand there is nothing that physically prevents me from stabbing another human being, of which my grandfather is an instance. On the other hand his death leads to problems down the road for me. Which possibility is more realistic, one where i can kill my grandfather and one where i cannot, given that i can travel back in time, is certianly far from clear to me.

The other counterfactual "if i were to go back in time i couldnt kill myself" is both vague and indeterminite. The vagueness is due to the counterfactual portion. The indeterminitness is due to the conditions of personal identity. I think that this counterfactual, like the grandfather counterfactual should be left unjudged in terms of its truth value until some more analysis is done!

[kennethamy]

It is definetly logically possible to go back in time and kill your gradnfather. I dont think you would disagree. I would also argue it is metaphysically possible to go back in time and kill your grandfather. It is, however, not physically possible to go back in time and kill your grandfather; though this is true because you cant physically go back in time.



I would definitely disagree, because it would entail a contradiction (given certain assumptions about generation) since it would entail that I could be both alive at T1, and destroy all the conditions for my being alive at T1 at T2. Killing myself at T2, and being alive at T1, is even more directly a contradiction, just assuming the impossibility of revival of the dead.

[kennethamy]

Or, in killing your grandfather, you generate an alternate and parallel reality that does not replace the one you came from. Therefore there is no paradox.

Not if you can make any sense of the notion of "an alternate and parallel" reality". The fact that a string of words are all meaningful, and syntactically in order, does not guarantee that the string of words is meaningful.

[rob117]

Not if you can make any sense of the notion of "an alternate and parallel" reality". The fact that a string of words are all meaningful, and syntactically in order, does not guarantee that the string of words is meaningful.

I don't see the problem.

[comiezapr]

I would definitely disagree, because it would entail a contradiction (given certain assumptions about generation) since it would entail that I could be both alive at T1, and destroy all the conditions for my being alive at T1 at T2. Killing myself at T2, and being alive at T1, is even more directly a contradiction, just assuming the impossibility of revival of the dead.

I dont see the logical contradiction. Ill put down the propositions ...

I am alive at T1.
At T1 i destroy the conditions for my being alive at T2.

Theres no contradiction here, we would need to supplement it with various premises ....

1) I am alive at T1.
2) If the conditions for me to be alive at T1 arent in place then i am not alive at T1.
3) If i kill my grandfather at T2 the conditions for me to be alive at T1 arent in place.
Therfore: If i kill my grandfather at T2 then i am alive at T1 and not alive at T1.

This is a contradiction, which means one of our assumptions is bad. Which assumption we should discard is a matter of debate. I find both 2 and 3 highly suspect. The same goes for killing myself.

This isnt a cut and dry matter, and more importantly, the meat of the debate isnt a matter of logic but rather a matter of personal identity. You see personal identity as somehow dependent on the historical chain of ancestry (in the case of the grandfather) whereas i do not.

[AdamWho]

What does time travel have to do with philosophy?

Logic notation doesn't imply or refute time travel.

[Infideliation]

It is definetly logically possible to go back in time and kill your gradnfather. I dont think you would disagree. I would also argue it is metaphysically possible to go back in time and kill your grandfather. It is, however, not physically possible to go back in time and kill your grandfather; though this is true because you cant physically go back in time.

I'm a bit puzzled what this time travel stuff has to do with the OP. I do agree with ken on this one though. If your exact past didn't already have an OLDER double of yourself that is created with the memory of travelling backwards in time before you were born it's not going to be possible to travel to your exact past and remember it. Think of it this way. You travel back in time to when you were five years old. Clearly, when you were five you don't recall travelling back in time to your five year old body. Why? Because you never did it. The way "time travel" works is that even assuming you could do it you won't remember the trip. Travelling to your exact past will place you in the exact mind and body that always existed in that past and then history will occur exactly as it did before, ie. what you remember of your past. When you step out of the "time machine" you won't remember the trip, you'll just remember stepping in and out of a box. The only way "time travel" is possible is that you travelled to an alternate reality. The only way to time travel in the same reality and remember it is if you were created from nothing as an adult before you were born as a child so that you have another body to step into in order to observe yourself (but given this scenario, even if you killed your child self, your adult self will still remain). The problem with the second scenario (besides being born from nothing as an adult before being born as a child) is that it's indistinguishable from the idea of simply travelling to an alternate reality. Ockham's razor does what it's supposed to do at this juncture. Realize what it means to travel backwards in time to your exact past. If it's not your exact past it's an alternate reality. Calling it time travel is superfluous magical thinking.

[Amedeo]

Just need a quick reminder regarding symbolic logic.

is it valid to say p implies p?

One can posit, set up, anything, such as any relationship between two propositions, as long as the relationship term is meaningless. (In that case, he has played with the physical constitution of the propositions -- the sounds or the written graphs.)

If we are to speak meangfully and we say, "proposition P is true because it is true," we are BEGGING THE QUESTION, we are committing a fallacy, precisely because, when asked why P is true, we assume that it is true and then we use this assumption to explain what makes it true.

"Implies" -- as a meaningful utterance -- does NOT state that if P occurs or exists, then P exists; it refers to the verbalized JUDGEMENT and asserts its truth; that is, for example, "Napoleon was defeated at Waterloo." Again, the proposition asserts a truth; or, it asserts that the predicate is factually true of the subject.

So, if you ask whether it is true that Napoleon was defeated at Waterloo, and I answer that he was, because -- I declare -- he was defeated, I am providing the concept that Napoleon was defeated at Waterloo for the truth of your bare proposition, "Napoleon was defeated at Waterloo."

So, if P means {"a is b" is true}

then {P implies P} begs the question.

On the contrary,

{fP impies P} is correct; it means:

factual (evinced) P implies truthful P.

When "p" is used without qualifications, "p is used equivocally. Hence,

{p -> p} constitutes a fallacy of equivocation. (The makers of symbolic logic were not very perspicacious logicians and committed various fallacies. However, if symbolic logic is intended to be a formal system which has no bearing on reality, then there are no fallacies.)

[mac_philo]

There is no fallacy of equivocation and no question is begged if we are talking about 'p->p' with its normal meaning in symbolic logic. The OP also used the word 'implies', and it isn't clear what is meant by that. '->' is the material conditional, it is not strict or logical implication.

Here is its truth table:

p p->p
T T
F T

By the definition of validity, p->p is valid.

Or you can illustrate it from the other direction. Suppose p->p is not valid. Then in some interpretation it is false. Well, -(p->p) is equivalent to p & -p. That is a contradiction, hence p->p is false in no interpretation, hence it is valid.

The English meaning of 'p->p' does not involve the English terms 'implies', 'true', 'because', 'factual' etc. The English meaning of 'p->p' is simply 'if p then p'. It makes no difference what 'p' stands for, and it has nothing to do with evidence or explanation.

[Dupesh]

is it safe to say that p implies p? yes. yes it is.
this strange '->' is nothing, what is your motive in using it?

saying p implies p is like saying "if p then p" as a single statement. so it's safe to draw the conclusion, "if p, then p and p," from that statement.

unfortunately you clearly beg the question and fall into an infinite regress. this reminds me of that kid who was jive talkin existence to function as a predicate or a property. you really can't prove something like that, just accept it as a given.

[Dupesh]

but yes it is valid by sheer inevitability

[Kronocide]

Obviously there is a loop occuring here, but what causes the first loop?

Actually, it's not a loop (except in the sense of a once-off loopback). After you have shot yourself and failed to kill yourself, what happens? That is the current timeline, and it proceeds normally (except you have gotten some time back). If you had actually managed to kill yourself, then you'd be in paradox land.

As for "p implies p." You don't need to involve a truth-functional definition of implication. It's just a formalization of "if p is true then p is true." Which quite obviously follows.

[Bobinius]

Just need a quick reminder regarding symbolic logic.

is it valid to say p implies p?

Yes. Actually, what you have here is not an implication, but an identity:

P <-> P.

And the identity is valid (it stands under all interpretations of p). It's not true or false, since an inference is not a proposition.

[Amedeo]

There is no fallacy of equivocation and no question is begged if we are talking about 'p->p' with its normal meaning in symbolic logic. The OP also used the word 'implies', and it isn't clear what is meant by that. '->' is the material conditional, it is not strict or logical implication.

Here is its truth table:

p p->p
T T
F T

By the definition of validity, p->p is valid.

Or you can illustrate it from the other direction. Suppose p->p is not valid. Then in some interpretation it is false. Well, -(p->p) is equivalent to p & -p. That is a contradiction, hence p->p is false in no interpretation, hence it is valid.

The English meaning of 'p->p' does not involve the English terms 'implies', 'true', 'because', 'factual' etc. The English meaning of 'p->p' is simply 'if p then p'. It makes no difference what 'p' stands for, and it has nothing to do with evidence or explanation.
A truth table [so badly named!] is a tabulation of correlations between TWO connected propositions -- connected by either/or [conjointly or disjointly], if/and [...], both/and. In all cases, you calculate thus, "IF p is true, how is q?" Or, "IF p is not true, how about q?" You are syllogizing and making inferences.

There does not have to be a realistic or cause/effect relationship between what is denoted by p and by q, as in the case, "If the sun is shining, then it is night." The point is that, assuming that p -> q,
if p is true, then q must be true.

If a single proposition is given, no inference can be made. There is no true table applicability.

On the other hand, we can make analytical stipulations about a propositions, such as
p <-> p (principle of identity); and

either p or else not p [expressible by equivalence or reciprocal implicatio or othewise].

I know you could deduce the principle of non-contradiction from some logical calculation (WHILE the principle is being adhered to in the statements you make).

You may also make this inference:

[(p <-> p ] ->.... (p -> p)

but the inferred portion is NOT the inferring of p from p. So, the inferred portion does NOT mean "p is true because p is true (which would constitute the begging of the question).

What can ( p -> p ) mean in a valid or non-fallacious way??? It means something like this:

John happens to be sitting on a cliff (he did not have to be there; he was not forced to be there). If he happens to be sitting on a cliff, he is certainly/factually sitting there.

What happens (or is not necessary) is a contingency. (The other two contradictory modalities are possibility and impossibility.) What is continent is a fact, not a hypothesis; one cannot extract a fact from a hypothesis.

So, if p asserts that "the sun happens to be shining," then we can assert the fact that the sun is shining. (This talking about propositions is meta-linguistic, whether we show any qualifier with the letters or not.)

p -> p is meangful and correct (about ASSERTIONS, not the sun or other denoted matters).

[mac_philo]

Amadeo, please refer me to a mathematical logic textbook, peer-reviewed article, or other scholarly source to back up your idiosynchratic understanding of 'truth table.' To find a debunking of all your claims about truthtables, read Goldfarb's "Deductive Logic", Quine's "Philosophy of Logic", or basically any logic textbook ever printed.

A truth table [so badly named!] is a tabulation of correlations between TWO connected propositions -- connected by either/or [conjointly or disjointly], if/and [...], both/and. In all cases, you calculate thus, "IF p is true, how is q?" Or, "IF p is not true, how about q?" You are syllogizing and making inferences.

Frankly, this is gibberish.
1. A truth table need not contain more than one atomic sentence. A truth table is nothing but columns of atomic sentences and compound sentences and rows of truth values, with a number of rows equal to two-to-the-nth-power, where n equals the number of atomic sentences.
2. A truth table's atomic sentences need no 'connection', such a need does not even make sense. Take a truth table that meets your imaginary standards. Add an irrelevent atomic sentence letter. IT IS STILL A TRUTH TABLE.
3. Nobody is syllogizing or making inferences in a truth table, they are taking the truth values of atomic sentences and, given the definitions of various connectives, assigning truth values to the non-atomic sentences. It has nothing to do at all with "IF [the antecedent] is true, how about [the consequent]?" '->' is nothing but a binary truth functional connective, it truth values are simply assigned mechanically from the truth values of its antecedent and consequent and the definition of '->'. There is no syllogizing or inference making and no connection asserted between the antecedent and consequent.

A truth table can contain nothing but the single proposition p. In any case,
a single proposition was not given in my truth table. There are TWO propositions: p, and p->p. These are NOT the same proposition. p->p is a valid proposition, a logical truth, it CANNOT be false. p can be false.

Further, nobody is 'inferring p from p.' You are talking about some type of English sentence that is not equivalent to 'p->p'. p->p is a truth-functional statement that means nothing but 'p or not-p'.

You can engage in any type of speculation or hand-waving you want about inferences, but if we are talking about the original question, the status of 'p->p' in symbolic logic, then you are spewing nonsense.

p -> p is meangful and correct (about ASSERTIONS, not the sun or other denoted matters).

This is more gibberish. In symbolic logic 'p' cannot be 'the sun' or some object. p is an atomic sentence, not a variable.

It is not an identity in symbolic logic either. Neither p->p nor p<->p are identity statements.

I apologize if I am being harsh, but after the thread about cardinality, and the one about whether .9999... = 1, my patience with absolute rubbish claims about math and logic has run out.

Again, you may or may not be making some valid point about English, or inference making or whatever, but this is absolute rubbish in terms of symbolic logic.

[Amedeo]

mac_philo


Just look at what you yourself stated:

A truth table can contain nothing but the single proposition p. In any case,
a single proposition was not given in my truth table. There are TWO propositions: p, and p->p. These are NOT the same proposition. p->p is a valid proposition, a logical truth, it CANNOT be false. p can be false. That's exactly my Point! You did a truth-table calculation on TWO CONJOINED SENTENCES:

(p) and (p -> p).

Can you please write just this on a fresh page:
p

and then use your truth table to show the following:

p -> p

[mac_philo]

No, you misread the truth table, or I should have created a JPG or used LaTeX or something. If I had meant what you say I would have used conjunction: p & (p->p). I did not.

Here is the exact same truth table with some '|' characters to make it look like a drawing or whatever.

p| p->p
T| T
F| T

That's it, p->p is valid (a logical truth). Its truth value is a function of the values of its antecedent and consequent. The truth table shows that it is true in every possible interpretation. That's what it is to be valid (a logical truth).

[comiezapr]

Just to chime in, mac is on point here.

I dont know what kind of logic Amedeo is ascribing to, or really what hes talking about. I think the demand made by mac is reasonable: where do you get this logical system from?

What i think is the case is that Amedeo has an aquiantace with logic and doesnt really know what is going on behind the symbols. A case in point of this is the failure to distinguish between model theory and proof theory, as mac points out here:

You are both misreading the truth table and now, it seems, asking me to derive p->p from p. Why are you asking me to start from 'P'? That's irrelevent.

There are two seperate ways to construct a logical system: model theory and proof theory. Model theory, in this case, is the system of truth tables; it corresponds, roughly, to the semantics of the symbols being used. Proof theory, in this case, are the rules of derivation; it corresponds to the formal properties of the symbols being used. For practical purposes, that is when actually using the logical system, the difference doesnt matter because of two properties of the system as a whole: (I use "tautology" for what is more frequently called "valid" and "derivable" for what is more commonly called "deducible" in order to speak at a more colloquial level.)

Completness: All of the propositions that are tautologies by the truth table method are derivable from the system of rules.

Consistancy: All of the propositions derivable from the rules are tautologies by the truth table method.

In other words there is an isomrphism between tautologies and derivable propositions. It doesnt matter what we use to analyze propositions, model theory or proof theory, we get the same results.

HOWEVER, and this is an enormous however, at the level of discussion here the distinction is definetly needed.

That's exactly my Point! You did a truth-table calculation on TWO CONJOINED SENTENCES:

(p) and (p -> p).

Can you please write just this on a fresh page:
p

and then use your truth table to show the following:

p -> p

As mac said, though in different words, you are asking to do one task with a tool not fitted for it. Model theory is one thing: you calculate whether a proposition is a tautology (or consistant or inconsistant). Proof theory is another thing: you do derivations. You dont do derivations with truth tables.

I hope this clears this little bubble in the line of argument up.

[mac_philo]

I edited those quoted comments out of my reply, but since they're preserved now, I'll follow up.

Even if you really wanted me to give a derivation, you wouldn't have me start with p. This thread is about p->p, not p.

Here's a derivation anyway. Assumptions are bracketed to the left:

[1]1. -(p->p) ~Assume for reductio ad absurdum
[1]2. -(p v -p) ~1, TF equivalent
[1]3. -p & --p ~2, TF equivalent
[1]4. p & -p ~3, TF equivalent
5. --(p->p) ~1, 4 reductio ad absurdum
6. p->p ~5, TF equivalent (No assumptions, thus a logical truth)

Here's the short version:
[1]1. p ~(assume to prove conditional, will discharge later)
[1]2. p ~(1)
3. p->p ~(1,2, discharge assumption 1) (no assumptions, thus a logical truth)

Sorry about the ugly formatting.

[Amedeo]

Comiezapr,

I read the original post and I understood the question to be this: Does a proposition imply itself?

That is why in the latest post I asked: posit p and show by the truth tables that p implies p. My earlier point was precisely that you cannot apply the truth tables on one proposition. You are simply concurring with what I was claiming:


Quote:
That's exactly my Point! You did a truth-table calculation on TWO CONJOINED SENTENCES:

(p) and (p -> p).

Can you please write just this on a fresh page:
p

and then use your truth table to show the following:

p -> p

As mac said, though in different words, you are asking to do one task with a tool not fitted for it.
===========================

Now I like to posit

p -> q

I understand that by the truth table, this implication holds if

p...............q
T and.........T
F and.........F
F and.........T

The same should hold for p -> p.

So, if p is F and p' is T, p -> p'.

p = p'

So, if p is self-contradictory, p implies itself. Anything wrong here?

[Nitrousoxide]

I edited those quoted comments out of my reply, but since they're preserved now, I'll follow up.

Even if you really wanted me to give a derivation, you wouldn't have me start with p. This thread is about p->p, not p.

There's really two ways you can read the OP's post.

1: The way you read it in that post.

2: That the OP has an argument with a premise which is "P" and wants to conclude "P"

You've already shown "1" and "2" is fairly simple to show as well.
1) P (premise)
---
2) P (from 1)

Either reading to the OP's post is "yes."

[mac_philo]

p is F and p' is T

[...]

p = p'

[...]

Anything wrong here?

Yes.

p cannot be true and false, so this example stops right there.

And what you are trying to do here conflates model theory and proof theory.

[Amedeo]

Yes.

p cannot be true and false, so this example stops right there.

And what you are trying to do here conflates model theory and proof theory.

What I am trying to find out is if I am making the right use of the truth Tables... which I am applying to P -> Q

Now I like to posit

p -> q

I understand that by the truth table, this implication holds if

p...............q
T and.........T
F and.........F
F and.........T

Is it correct to say about (p -> q) that

if p is false and q is true, then the implication [p -> q] is true?

[LogicalRoy]

Amedeo,

I want to let you know that others have pointed you in the correct direction. I also concur that Mac_philo was on point about what he has posted. You are confusing multiple thoughts all at once. Let's get somethings straight:
If you are using P as a varible then how can the same letter have different values? (On one accurence P=T and the same P=F in the same argument [better yet, how could it be different in the same premise?]

[Oldal.]

What I am trying to find out is if I am making the right use of the truth Tables... which I am applying to P -> Q



Is it correct to say about (p -> q) that

if p is false and q is true, then the implication [p -> q] is true?Yes.

p q p -> q

T T T
T F F
F T T
F F T

This is the complete Truth Table for the conditional p -> q.

This seems odd, but putting the four possibilities into English will, I hope, make it clear.

a) If the Eiffel Tower is in France then the Eiffel Tower is in Europe.
b) If the Eiffel Tower is in France then the Eiffel Tower is in the U.S.A.
c) If the Eiffel Tower is in Germany then the Eiffel Tower is in Europe.
d) If the Eiffel Tower is in Ohio then the Eiffel Tower is in the U.S.A.

The important word to bear in mind is the first on each line if.

Clearly both parts of a) are true because the Tower is in France and France is in Europe.
b) is certainly false because France is not in the U.S.A.
c) is true because, although the Tower is not in Germany, if it were it would still be in Europe because Germany is in Europe.
d) is true but needs a little thought. If the tower were in Ohio, then clearly it would be in the U.S.A. on the ground that Ohio is in the U.S.A. So whilst both antecedant and consequent are false, the whole implication is true.

Sorry about the truth table coming out badly. On my original it was, and is, OK. but it won't transfer lined up.

Oldal.

[LogicalRoy]

Amedeo,

You are confusing many thoughts at once. The proposition P-->Q is not equivalent to all material implications. If you desire to use the letter P as a variable then each time you use the P it must hold the same value. You want the same P to have different values each time the P occurs. How could that be possible at all even if used in the same argument? Beter yet, how could that be possible in the same proposition P-->P?
If P= T in the antecedant, then the same letter P must remain T in the consequent.

[LogicalRoy]

Amedeo,

I want to clarrify what I stated earlier. You are confusing many thoughts at once. The proposition P-->Q is not equivalent to all material implications. If you desire to use the letter P as a variable then each time you use the P it must hold the same value. You want the same P to have different values each time the P occurs. How could that be possible at all even if used in the same argument? Beter yet, how could that be possible in the same proposition P-->P?
If P= T in the antecedant, then the same letter P must remain T in the consequent.

Secondly, you seem to try to use an absolute definiton to the english use of "If . . . , Then . . ." Don't you know that there are many context in which english speaking people can use "If . . . , Then . . ." ?

The words "If . . . , Then . . ." can be used in the following contexts:
-- to express a hypothetical scenario [because the event has not actually happened]; ie, If my parents had super powers, then I would be born a mutant.
-- to express that the consequence an actual event could have been different (and most certainly would be different) if some minor details changed. ie, if a boxer [meldrick Taylor] ducked the that last punch he would of won the fight and become the unified welterweight title holder (four belts at once). Taylor who was clearly winning the match actually loses because he gets knocked out with less than 15 seconds on the clock of the very last round of the match. [Julio Cezar Chavez vs Meldrick Taylor 1990].
-- to express unbelief or sarcasim; ie, If you are the [actual]Pope, then I am a monkey's uncle.
-- to express an agreement; ie, if you pay $200.00, then I will teach you jui-jitsu.
-- to express a truth functional proposition; ie, Writing a philosophical paper.
-- to express the consequence after a series of operations or procedures; ie, if one domino falls then the 16 th domino will also fall and the ball would drop.

This list is not even exhaustive. There are probably more context for the expression "If . . . , then . . .". So you can't use the same formula (if P, then Q) to express all of that.

[comiezapr]

I have a few problems of a technical nature with this post (that follows). Im going to be nitpicky and i dont really want to be argued with (though im sure argument will ensue) i am simply clarifying language and clearing some technical points up. I assume, of course, that we are talking about first order propositional logic.

A truth table [so badly named!] is a tabulation of correlations between TWO connected propositions -- connected by either/or [conjointly or disjointly], if/and [...], both/and. In all cases, you calculate thus, "IF p is true, how is q?" Or, "IF p is not true, how about q?" You are syllogizing and making inferences.

There does not have to be a realistic or cause/effect relationship between what is denoted by p and by q, as in the case, "If the sun is shining, then it is night." The point is that, assuming that p -> q,
if p is true, then q must be true.

A truth table is a tabulation, but it is NOT a tabulation of correlations. A truth table is a calculational device that either:

1) Defines the model theory of the logical system or
2) Adheres directly to the model theory of the logical system (in which case a proof would need to be given, metalinguistically, that the results given by the calculational device correspond to the antecedantly decided status of the propositions within the logical calculus.)

The end portion of this quote is completly off: "The point is that, assuming that p -> q, if p is true, then q must be true." This is exactly NOT the point. If i assume that "p -> q" is true, and that "p" is true that "q" must be true is a PROOF. You would use the rules of the logical calculus to prove this statement and would NOT reley on truth tables or the model theory of the system in any way.

As i said in my previous post, PLEASE make the theoretical distinction between proof theory and model theory.

If a single proposition is given, no inference can be made. There is no true table applicability.

This is misleading in two ways. Firstly the word "inference" refers to part of the PROOF theory of the logical calculus. You infer one proposition from another given the rules of derivation of the system.

Secondly if you are given a single proposition you can certianly infer something. This is misleading because another distinction is not being made: The distinction between propositions and propositional variables.

A proposition is a string of symbols that is constructed in the correct way (the correct way being established by a definition given). These are sometimes refered to as WELL FORMED FORMULAS. I wont go into detail, if you know a little about logic you know what a well formed formula is and are aquianted with the rules of determining what is and isnt a WFF. A proposition is just a well formed formula acording the the definition of a well formed formula given in a propositional calculus. Thats it, nothing special.

A propositional variable, however, is a single symbol. It is a symbol that can be replaced by one member from a domain of objects. In the case of a propositional variable the domain of objects would be "propositions". Now while a propositional variable can take on the value of (that is, be replaced by) a proposition as stated in the preceding paragraph (that is a WFF in the propositional calculus) it can also take on the value of other things. These other things are set out in the part of the propositional calculus where INTEPRETATION takes place: what do these symbols mean to me? Intuitivly propositions are sentences not indexed with respect to time or place, but i wont argue about metaphysics when dealing only with technicalities.

So if i am given a proposition, that is a WFF, then i can definetly infer lots of things. That is, after all, the point of the proof theoretic portion of a logical calculus: to infer one WFF from another! But, if i am given a propositional variable i CANNOT infer anything from it.

However, and this is tricky, one of the criteria for a WFF is that any propositonal variable is a WFF. This is where mac comes in and says that things can be infered from just "p". Unfortunaly this "p", one is is deemed ready for inferance no longer functions as a variable: it functions as a proposition. I can calrify this point further if it needs clarification, but i will leave it here for now.

On the other hand, we can make analytical stipulations about a propositions, such as
p <-> p (principle of identity); and

either p or else not p [expressible by equivalence or reciprocal implicatio or othewise].

I dont know what you could possibly mean by "analytic". You might be thinking in terms of some logical positivist theory of analycity where tautologies are what are analytic (at least, i think this is what youre thinking). If this is the case then "analytic" really just means "tautology". (As a small rejoinder, tautologies arent stipulated: tautolgies are a set of propositions that have a certian property acording to the model theory of the propositional calculus. What is stipulated are axioms of a proof theory. The fact that axioms correspond to tautologous propositions is a meaningful and hard won result of logicians and they are not a priori identical. This misuse of language has to do with the lack of distinction between proof and model theory.)

I know you could deduce the principle of non-contradiction from some logical calculation (WHILE the principle is being adhered to in the statements you make).

Again a failure to distinguish between model theory and proof theory looms large. There are a few true things and a few misleading things about this mini quote:

Yes, we could deduce the principle of non contradiction (in the form it would have within the propositional calculus, anyway) from the axioms of the PROOF theory of the propositional calculus. However, its not clear in what way we "adhere" to the principle while we derive it: it is a consequence of axioms and rules of derivation that DO NOT explicilty state the law on non contradiction.

Alternativly we could show that the principle of non contradiction is a tautology within the MODEL THEORY of the logical calculus. We would be doing no derivations here.

Here is where the post goes from misleading to outrageous:

but the inferred portion is NOT the inferring of p from p. So, the inferred portion does NOT mean "p is true because p is true (which would constitute the begging of the question).

What can ( p -> p ) mean in a valid or non-fallacious way??? It means something like this:

John happens to be sitting on a cliff (he did not have to be there; he was not forced to be there). If he happens to be sitting on a cliff, he is certainly/factually sitting there.

What happens (or is not necessary) is a contingency. (The other two contradictory modalities are possibility and impossibility.) What is continent is a fact, not a hypothesis; one cannot extract a fact from a hypothesis.

The question of what the terms of the propositonal calculus mean has not arisen yet. More importantly it should not arise in response to the OP. But, since its here ill deal with it.

The propositional calculus is unintepreted: it is a formal system that does not hinge on a natural language to do its work. That really is the point of a logical calculus, to make a formal system. Of course there is a natural intepretation of the symbols of the calculus in terms of English, i wont go through them.

"What can ( p -> p ) mean in a valid or non-fallacious way??? It means something like this:"

What could it mean in a valid way? Well, first we need a NATURAL LANGUAGE intepretation of "validity". "Validity" normally refers to a property or propositions derived from truth tables and defined by the model theory of the propositional calculus. What does it MEAN in terms of this validity? Well it means something like: (p->p). Yes, thats right; we are using a word from the metalanguage of our formal system and it, quite predictably, applys to things from the language of our formal system. Those things happen to be WFFs, of which this is one that is valid. Any sentence of english automatically cannot be valid because it ISNT a WFF.

So we clearly need a new definition of valid in terms of natural language. I dont know what it would look like and wont make conjectures. What i do know is that 1) this meaning of the word "validity" is nowhere to be seen in the OP and 2) that the result of replacing the symbols in (p->p) by thier normal intepretations would definetly be valid by this definition of "valid".

"John happens to be sitting on a cliff (he did not have to be there; he was not forced to be there). If he happens to be sitting on a cliff, he is certainly/factually sitting there."

I think i know what youre talking about here and will translate it into more precise language while also parceling it out into a form that correlates with WFFs:

if (John is sitting on a cliff and it is possible for John to not be sitting on the cliff) then (in the actual world John is sitting on the cliff).

Now clearly this isnt anything that (p->p) means. The reason is that the antecedant "John is sitting on a cliff and it is possible for John to not be sitting on the cliff" and the consequent "in the actual world John is sitting on the cliff" are not identical while clearly p is identical to p. This is assuming the standard intepretation of the symbol "->". What you need, then, is a new intepretation of "->" that includes with it all of the information you want to enter into this sentence. I dont see any conditional in the English language that would do this, nor any reason for this conditional: it would be merely the regular conditional "if p then q" with the aditional assertion that p is not necessary. I further dont see how the model theory of the propositional logic would distinguish the two conditionals (the normal one and the one you need) from one another. I must conclude, then, that your intepretation of (p->p) is off the mark.

What happens (or is not necessary) is a contingency. (The other two contradictory modalities are possibility and impossibility.) What is continent is a fact, not a hypothesis; one cannot extract a fact from a hypothesis.

You are diving into deep waters without even a bubble of oxygen here. There are three modal distinctions for propositions: possible, necessary and impossible. If you stipulate that the propositions in question are the ones that hold in the actual world the distinctions turn into: contigent (which means both possible and actual) and necessary; impossible obvioulsy drops out.

What is contigent is true in the actual world; im not sure what a fact is. There doesnt seem to be anything that excludes a contingent proposition from also being a hypothesis, but you are quite correct (with some more precise language) that you cannot conclude, given p is contingent that p is a hypothesis.

The important thing though, and it is why the bottom of this post is a disaster, is that none of this matters. Perhaps these metaphysical distinctions would be worthwhile if some of them were actually incorporated into "p->p". They are not, this is propositonal logic and we have no way of forming the intuitive meanings of "necessary" or "possible" or ANY intentional words whatsoever. But even stranger is that theres no mention of "hypothesis" or anything that could be a paraphrase of hypothesis in YOUR intepretation of "p->p":

John happens to be sitting on a cliff (he did not have to be there; he was not forced to be there). If he happens to be sitting on a cliff, he is certainly/factually sitting there.

It is a disaster due to lack of analysis.

[comiezapr]

Comiezapr,

I read the original post and I understood the question to be this: Does a proposition imply itself?

That is why in the latest post I asked: posit p and show by the truth tables that p implies p. My earlier point was precisely that you cannot apply the truth tables on one proposition. You are simply concurring with what I was claiming:


===========================

Now I like to posit

p -> q

I understand that by the truth table, this implication holds if

p...............q
T and.........T
F and.........F
F and.........T

The same should hold for p -> p.

So, if p is F and p' is T, p -> p'.

p = p'

So, if p is self-contradictory, p implies itself. Anything wrong here?

Please, PLEASE, actually read my post. You are confusing truth tables with deductions. And read the post imediatly preceeding this one.

You can apply truth tables to propositions, that is the whole point of a truth tables. Propositions are the WFFs of the logical calculus. While you cannot apply truth tables to PROPOSITIONAL VARIABLES you can apply a truth table to the WFF "p". You are not making theoretical distinctions that you must.

P always implies itself by the normal propositional calculus. And really, i have no idea in what sense of the word "imply" that a proposition wouldnt imply itself.

[comiezapr]

Yes.

p q p -> q

T T T
T F F
F T T
F F T

This is the complete Truth Table for the conditional p -> q.

This seems odd, but putting the four possibilities into English will, I hope, make it clear.

a) If the Eiffel Tower is in France then the Eiffel Tower is in Europe.
b) If the Eiffel Tower is in France then the Eiffel Tower is in the U.S.A.
c) If the Eiffel Tower is in Germany then the Eiffel Tower is in Europe.
d) If the Eiffel Tower is in Ohio then the Eiffel Tower is in the U.S.A.

No, no, no. You have here a truth table for the proposition "p -> q". In your intepretation you have 4 different propositions! (The four propositions are "The Eiffel Tower is in France/Germany/USA/Europe.) I assume that you think that when you have a T of an F in the truth table evaluation you simply replace the propositional variable (p or q) with a true or false proposition.

NO NO NO! You do not do this! You replace the propositional variable with THE VALUE true or false. You dont replace it with a proposition; you replace it with simply TRUE or FALSE. (This is what led Frege and Carnap to include in thier model theory the idea of "the true" and "the false" as special extensional objects that are to be placed into the propositional variables when they are being evaluted model theoretically.)

The proper intepretation of your truth table for (p->q) would be something like this:

If p is true and q is true then if p then q is true.
If p is true and q is true then if p then q is false.
If p is false and q is true then if p then q is true.
If p is false and q is false then if p then q is true.

Yes, thats ALL that can be intepreted about the truth table. To further intepret it you need to replace the variables p and q with propositions. Lets say p is "The Eiffel tower is in France" and q is "The Eiffel tower is in Germany". The important thing to remember is that you MUST KEEP THE PROPOSITIONS QUOTED! You are mentioning these propositions in the intepretation not using them!

Ill do a single line as an example:

If "The Eiffel tower is in France" is true and "The Eiffel tower is in Germany" is true then if "The Eiffel tower is in France is" then "The Eiffel tower is in Germany" is true.

Thats it, thats as far as intepretation goes. You cant drop the quotations, you cant drop the formality of the if-then structures, you cant drop the "true" and "false" out of the intepretation and you certianly cannot add in more propositions to substitute for the propositional variables than you have propositional variables!

The remainder of this post is beguiled by these confusions and i would suggest rethinking them in light of what i said. If you stand by what you say i will further critique the assertions.

Edit: To sort of bring a point home, when i say "p is true" that is the "is" of identity: "p is true" means p is identical to truth, or "the true". This isnt some metaphysical thesis about truth or "the true" or anything like that, it is simply a reflection of how the formal system is constructed.

[Amedeo]

Gentlemen [or Ladies and Gentlemen],

you point to a lot of confusions on my part, for in my discussions about inferences I was using the truth/false value terminology. (As far as I know, this terminology was not patented by symbolic logicians, but it was unwise of me to use it, or to interpret your use of the terminology according to my notions of truth and falsity.)

Ultimately the problems arises from the original post and the title of the thread:

Can P -> P ?
# 1
Just need a quick reminder regarding symbolic logic.

is it valid to say p implies p?

I focused on the title question, which I read thus:

CAN P imply P?
That is, given a proposition, p, can it be that it implies p ?

In Post # 1, it seems that there is a question about this assertion: "p implies p", and apparently all of you dealt with. Your use of truth tables was related to it.

However, to me, the question, "is it valid to say p implies p," meant:

is it logically correct to think that p implies itself?

So, the me the title and the post are alike in asking something about p. So, I should not have gotten embroiled in the discussion about "p implies p," precisely because my original issue was NOT about a given proposition such as "p implies p."
=============================
The following is an Original Message, which has nothing to do with the above discussion or with symbolic logic.

I like to set up an INFERENTIAL LOGIC SYSTEM.
I start by defining relators between propositions. Thus the system is an inferential calculus limited to those relator. (There are other relators, such as class-membership, which are excluded here.)

The DEFINITIONS are in Peirce's pragmaticist manner; that is, a concept [in this case, a relator] is defined by its consequences, but I postulate the consequences for the relators I wish to define.

The AXIOMS include the principle of non-contradiction: something may not both occur and not occur. ....

The propositions (f, g, h, ...) are assertions of occurrences.

(1) IMPLICATION. ( -> means "implies")

To say that f implies g means that:
if f occurs, then g occurs; or,
if g does not occur, then f does not occur.

Corollary:
f cannot be said to imply g
if f simply does not occur, or
if g simply occurs, or, by the principle of non-contradiction [and an argument to be formalized]:
if f occurs and g does not occur, or
if g occurs and f does not occur.

For example:
Hypothesis: The fact that one places his hand on a fire implies that his hand burns.
Adduced facts: I placed my hand on a fire and [under equal stipulated conditions] my hand did not burn. Therefore,
the hypothesis is refuted:There is no implication between those two hypothetical facts. [The adduced facts refute the major premise; they do not prove something else, such as the occurrence of a miracle.]
........................

Once the other relators are defied, one will have to see if they are coherent with each other, for it is impossible for something to occur and and to occur; therefore, major [relator-] premises are inadmissible, if an occurrence can be inferred from one, and the non-occurrence can be inferred from another, which can be stated thus:

~ [ (C -> g) & (D -> ~g)] (This may turn out to be a theorem in the system, but, like the principle of non-contradiction, it is operative in the reasoning/deductive process, which means that it is assumed before it is demonstrated. The demonstration is not what establishes it; it establishes the formula, wherefore one can make verbal or symbolic substitutions in the formula.)

......................

There are RULES of INFERENCE (demonstration or argumentation), such as not adducing self-contradictory claims [hypothetical facts].
.......................

Whether the theorems of the deductive system can be used for realistic demonstrative purposes:

Can occurrences or non-occurrence be inferred on the basis of major premises [which contain a relator] and adduced facts (propositions stating some occurrences or non-occurrences)?

For instance, the validity of a conditional syllogism,
[(f -> g) & f.; therefore, g]
depends on there being an implication between two propositions and on fact f.
However, the implication is admissible if
f occurs and g occurs, or
g does not occur and f does not occur.
but then, if the occurrence of f and g is known, one does not deduce g from the occurrence of f.
So, a conditional syllogism is not demonstrative at all, since the conclusion is already assumed in asserting the validity of the relator (in admitting that there is an implication between f and g).

If we do not define IMPLICATION at all, then it is asserted hypothetically; it is assumed. In that case, the word "implies" should not be used AS IF it were legitimately defined; one should speak unambiguously thus:
f -p-> g, that is, f presumably implies (or is hereby postulated as implying) g.
Then, by the analytical formulations of the conditional syllogisms, if f occurs, one can infer that g occurs; of if g does not occur, f cannot possibly occur.

By the way, inference is a modal implication. (Conclusions are assessible as either necessary or Contingnet, that is, not necessary, which is the only thing that invalidity means.) Therefore, a system need define validity and invalidity by the Modes, not by truth and falsity. Also this is the case, that what is inferred is a categorical proposition; it is detachable from the sentences that imply it, whereas g is not detachable, categorically assertable, from therelator proposition "f implies g." (The existing Calculus of Propositions System is a formal deductive system, which mat not be used for demonstrative purposes, because there is no way of inferring a categorical proposition. It lacks a distinction between hypothetical implication [a relator] and inferential implication.)

Now, then, if "implies" is left undefined but is assumed to hold between two proposition, the valid conclusion of a syllogism should be qualified by "presumably." For example (expressing "implies" by If/Then):

If a rock falls on a pool of water, Then it falls to the bottom of the pool;
but a rock fell on a pool of water;
therefore, necessarily it presumably fell to the bottom of the pool.

If the relator is stated modally as "necessarily implies," then the logic is demonstrative for things which are forced to happen. One can predict what happens to the rock on the pool; one cannot predict that if the sun rises, a rooster will crow. (Crowing is initiated by a rooster; it is not an effect on the rooster, like "getting warm".) So, in order for a logic system to be suitable for demonstration, it cannot have its relators arbitrarily defined or left totally undefined (wherefore the relators have ad hoc functions).

A system where If/Then is so defined that an occurrence necessitates another, is for reasoning about things that necessitate others; the syllogisms or modes of demonstration do not have universal validity (that is, for anything that is expressed in terms of If/Then). For example,

-- the existence of anything does not necessitate the existence of aything else, whereas the fall of a rock in water necessitates a water displacement;
-- my becoming sad does not necessitae any mode of being in other things (as being sad is not a causing event);
-- the occurrence of certain propositions in my mind does not necessitate the making of any inference;
etc.

A definition for a demonstrative inferential system:

f -n-> g :: f necessarily implies g :: if f, then necessarily g :: g necessarily presupposes f.

Note: In view of the valid syllogisms [which have not been discussed or formalized], one can say, after the fact, that "necessary implications" is [I]de facto defined or definable as I did in the beginning, only that by using that procedure, one has to know in advance what, in another situation, is yet to be demonstrated. Anyway, that definability is coherent with the function that conditional major premises have in demonstrative arguments. The coherence with the other definitions [not made yet] is yet to be established.

(In these few lines, that is, for a few moments, I have continued Aristotle's discourse on the realistic demontrability value of syllogisms, although what he was discussing was his Logic or Analytics of predicates, not of propositions, which the Stoics later developed.)

[Oldal.]

No, no, no. You have here a truth table for the proposition "p -> q". In your intepretation you have 4 different propositions! (The four propositions are "The Eiffel Tower is in France/Germany/USA/Europe.) I assume that you think that when you have a T of an F in the truth table evaluation you simply replace the propositional variable (p or q) with a true or false proposition.

NO NO NO! You do not do this! You replace the propositional variable with THE VALUE true or false. You dont replace it with a proposition; you replace it with simply TRUE or FALSE. (This is what led Frege and Carnap to include in thier model theory the idea of "the true" and "the false" as special extensional objects that are to be placed into the propositional variables when they are being evaluted model theoretically.)

The proper intepretation of your truth table for (p->q) would be something like this:

If p is true and q is true then if p then q is true.
If p is true and q is true then if p then q is false.
If p is false and q is true then if p then q is true.
If p is false and q is false then if p then q is true.

Yes, thats ALL that can be intepreted about the truth table. To further intepret it you need to replace the variables p and q with propositions. Lets say p is "The Eiffel tower is in France" and q is "The Eiffel tower is in Germany". The important thing to remember is that you MUST KEEP THE PROPOSITIONS QUOTED! You are mentioning these propositions in the intepretation not using them!

Ill do a single line as an example:

If "The Eiffel tower is in France" is true and "The Eiffel tower is in Germany" is true then if "The Eiffel tower is in France is" then "The Eiffel tower is in Germany" is true.

Thats it, thats as far as intepretation goes. You cant drop the quotations, you cant drop the formality of the if-then structures, you cant drop the "true" and "false" out of the intepretation and you certianly cannot add in more propositions to substitute for the propositional variables than you have propositional variables!

The remainder of this post is beguiled by these confusions and i would suggest rethinking them in light of what i said. If you stand by what you say i will further critique the assertions.

Edit: To sort of bring a point home, when i say "p is true" that is the "is" of identity: "p is true" means p is identical to truth, or "the true". This isnt some metaphysical thesis about truth or "the true" or anything like that, it is simply a reflection of how the formal system is constructed.The intent of my post was to illustrate the meaning of conditional statements which, it seemed to me were at the heart of the confusion.

Being a lazy sod I lifted the examples straight from Layman. The propositions in English make clear what the symbolic form means. I saw no need to indicate which were true and which false in your way. They seemed self evident.

Is it correct to say about (p -> q) that

if p is false and q is true, then the implication [p -> q] is true?This was the reason for my response and the first word in it 'Yes.' referred specifically to the query. I am sorry it was not as clear to you as it was to me.

Oldal.

[Amedeo]

From # 45


Quote:
Is it correct to say about (p -> q) that

if p is false and q is true, then the implication [p -> q] is true?
This was the reason for my response and the first word in it 'Yes.' referred specifically to the query. I am sorry it was not as clear to you as it was to me.

Oldal.

Now that I have an answer to my question, I'd like you to consider the following truth table.

p.....p....(p -> p)
T.....T....T
F.....F....T
T.....F....F
F.....T....T

The last line read: if, in (p -> p), antecedent p is false and consequent p is true, then (p -> p)
For example:

if, in (if a ball is on a slope, then a ball is on a slope), it is false that a ball is on a slope and it is true that a ball is on a slope, then "a ball is on a slope" implies "a ball is on a slope."

So, the fact that the value of the antecedent and the consequent are materially contradictory is irrelevant to the existence of the implication.
-----------
Now consider the case of two different propositions:
p -> q
There is no material contradiction between p and q and, at any rate, any realistic impossibilty for what is denoted by p to imply what is denoted by q is besides the point -- as we have seen in the analysis of (p -> p).

Now, let us go into an inferential process and assume the truth of the major premise, (p -> q).

We can adduce four possible facts (atomic propositions): affirmative and negative for the antecedent as well as the consequent:

(p -> q) & [p] || & [q] . Hence ...
"..............+p........................necessarily +q
"...........................-q............necessarily-p
"............................+q..........possibly +p
"............................-p...........possibly -q

These possibilities are assertible on the assumption that there is an implication between p an q; .... And because of the possibilities, it would be erroneous to infer that
... & + q, hence -p
or
... & -p, hence -q.

Therefore, the -> used in symbolic models does NOT means IMPLIES or " if...., then necessarily..." at all. It means, "if...., then also....". Thus, the truth table DEFINES the factual concomitance or factual consecutiveness (not implication) between p and q. [It is erroneously called logical or formal implication, for it not implication at all.]

If the truth table defines implication, then there is a logical inconsistency between a posited implication and the function it has in an inferential process.

"If... then also...." or ".... concurs with...." is suitable for dealing with individuals that are not causally related or that are treated in isolation from one another. Such individuals are also called arithmetical units.

Concurrence is nicely defined by the total truth table. A speaker actually says:

1. (p & q ) -> (p concurs with q)

2. (-q & - p) -> (p concurs with q), since -q concurs with -p

3. (p & -q) -> -(p concurs with q), otherwise (1) would be contradicted

4. (- p & q) -> (p concurs with q), since it is not the case that -p concurs with q.

Of course, this way of thinking would be erroneous:

(p & q) -> (p -> q), for you may not infer necessity from a fact.

[Oldal.]

Amedeo,
p.....p....(p -> p)
T.....T....T
F.....F....T
T.....F....F
F.....T....TUnfortunately the last two lines are not possible. They are self contradictory.

Again let me try to remove the symbols and put it into English english.(My English).

The first will read: 'Cheese is edible' 'Cheese is edible' & 'If cheese is edible then cheese is edible' You will not, I suspect, argue with that.
The second reads: 'Cheese is poisonous' , 'Cheese is poisonous' & If cheese is poisonous then cheese is poisonous'. I cannot see you quarrelling with that either. 'Cos if cheese is poisonous then it is poisonous! The fact that it is not is neither here nor there but if it were poisonous then ..well don't eat it! O.K. You see, Logic,with a capital 'L' has nothing to say about the real world. It is a tool for testing arguments. I don't mean rows with your wife, if you have one, but about strings of propositions, one of which is the conclusion which is supported or not, by the other propositions. It is the responsibility of the user of logic to supply true propositions.

Whatever 'P' might represent, it is surely self evident that a thing is identical with itself. So, in any argument, P is identical with, congruent with P. Your keyboard is identical to your keyboard. So, if your keyboard is wireless then your keyboard is wireless. Replace 'keyboard' with the variable 'p' and there you have it p->p. Or, 'If p then p'. If it's raining it's pissing down!

Oldal.

[Amedeo]

Amedeo,
p.....p....(p -> p)
T.....T....T
F.....F....T
T.....F....F
F.....T....TUnfortunately the last two lines are not possible. They are self contradictory.

Again let me try to remove the symbols and put it into English english.(My English).

The first will read: 'Cheese is edible' 'Cheese is edible' & 'If cheese is edible then cheese is edible' You will not, I suspect, argue with that.
The second reads: 'Cheese is poisonous' , 'Cheese is poisonous' & If cheese is poisonous then cheese is poisonous'. I cannot see you quarrelling with that either. 'Cos if cheese is poisonous then it is poisonous! The fact that it is not is neither here nor there but if it were poisonous then ..well don't eat it! O.K. You see, Logic,with a capital 'L' has nothing to say about the real world. It is a tool for testing arguments. I don't mean rows with your wife, if you have one, but about strings of propositions, one of which is the conclusion which is supported or not, by the other propositions. It is the responsibility of the user of logic to supply true propositions.

Whatever 'P' might represent, it is surely self evident that a thing is identical with itself. So, in any argument, P is identical with, congruent with P. Your keyboard is identical to your keyboard. So, if your keyboard is wireless then your keyboard is wireless. Replace 'keyboard' with the variable 'p' and there you have it p->p. Or, 'If p then p'. If it's raining it's pissing down!

Oldal.

Now you are saying that a truth table has to be constructed in view of what the proposition say... The issue here is one of procedure.

Using the old language --
Under what conditions can you say that (p implies q)? or When can the implication be said to hold [to be true]?

the old answer is:
-- when the antecedent is true and the consequent is true
--when the antecedent is false and the consequent is false
-- when the antecedent is false and the antecedent is true
but not when
-- the antecedent is true and the consequent is false.

It does not matter what the ps and qs say, because you are dealing with the implication-relationship between two units.

SO, IF I POSIT (P -> P), IT IS REQUIRED to see whether is true

-- when the antecedent is true, and..
--
--
--
If you happen to notice that a contradiction results from your procedure of assigning values, then there is something wrong somewhere. What is wrong is not in using the procedure....
---------------
1. (p & p) -> (p Concurs with p).

2. (-p & -p) -> (p C p).

3. (p & -p ) -> -(p C p) because p and the opposite of -p [see 1] imply that p concurs with p.

4. (-p & p) -> -(-p C p) -> (-p C -p) -> (p C p).

There was nothing wrong in the tabulation of the values for (p -> p). (But if the relating -> means Implies, then there will be an incoherence with the conditional syllogisms.)

[mac_philo]

There was nothing wrong in the tabulation of the values for (p -> p).

YES THERE IS.

Read more. Write less.

This is like yammering on about Timecube or some creationist nonsense. You've typed page upon page of complete bullshit, and have not registered ANYTHING from the pages written by people who know formal logic and have wasted their time correcting you.

Read some formal logic (a textbook on post-Frege logic) before you create your own system.

[Amedeo]

There was nothing wrong in the tabulation of the values for (p -> p).

YES THERE IS.

Read more. Write less.

This is like yammering on about Timecube or some creationist nonsense. You've typed page upon page of complete bullshit, and have not registered ANYTHING from the pages written by people who know formal logic and have wasted their time correcting you.

Read some formal logic (a textbook on post-Frege logic) before you create your own system.

If You interpret the -> in (p -> q) to mean "necessarily implies," you may as well throw the tabulation logic books out of the window.

[mac_philo]

Since you aren't taking anything from the massive amount written for your benefit, I'll just make a PSA to any impressionable youth reading this crackpot bullshit.

'->' does not mean what Amadeo says, and Amadeo's attempts to make truthtables utterly fail.

There is a symbol for necessity, and a symbol for logical (as opposed to material) implication, but you have to know logic to know what they are and what they mean, and they have nothing to do with what Amadeo is saying.

[Amedeo]

Since you aren't taking anything from the massive amount written for your benefit, I'll just make a PSA to any impressionable youth reading this crackpot bullshit.

'->' does not mean what Amadeo says, and Amadeo's attempts to make truthtables utterly fail.

There is a symbol for necessity, and a symbol for logical (as opposed to material) implication, but you have to know logic to know what they are and what they mean, and they have nothing to do with what Amadeo is saying.
Ladies and gentlemen,
listen to what mac_philo, the voice of orthodoxy, says.

KNOW also that the symbols used in symbolic logic logic are NOT representatives of commonplace things. As you can read in one of the posts, there are at least 20 different meangs for "if... then..." and certainly one symbol cannot include all of them, unless one wishes to equivocate.

When a truth table is set up for (p -> q),
-> has only one meaning, AND IT IS NOT "necessarily implies."

I could not give shit about truthtables, and I never tried to replicate done work: I STUDY THE THINKING OF LOGICIANS and see what they do and the fallacies they commit.

If you want to know logic, go to mac_philo. If you want to know physics, go to physicists; if you want to know God, go to the Bible.

My issue started with the question whether a proposition implies itself, and eventually only I have been able to demonstrate that it does.... by specifying what it means to say, "implies itself." BUT DON'T TAKE MY WORD; find out for yourself. I neither preach nor bow to others.
---

In case I have corrupted minds of the youth of Athens, I want to repeat to all the impressionable minds: learn from the pros. The voice of orthodoxy does not fail. Pay heed to your benevolent mentor, Philo Judaeus or or any other defender of the faith.
Sleep well,
Amygdale

[comiezapr]

Amadeo, there is a bit of an issue with some of your posts. You use words like "fact" and "imply" frequently in very critical portions of your exposition but leave them undefined. I dont really know what your saying in alot of your posts because your usage of these words is totally non standard (either that or you are just speaking absurdities). You need to explain yourself better; that is you need to stop using words that have a very specific and technical meaning when you are not using them in THAT way.

To a more philosphical point:

Ladies and gentlemen,
listen to what mac_philo, the voice of orthodoxy, says.

KNOW also that the symbols used in symbolic logic logic are NOT representatives of commonplace things. As you can read in one of the posts, there are at least 20 different meangs for "if... then..." and certainly one symbol cannot include all of them, unless one wishes to equivocate.

When a truth table is set up for (p -> q),
-> has only one meaning, AND IT IS NOT "necessarily implies."

I could not give shit about truthtables, and I never tried to replicate done work: I STUDY THE THINKING OF LOGICIANS and see what they do and the fallacies they commit.

If you want to know logic, go to mac_philo. If you want to know physics, go to physicists; if you want to know God, go to the Bible.

My issue started with the question whether a proposition implies itself, and eventually only I have been able to demonstrate that it does.... by specifying what it means to say, "implies itself." BUT DON'T TAKE MY WORD; find out for yourself. I neither preach nor bow to others.

Im going to sort of summarize what you say into an argumentative thing (and highlight portions):

1) The symbols of logic dont have the same MEANING as normal english words.
2) The symbol "->" has only one meaning.
3) The meaning of the symbol "->" is irrelevant to inquiries into the English language.
4) The proposition "p implies itself" means some one thing which has been elucidated without the help of logical analysis.


A quick response is: 1 is true, 2 is sort of mistated but false, 3 is false, 4 is false. There are specific reasons i could state for why these things are this way but it means nothing to say them unless youre pretty good with the philosophy of language, and if youre good with the philosophy of language then the things dont need saying. So ill sort of paint a picture.

Lets say that theres various components to the meaning of a term. For example some of the components of the meaning of "red" are related to color, what things are red, how to make things red, the nature of colored light and reflectance ... etc. We could combine all of these things into one large thing to compose the meaning of "red". This would be a long and pretty stupid task.

Logic seeks to analyze one portion of the meaning of certian terms: the truth functional portion. It states the conditions for some terms to be true based on the truth of other terms its connected to. For instance "Duck and Geese quack" would be true if "Ducks quack" and "Geese quack"; this is an analysis of the truth functional portion of the term "and". Logic is incredibly sucsesful here.

To tie what has been said so far in with the enumerated list: 1 is true because the terms of logic dont really have a meaning, they are just a portion of the meaning of certian other terms. 2 is false because it isnt really proper to say that the terms of logic mean anything: they arent inside of some language thats robust enough to give a meaning to its terms, the symbols are just an analysis of part of the meaning of a certian subsection of language. 3 is false because the symbol "->", as stated, doesnt really have a meaning; but further than this, the behavior of "->" within the propositional calculus isnt irrelevant to the meaning of terms of the English language: it is an analysis of part of the meaning of certian English words.

Now 4 is false because i dont see an elucidation of the meaning of "implies". However, i can sort of do a little analysis of "implies" on my own that is releavnt to the topic at hand:

Certianly a portion of the meaning of "implies" is truth functional. That portion that is truth functional is analyzed by the symbol "->" in the propositional calculus. From this analysis "p implies p" is true because "p -> p" is true.

To counter what i say here you would need to establish more fully, that is to say establish AT ALL, that the symbols of logic have no relationship whatsoever to English words.

I dont see where you specify the meaning of "implies itself" except here:

What can ( p -> p ) mean in a valid or non-fallacious way??? It means something like this:

John happens to be sitting on a cliff (he did not have to be there; he was not forced to be there). If he happens to be sitting on a cliff, he is certainly/factually sitting there.

I put this into more precise terms:

"if (John is sitting on a cliff and it is possible for John to not be sitting on the cliff) then (in the actual world John is sitting on the cliff)."

Where we see that the meaning of implies to YOU is simply the meaning of implies to the rest of us plus an aditional stipulation that the preceding term in the implicature is contingent. To make this more concrete ill do two translations of "John is sitting on a cliff implies John is sitting on a cliff":

My translation is "If John is sitting on a cliff then John is sitting on a cliff" and we see that the term "implies" is replaced by the schema "if x then y" where x and y are variables that range over propositions.

Your translation is "If John is sitting on a cliff and it is possible for John not to be sitting on a cliff then in the actual world John is sitting on a cliff." The term "implies" here is replaced by the scheme "If x then y and it is possible that not x" where x and y are variables that range over propositions.

So your translation is just mine with another stipulation. This is an eroneous stipulation. As i said before THERE IS NO WORD IN THE ENGLISH LANGUAGE THAT HAS THIS MEANING: where it is the standard implicature plus a stipulation that the first proposition is contingent.

To prove my point lets take another example: That 3 is prime implies that 3 is prime. Now, 3 is prime necessarily (there is no possible world where 3 is composite). Surely this is the same "implies" from "John is sitting on a cliff implies John is sitting on a cliff," and yet the aditional stipulation that you add to "implies" prevents these two words from having the same meaning! LUDICROUS: THIS IS THE SAME WORD! And if you dont like this example how about these:

Cats means Cats implies Cats means Cats.
Orange is identical to Orange implies Orange is identical to orange.
"p implies p" implies "p implies p".

All of these uses of "implies" cant mean the same thing as the original implies. This is OUTLANDISH!

So unless you have some other analysis of the meaning of "implies" then youre wrong. Not just a little wrong either, youre way off; whatever meaning you were trying to breath into "implies" not only doesnt belong THERE but doesnt belong ANYWHERE.

A small rejoinder here: dont harp on the fact that i say a phrases meaning has components. I dont believe this literally but just say it to simplify what i would have prefered to said. "The meaning of a word has components" is shorthand for something else that i can espouse if needed, within the framework of possible worlds, but really dont want to.

[comiezapr]

Whatever 'P' might represent, it is surely self evident that a thing is identical with itself. So, in any argument, P is identical with, congruent with P. Your keyboard is identical to your keyboard. So, if your keyboard is wireless then your keyboard is wireless. Replace 'keyboard' with the variable 'p' and there you have it p->p. Or, 'If p then p'. If it's raining it's pissing down!

Oldal.

More properly the variable "p" would replace the proposition "your keyboard is wireless" and not "keyboard". You can see this because "keyboard -> keyboard" isnt well formed. I know you know this but please dont be sloppy!

You also cant go from "p is identical to p" to "p implies p" without the further asumption that identical propositions imply themselves. That is what we are debating and so this argument is a question begger. What you need to do is argue it like this:

1) p is identical to p
2) this can be translated into the propositional calculus with the symbols p <-> p
3) this is equivalent, in the propositional calculus, with the symbols (p -> p) (and) (p -> p). (and) here is a symbol of the logical calculus and not the standard english word "and".
4) this sentence of the propositional calculus can be translated into english as p implies p and p implies p
5) from this we can derive that p implies p

Amedeo would reject steps 2 and 4 on the grounds that you cant translate from logic into English. This renders your argument dialectically useless at this particular time in the discussion, though it is a good argument and i will make use of it in the rest of the thread as an outline.

Heres a roadmap of this debate:

The steps to proceed further into cornering Amedeo (as he inevitably will be cornered or leave the thread) is to show that you can translate the relevant portions of "implies" into logical symbolism as "->". I have taken this strategy in my previous post by doing two things:

1) Giving a general theory of meaning that shows the relevance of logic to language analysis.
2) Giving the specific meaning of "implies" (in two ways, actually) that fits with intuition and shows that it can be analyzed well with logical aparatus.

Since ive done this Amedeo's move is to do two things:

1) Refute this general theory of meaning.
2) Refute this specific meaning of "implies".

He has sort of done 2 by giving an alternative meaning. However in my previos post showed this alternative to be rediculous and so he still is burdened with objective 2.

The burden of proof, currently, is on Amedeo because the general theory of meaning is prima facie plausible and the specific meaning of "implies" is prima facie correct.

[Amedeo]

--- RUSSELL ON PROPOSITIONS ---
A couple of statements by Russell are conveniently found in "the Monist",
http://www.books.google.com/Books?id=nawLAAAAIAAJ...

The significance Mr. Russell gives to "proposition" goes hand in hand with his peculiar use of the term... "It may be observed that although implication is indefinable, proposition can be defined. Every proposition implies itself, and whatever is not a proposition implies nothing. Hence to say 'p is a proposition' is equivalent to saying 'p implies p';and this equivalence may be used to define propositions."(27).... "A proposition, we may say, is anything that is tue or that is false."

It is not true that implication is indefinable; Russell should have said that he did not know how to define it. It is true that the word "implications" has a simple meaning [or actually many possible simple meanings] and that, therefore, it cannot be NOMINALLY defined by other words, but if "implies" is a relator or operator between two propositions, then its function is definable. So, I defined one meaning of the term pragmaticistically, from the 'effects' or consequences that it has for the related propositions.

On the other hand, it is axiomatic for Russell that a proposition implies itself.... without knowing exactly what the word 'implies' means. Since he states that propositions are true or false, one could presume that what 'implies' does is this: It asserts that a true propositions makes another proposition true, and that a false proposition makes another proposition false. Thus the truth or falsity of the consequent is contingent of the truth or falsity of the antecedent. But this interpretation is not coherent with his definition of 'proposition':
If "p implies p" means that the truth of the second p is contingent on the truth of the first p, then the second p is a neutral proposition, a proposition without the truth value or the falsity value. If the second p is already either true or false, then the first p does not endow the second one with a value.

What Russell said was in effect: If p is a proposition, then p implies p, or, vice-versa: if p implies p the p is a propostion. What could "imply" means, if does not means "causes"/ "engenders" or "value endows"? It could mean something like this: "Where there is love, thereis God" [Uni amor, ibi deus -- as a Medieval hymn goes]. I could say, Where there is a proposition (the statement that oranges are round) -- which is either true or false, there a proposition is enunciated (or there occurs the stating of the proposition), or, more generally: a patent essence [a such-and such a thing or judgement] presupposes that it exists or occurs. The consequent is not an effect (and the antecedent is not a cause), but the consequent is a "must be" inasmuch as the antecedent is an "is."
So, we can speak of presuppositional implication, not a causal implication.

(p implies p) = where there is p, there must be p =
p and necessarily p.

Now, when a proposition is said to be either true or false, the meaning of these value-terms is taken from conventional usage. For instance, it is false that "an orange is oblong", in view of the fact that an orange is round. The truth and falsity terms are verisimilitudinal, since when we speak of relationships between propositions we are not engaed in using the propositions are statements of facts; we speak of propositions as true or false abstractly, without denothing anything. But then, it is sufficient to say that a proposition is either affirmative or negative. (There is nor reason or point for using the words Truth and Falsity.) The reason for this terminological change is that, as everybody admits, propositions are assertions, and assertions can be categorical, hypothetical (such as "p implies q"), or modal.

Finally, Russell's statement that what is not a proposition implies nothing is obviously meant to assert that ONLY propositions imply something (some other propositions). But it is certainly true that complex concepts or associated can be explicitated. An explicitation is a type if implication. For instance, being a vertebrate implies that a man can bend his back. Furthermore, verbal nouns cannot be reduced to class-concepts, and they may have implications just as propositions may. For instance, walking implies a rigid ground.

Does any word [any concept] imply itself? In some sense of the term "implies," the answer is Yes. Ubi... ibi....

[comiezapr]

The significance Mr. Russell gives to "proposition" goes hand in hand with his peculiar use of the term... "It may be observed that although implication is indefinable, proposition can be defined. Every proposition implies itself, and whatever is not a proposition implies nothing. Hence to say 'p is a proposition' is equivalent to saying 'p implies p';and this equivalence may be used to define propositions."(27).... "A proposition, we may say, is anything that is tue or that is false."

What you just posted was about the logic of Russel, not his philosophy. Implication was indefinable because every axiomatic system needs undefinable terms and his happened to be implication and negation.

What Russell said was in effect: If p is a proposition, then p implies p, or, vice-versa: if p implies p the p is a propostion.

This is incorrect. What Russel said was something more like this:

The basic symbols that i will use are as follows (insert symbols here including "->", "~" and variables for propositions). These symbols cant be defined WITHIN MY SYSTEM and because of that SHOULD BE THE MOST CLEARLY DEFINED. Here is what these primitive symbols mean: (insert meaning here). The following definition is for well formed formulas (insert methods of sentence construction here). The following few well formed formulas are going to be held true, they are my axioms: (insert axioms here, including the axiom "p->p").

What are these things that are propositions? Well the first thing to note about propositions is that they are the things that go in place of variables in my system; that is how i defined them after all. Because of this we can deduce that the various properties that propositions have within my system are had by propositions as they are in the world. One such property comes from the axiom "p->p" where we see that propositions have the property of implying themselves.

The end!

Thats something like what Russel said. It has nothing to do with what you think its talking about:

On the other hand, it is axiomatic for Russell that a proposition implies itself.... without knowing exactly what the word 'implies' means.

NO! It isnt axiomatic that a proposition is this or that, it is a CONSEQUENCE OF THE AXIOMS that a proposition is this or that. This is exactly the opposite! And he knew exactly what "implies" means, thats why he took it as one of his primatives. What he cant do is derive, within his system, anything about the meaning of "implies".

Enough of quoting things on material you dont have a full understand of PLEASE!

So onto this point:

(p implies p) = where there is p, there must be p =
p and necessarily p.

I take this to be an alternative meaning for "implies". Here the meaning can is totally absurd. Take the general form of this shcema: x implies y. On your acount this turns into the schema: x and necessarily y. Lets see if this is what it really means by doing some examples:

"The kite is on a string implies that the string exists" is translated into "The kite is on a string and necessarily the string exists". So not only does your proposed meaning of "implies" not captrue the meaning of "implies" at all, but it isnt even close to realistic! If anything implies that something exists, then that something exists necessarily!

"My wallet is empty implies that my wallet is not full" is translated into "My wallet is empty and necessarily my wallet is not full". Again, crazyness. This says that if my wallet is empty that necessarily it is not full: it could be no other way! Its as if by having an empty wallet i NECESSARILY have an empty wallet! It just isnt possible for me to have anything in my wallet (i might as well quit my job then!) And all this simply because "my wallet is empty" implies "my wallet is not full."

We dont need more examples, clearly this is a rediculous meaning of implies.

Perhaps you want to reply with "but i was talking about just the schema "x implies x". Ok, so the use of implies in "x implies x" is different from the use of implies in "x implies y". Good luck with that. Perhaps each time a word apears its used in a different way? Hell, whats to say that every word means something different? Or maybe every word means something different on tuesday. Perhaps words change meaning at random, and we, the users of the language are unaware of it!

Get out of here with that! Obviously the use of implies in "x implies x" and "x implies y" is the same use of the word "implies".

The rest of your post just sort of rambles on vaguely, and alot of it is a crime against technical vocabulary:

But it is certainly true that complex concepts or associated can be explicitated. An explicitation is a type if implication. For instance, being a vertebrate implies that a man can bend his back. Furthermore, verbal nouns cannot be reduced to class-concepts, and they may have implications just as propositions may. For instance, walking implies a rigid ground.

No examples of an explication? Actually, an explication, as used in the philosophical literature, is an analysis of a concept in terms of a more clear and precisly defined concept within a logical system.

And verbal nouns have implications? What is the implication of "runing"? Well, nothing. There are, of course implications of propositions incorporating verbal nouns: for example "the man is in a state of running" implies that "the man is on rigid ground." Your example "walking implies a rigid ground" is really a shortened version of a propositional implication in diguise that can be teased out with the help of quantifiers (being an astute logician you should have realized this): "there is some x such that the x is walking implies that the x is on rigid ground" where the propositions are "the x is walking" and "the x is on rigid ground". Dropping the logical structure of a sentence doesnt somehow prove a philosophical point, it shows carelessness.

What Russell said was in effect: If p is a proposition, then p implies p, or, vice-versa: if p implies p the p is a propostion. What could "imply" means, if does not means "causes"/ "engenders" or "value endows"? It could mean something like this: "Where there is love, thereis God" [Uni amor, ibi deus -- as a Medieval hymn goes]. I could say, Where there is a proposition (the statement that oranges are round) -- which is either true or false, there a proposition is enunciated (or there occurs the stating of the proposition), or, more generally: a patent essence [a such-and such a thing or judgement] presupposes that it exists or occurs. The consequent is not an effect (and the antecedent is not a cause), but the consequent is a "must be" inasmuch as the antecedent is an "is."
So, we can speak of presuppositional implication, not a causal implication.

Seriously, common! Be more clear than this! I dont want to nitpick so ill say this: this entire section is gibberish. An essense has nothing to do with implication and nothing to do with necessary propositions, it has to do with modality de re (necessity with respect to propositions is modality de dicto).

Presuppositional implication has nothing to do with the meaning of implication nor propositions! Presuppositional implication is a phrase from the philosophy of language that describes a certian feature of conversation: certian SENTENCES (not propositions, because they dont apear here) in a conversation are stated or not stated only because there is a presupposition embeded in the conversation that implies certian information is mutually understood between the conversants.

It is not true that implication is indefinable; Russell should have said that he did not know how to define it. It is true that the word "implications" has a simple meaning [or actually many possible simple meanings] and that, therefore, it cannot be NOMINALLY defined by other words, but if "implies" is a relator or operator between two propositions, then its function is definable. So, I defined one meaning of the term pragmaticistically, from the 'effects' or consequences that it has for the related propositions.

We already discussion what Russel said and why you were way off on that. And youre actually right about the fact that you can define somethings fuction if it is an operator between two terms (if only because a function is defined as an operator between variables); you forgot to mention that terms that it connects can be replaced by other terms and so you can make a schema of implicature "x implies y" that replaces the terms with generalized variables that range over the terms that can go in that place.

I dont know what pragmaticisticism is, but i assume you mean pragmatism. The school of pragmatism, in language, doesnt determine the effects or consequences of anything, and a pragramtic aproach in language has nothing to do with the effects of words or sentences. That endevour is acuratly categorized as "Speech Acts" and studies how various assertions and other linguistic objects do things in the world (like describe, ask, promise, demand, etc.).

A pragmatic aproach would go out into a language community, take examples of speech or sentences, and see what the various terms meant based on the relationships between them. This is the pragmatic aproach, and ironically I have been the one to do it, not you. Im the one whos giving examples of the word "implies" in sentences and seeing how it behaves you have done nothing like this. Infact you dont give any examples of your words in action at all except to clarify your theorizing!

Im tired. This can go on forever. You need to stop using philosophical language in a philosophy forum in a non standard way; you need to stop taking quotes way out of context; you need to stop pretending to know a subject and closing your ears. Ya, posters come on strong and will knock you down in an adversarial manner, especially if theyre strong in a subject you arent. You dont respond to this by lashing back when you have only passing knowledge; take the criticism, as harsh as it may be, mull it over, and mold your opinion around it.

[comiezapr]

To make things ultra clear and sort of start a new slate in the discussion: what is the problem with this argument?

1) p is identical to p
2) this can be translated into the propositional calculus with the symbols p <-> p
3) this is equivalent, in the propositional calculus, with the symbols (p -> p) (and) (p -> p). (and) here is a symbol of the logical calculus and not the standard english word "and".
4) this sentence of the propositional calculus can be translated into english as p implies p and p implies p
5) from this we can derive that p implies p

I think that there is no problem with the argument but clearly others do. Elucidate that problem if you think otherwise!

[Amedeo]

Continuation of an exploration:


--- RUSSELL ON PROPOSITIONS ---
A couple of statements by Russell are conveniently found in "the Monist",
http://www.books.google.com/Books?id=nawLAAAAIAAJ...

Quote:
The significance Mr. Russell gives to "proposition" goes hand in hand with his peculiar use of the term... "It may be observed that although implication is indefinable, proposition can be defined. Every proposition implies itself, and whatever is not a proposition implies nothing. Hence to say 'p is a proposition' is equivalent to saying 'p implies p';and this equivalence may be used to define propositions."(27).... "A proposition, we may say, is anything that is tue or that is false."

"p is a proposition" = (p -> p)
p is a proposition if and only if p implies p.

so, if p does not imply p, it is not a proposition.

Indeed, if a proposition could directly or indirectly imply its opposite, then a propositions could imply its contradictory:

suppose
p -> q

q -> ~p

therefore, p -> ~p

therefore, p is not a proposition.

I stated earlier that defining a proposition as something that implies itself is axiomatic, when in fact (p -> p) is required by the principle of non-contradiction: A proposition is a statement that does not contradict itself... which implies that a proposition is a statement which must imply itself.
It is also the case that a concept (a meaningful word) is a concept if and only if it doers not imply its contradictory; it imples itself.

The logic of propositions is also a logic of concepts [such as verbal nouns, rather than classes], as it is founded on the principle of non-contradiction of whatever is asserted or enunciated.

The principle of non-contradiction is (in the system I outlined earlier) both an axiom or ule for inferential purposes and a criterion for the categorematic terms [the meaning-ful terms: propositions; concepts] about which the reasoning is done. The syncategorematic terms comprise operators/relators, quantifiers, etc.

[mac_philo]

Gibberish, nonsense, balderdash.

Even within the senseless and incoherent system you are creating, you are making blunders that would be unacceptable in an introductory course on logic. Yet you are here, creating logical systems, telling us what counts as a truthable, as a proposition, etc? Get a fucking grip on yourself. Do you also do this for physics and evolutionary biology, or is it just logic where you feel qualified to make shit up?

Assume this meaningless claptrap about propositions is true. Now take this example of yours:

p -> q

q -> ~p

therefore, p -> ~p

therefore, p is not a proposition.

WRONG, even within this crazy system you are concocting.

Assuming p->q and q->-p, you get p->-p and -p and p->p. So by your insane standard, p IS A PROPOSITION.

YOU CAN ONLY MAKE THIS MISTAKE IF YOU DON'T KNOW WHAT THE FUCK '->' MEANS! Yet you continue to construct theories or whatever the fuck you're doing. In the most literal sense of the expression, you have no idea what you are talking about. Period. I applaud your interest in logic, now give it a useful outlet and read a book on formal logic.

I STUDY THE THINKING OF LOGICIANS and see what they do and the fallacies they commit.

Wow. Just, wow. You aren't even fluent in the technical or nontechnical language of logic, you don't understand implication, you don't know the difference between model and proof theory, you think an atomic sentence can be assigned two truth values in the same interpretation, yet you 'see what fallacies [logicians] commit'. Super.

Oh, and thanks for the ridiculous comments about my 'orthodoxy'. Do you treat physics and evolutionary biology as you treat logic? Are you a brave fighter against "orthodoxy" in those areas as well? Dozens of your errors have been pointed out, yet you carry on, ignoring all corrections, producing more gibberish, sinking deeper into contradiction and senselessness.

If you were talking about evolution or the age of the earth in this manner, the IIDB members would be crawling out of the woodwork to destroy your claims. But since this is about math and logic, and not directly to do with atheism or any religious tradition, you get a free pass.

[comiezapr]

It seems as though were at an impase. Im bowing out.

[Amedeo]

Just need a quick reminder regarding symbolic logic.

is it valid to say p implies p?

Dear HereLiesTheBible,

I don't know if you got the answer you were looking for. I am still dealing with (p -> p), since I found it to be valid but, as I am working on a "logic of denoted occurrences", now there is a new ball-game, and I don't know yet whether it is possible that the axiom of non-contradiction [about occurrences] can imply this nonsense, "an event necessitates itself", or implies the pointless tautology, "an event is an event.; or implies something else.
_______________

my motto:UBI CASUS IBI RATIO

[Amedeo]

[sequentia sancti logiou....]

Can an occurrence proposition be characterized by self-implication?

Direct discourse, e.g.: a body is falling.
Indirect discourse:
I say that body is falling
or
I say "a body is falling"
or
"a body is falling" is being said
or
"a body is falling" is WHAT I am saying
or
I assert that a body is falling.

Now, what is being said is the following words in succession: a, body, is, falling.

Those words in succession are not a species of a genus. There is no analogy with "a dog is an animal.&qu