is the law of non-contradiction analytic tautology?

[gnosis92]

i am curious as to whether the law of non-contradiction of logic which states a statement a cannot be both a and non-a at the same time and true, is merely the result of what the word a and non-a mean. does the word non- imply in itself the law- of contradiction?

does this law of logic apply equally to all known languages? the spanish language use double negatives to mean a negative "no nunca" literally translates no never but it means not ever.

supposedly the hopi language has no terms for tense and time (perhaps an urban legend?) so another aspect of the law of non-contradiction may not apply in their language.

supposedly in many eastern thought a and non-a can be true (at least that's how ken wilbur explains eastern mysticism)

[Preno]

does this law of logic apply equally to all known languages? the spanish language use double negatives to mean a negative "no nunca" literally translates no never but it means not ever.The laws of logic have little to do with the particularities of how languages express negation. It's not relevant to logic that the Spanish use double negatives.
supposedly the hopi language has no terms for tense and time (perhaps an urban legend?) so another aspect of the law of non-contradiction may not apply in their language.Hopi does not include the traditional distinction between past/present/future tense, that's true (it apparently has other tenses, though). It can, however, include time information using adverbs.
supposedly in many eastern thought a and non-a can be true (at least that's how ken wilbur explains eastern mysticism)Supposedly in some Middle Eastern thought, three Gods can be one. Supposedly if you play with words long enough, you can come to any conclusion, however absurd.

[Foobear]

supposedly in many eastern thought a and non-a can be true (at least that's how ken wilbur explains eastern mysticism) The Law of Non-Contradiction and the Law of the Excluded Middle are two different but related concepts. The law of non-contradiction says that nothing can be both true and false at the same time, the law of the excluded middle says that truth values must be either true or false, not somewhere in between.

The two laws are often conflated, and sometimes expressed or defined in the same way, so your mileage may vary when talking about it, but those are the concepts in a nutshell.

You're right, Eastern Philosophy allows shades of grey (they don't treat the Law of the Excluded Middle as an axiom), and in some cases like Taoism revel in contradiction.

"Since before time and space were,
the Tao is.
It is beyond is and is not.
How do I know this is true?
I look inside myself and see."
--Laozi, in the Dao De Jing

[gnosis92]

The laws of logic have little to do with the particularities of how languages express negation. It's not relevant to logic that the Spanish use double negatives.
Hopi does not include the traditional distinction between past/present/future tense, that's true (it apparently has other tenses, though). It can, however, include time information using adverbs.
Supposedly in some Middle Eastern thought, three Gods can be one. Supposedly if you play with words long enough, you can come to any conclusion, however absurd.

i gave spanish as an example of how the concept of negation and the law of noncontradiction is a mere tautology, which in a different language may not be true b/c it is only true by definition

[Preno]

i gave spanish as an example of how the concept of negation and the law of noncontradiction is a mere tautology, which in a different language may not be true b/c it is only true by definitionNo, you're just conflating grammar and logic. If you "translate" the statement "No se nada" literally into English, you will "I don't know nothing". That doesn't change the fact that "No se nada" means "I don't know anything". Certainly Spanish speakers don't have a different concept of logic than English speakers?

[gnosis92]

No, you're just conflating grammar and logic. If you "translate" the statement "No se nada" literally into English, you will "I don't know nothing". That doesn't change the fact that "No se nada" means "I don't know anything". Certainly Spanish speakers don't have a different concept of logic than English speakers?

maybe spanish isn't the best example, but is the reason the law of non-contradiction true is the result of the definition of negation?

[Preno]

maybe spanish isn't the best example, but is the reason the law of non-contradiction true is the result of the definition of negation?I don't quite understand the question, but my point was that logical negation has little to do with the particular implementation of linguistic negation in particular languages. Every Spaniard knows that the negation of "No se nada" is not "Se nada" but "Se algo". Whether the language has two words for expressing negation or just one is irrelevant.

[YadaYada]

The Law of Non-Contradiction and the Law of the Excluded Middle are two different but related concepts. The law of non-contradiction says that nothing can be both true and false at the same time, the law of the excluded middle says that truth values must be either true or false, not somewhere in between.These laws are rules of Aristotelian logic, chosen for their simplicity in permitting certainty from deductions.

Other rules are possible and are employed when it becomes necessary. For example, three-valued logics that allows for undecided, both, neither, etc., and probabilistic logic that allows for degrees of truth.

[kennethamy]

i am curious as to whether the law of non-contradiction of logic which states a statement a cannot be both a and non-a at the same time and true, is merely the result of what the word a and non-a mean. does the word non- imply in itself the law- of contradiction?



The expression, ~(p & ~p) is easily shown to be a logical truth by placing it on a truth-table, and deriving a row of "t's". It is a result of how we use the connective, conjunction, and the operation of negation. All three of the "laws of logic": the law of the excluded middle (p or ~p); the law of identity; (p -> p); and the law of non-contradiction (as above), are logical truths (tautologies) and therefore, are logically equivalent (the expression of their equivalence is a tautology or logical truth), They can, of course, be transformed into one another by the use of De Morgan's laws.

[Minnesota Joe]

supposedly in many eastern thought a and non-a can be true

The law of non-contradiction is probably the one safest from reproach. How are you going to contradict it without it?

So, I don't think this eastern thought abandons non-contradiction so much as it is confused or speaking metaphorically. For example, we might refer to the Death Star in Star Wars as the star that is not a star, but we mean star in two distinct senses--so there is no contradiction.

[kennethamy]

The law of non-contradiction is probably the one safest from reproach. How are you going to contradict it without it?

So, I don't think this eastern thought abandons non-contradiction so much as it is confused or speaking metaphorically. For example, we might refer to the Death Star in Star Wars as the star that is not a star, but we mean star in two distinct senses--so there is no contradiction.

In English, too, someone may ask me (who has just come in from outdoors) "Is it raining?" And I might reply, "Well, it is, and it isn't". Am I violating the law of non-contradiction? Or, someone might upbraid me for conducting a slightly shady business deal, and I might reply, "Well, business is business." Have I defended myself by uttering a tautology, and if he replies, "I disagree with that" is he violating the law of non-contradiction?

[Minnesota Joe]

In English, too, someone may ask me (who has just come in from outdoors) "Is it raining?" And I might reply, "Well, it is, and it isn't". Am I violating the law of non-contradiction? Or, someone might upbraid me for conducting a slightly shady business deal, and I might reply, "Well, business is business." Have I defended myself by uttering a tautology, and if he replies, "I disagree with that" is he violating the law of non-contradiction?

Yup, those are good examples. The second one is particularly interesting to me.

The first one equivocates. Perhaps you meant that technically it is raining, but it isn't raining very hard. Or perhaps you mean that water is falling from the sky, but its source isn't clouds.

The second one seems to poetically convey the inevitability of shady dealing in business. When the other person disagrees, I submit that he is disagreeing with this inevitability claim and violating no law at all.

It seems to me that for every contradiction that allegedly has meaning, there is some transformation that exposes either inconsistency or a real truth claim--perhaps it is a claim of inevitability or absurdity, but it is there nonetheless. It makes the language interesting, but it isn't much of an argument that we ought to abandon the law of non-contradiction.

[trip]

In English, too, someone may ask me (who has just come in from outdoors) "Is it raining?" And I might reply, "Well, it is, and it isn't". Am I violating the law of non-contradiction? Or, someone might upbraid me for conducting a slightly shady business deal, and I might reply, "Well, business is business." Have I defended myself by uttering a tautology, and if he replies, "I disagree with that" is he violating the law of non-contradiction?

You may be violating the law of non-contradiction, but reality isn't. Either it's raining or it's not.

And when you say "Buisness is buisness," you're not actually uttering a tautology there, since the second use of the term 'buisness' is being used as an adjective to describe the first use of the term; specifically you're saying "Buisness is a shady, amoral thing," and the other person would be disagreeing by saying, in essence, "No, business has moral restrictions." Semantics, not logic.

[trip]

A confusion here may be thinking that language is reality. Language is a way to describe reality, but the map isn't the territory. Reality precedes language, and the logical axioms are about reality, not the use of language. You can avoid language altogether and use a truth table to prove these things, sans english, spanish, or whatever.

[kennethamy]

Yup, those are good examples. The second one is particularly interesting to me.

The first one equivocates. Perhaps you meant that technically it is raining, but it isn't raining very hard. Or perhaps you mean that water is falling from the sky, but its source isn't clouds.

The second one seems to poetically convey the inevitability of shady dealing in business. When the other person disagrees, I submit that he is disagreeing with this inevitability claim and violating no law at all.

It seems to me that for every contradiction that allegedly has meaning, there is some transformation that exposes either inconsistency or a real truth claim--perhaps it is a claim of inevitability or absurdity, but it is there nonetheless. It makes the language interesting, but it isn't much of an argument that we ought to abandon the law of non-contradiction.

Of course not. Tautologies are not much use in ordinary conversation. There would be no point in uttering one, since it wouldn't convey any information. Therefore, literal tautologies a put to different use, to convey information in a sprightly style. "Business is business" usually means something like the only goal of business is profit, and (trivial) ethical considerations need not apply. It is like "War is war" which has much the same kind of message. The "it is and it isn't" (raining example) can be given a number of interpretations. The one you gave is one: but sometimes it means that the rain is intermittent; and sometime that it is only drizzing. One thing it isn't, is a counter-example to the law of non-contradiction.

[Minnesota Joe]

The one you gave is one: but sometimes it means that the rain is intermittent; and sometime that it is only drizzing.

Right, that is a good point--there is always the time factor. The sky is blue and not blue if I'm talking about different days of the week (or time of the day).


One thing it isn't, is a counter-example to the law of non-contradiction.

Agreed, it just means language can be complicated.

[kennethamy]

Right, that is a good point--there is always the time factor. The sky is blue and not blue if I'm talking about different days of the week (or time of the day).


.

That doesn't seem quite right to me. "The sky is blue" when ordinarily used is an incomplete sentence. It usually means, "The sky is currently blue" and the sentence, "The sky is currently blue, and the sky is not currently blue" is a contradiction. If I want to talk about the color of the sky at different times, I would index the sentence to times and places. I would say "the sky is (was, will be,) blue at such and such a time, in such and such a place". To assert that the sky is not blue at a different time, or at a different place (or both) is not to contradict my former assertion.

[Minnesota Joe]

That doesn't seem quite right to me. "The sky is blue" when ordinarily used is an incomplete sentence. It usually means, "The sky is currently blue" and the sentence, "The sky is currently blue, and the sky is not currently blue" is a contradiction. If I want to talk about the color of the sky at different times, I would index the sentence to times and places. I would say "the sky is (was, will be,) blue at such and such a time, in such and such a place". To assert that the sky is not blue at a different time, or at a different place (or both) is not to contradict my former assertion.
Right, but the point is that if I neglect time, then I'm bound to make all sorts of seemingly contradictory statements. But we don't usually do so which is why it seems awkward to you. By saying, "It is raining, and it's not raining" and meaning "It is raining intermittently" you are assuming, but neglecting to mention, the temporal process.

[kennethamy]

Right, but the point is that if I neglect time, then I'm bound to make all sorts of seemingly contradictory statements. But we don't usually do so which is why it seems awkward to you. By saying, "It is raining, and it's not raining" and meaning "It is raining intermittently" you are assuming, but neglecting to mention, the temporal process.

I don't have to mention what any listener would have to assume. Otherwise, he would have to believe I am contradicting myself.

[Minnesota Joe]

I don't have to mention what any listener would have to assume. Otherwise, he would have to believe I am contradicting myself.
Why, suddenly, has it become about what you have to do and not about the what makes things appear contradictory? Are you trying to start an argument? :D

[y_feldblum]

i am curious as to whether the law of non-contradiction of logic which states a statement a cannot be both a and non-a at the same time and true, is merely the result of what the word a and non-a mean. does the word non- imply in itself the law- of contradiction?


The law of non-contradiction relates to things, not statements. A thing cannot have some property and not have that property, and it cannot have a property to some degree and also have that property to a different degree. The law says that reality is non-contradictory.

The law is a part of the foundation upon which logic is built. It is not a law of logic. It does not explain the proper methods of thinking, which is what logic does. It is a principle underlying logic, a principle without which logic could not exist. It is a principle which tells you that if, by a system of logic, you think you find some part of reality contradicting itself, then it is your system of logic that is flawed and which you must correct.

[YadaYada]

Right, but the point is that if I neglect time, then I'm bound to make all sorts of seemingly contradictory statements. But we don't usually do so which is why it seems awkward to you. By saying, "It is raining, and it's not raining" and meaning "It is raining intermittently" you are assuming, but neglecting to mention, the temporal process.
I agree. When you think of variability wrt time, then variability wrt space also comes to mind, since they're inseparable. Nothing can "happen" without them.

The weather man points to a radar map of my area and says that it shows that "it is raining". Proof enough? What if the rain does not reach the ground? What if is raining across the street but not on my side? Seems to be both "raining" and "not raining" at the same time, depending whether I am on the first floor or the fifth.

[kennethamy]

The law of non-contradiction relates to things, not statements.

Since when?

[kennethamy]

I agree. When you think of variability wrt time, then variability wrt space also comes to mind, since they're inseparable. Nothing can "happen" without them.

The weather man points to a radar map of my area and says that it shows that "it is raining". Proof enough? What if the rain does not reach the ground? What if is raining across the street but not on my side? Seems to be both "raining" and "not raining" at the same time, depending whether I am on the first floor or the fifth.

It is a matter of defining what it is to rain. But why is it not raining if the rain does not reach the ground? What reason would anyone have for saying that? (You mean if I am holding an umbrella which does not let the rain reach the ground there is any question about whether it is raining?)
If it is raining on my street and not across the street (a most unlikely happening) then, it is raining on my street and not across the street. What's the problem? I have no idea what you mean by the "floors" example.

People say things when they are philosophizing that they would be ashamed to say in other contexts-even if they thought of them.

The question of how we know, or whether we know it is raining is one thing. But whether the statement it is raining and it is not raining is contradictory is a different thing. What has one to do with the other?

[YadaYada]

It is a matter of defining what it is to rain. But why is it not raining if the rain does not reach the ground?

The question of how we know, or whether we know it is raining is one thing. But whether the statement it is raining and it is not raining is contradictory is a different thing. What has one to do with the other?Yes, there are two issues here.

Whether it is or is not raining can never be ascertained except by a qualified observer at a specific place and time. It is really quite common for rain to evaporate before reaching the ground. Not only are space and time variable, but what rain means is quite vague as well. Maybe it's only a mist, or its sleet.

But once we choose to ignore linguistic and epistemic issues then the logic is cut and dry. But do we really want to do that? What good is logic without meaning?

[comiezapr]

I agree. When you think of variability wrt time, then variability wrt space also comes to mind, since they're inseparable. Nothing can "happen" without them.

The weather man points to a radar map of my area and says that it shows that "it is raining". Proof enough? What if the rain does not reach the ground? What if is raining across the street but not on my side? Seems to be both "raining" and "not raining" at the same time, depending whether I am on the first floor or the fifth.

All you need to do here is relatavize a statement to as many parameters as you see fit. For example: "It is raining, now, on this side of the street and it is not raining, now, on this side of the street" is a contradiction. The reason that we dont normally use these extra parameters in our language is becase we dont need to be specific. The reason we dont use extra parameters when explaining logic is because logic is a deductive system to show the inter-relations of various statements; the precision of the terms that are being analyzed are already assumed.

Your problem isnt with logic, or non-contradiction, its with the vagueness of terms that appear within logical formulas. Your considerations are good ones, but they dont have anything to do with logic, they have to do with the failure of natural language expressions to be well defined formal systems. Would we expect anything less though?

The fact that natural language doesnt conform to a well defined formal system doesnt undermine logic in any way. The formal systems where logic is encapsulated are vindicated by thier ability to reflect, very accuratly, what is intuitivly correct reasoning after assuming that there is no vagueness within the terms that appear within the system.

A better way to state the law of non-contradiction is with respect to propositions and not sentences. Propositions are explicit, unequivocal descriptions of ways that the world are. Sentences express propositions (and vague expression express a set of propositions). The law on non contradiction would read "not both A and notA" where A range over propositions and not sentences. Your musings about what different sentences mean and how that relates to togic would then be completly irrelevant; propositions cannot be vague.

Edit: I posted in response to this mostly because im lazy. I am arguing against a general impression i get from the series of post within this thread, not this post in particular.

[kennethamy]

Yes, there are two issues here.

Whether it is or is not raining can never be ascertained except by a qualified observer at a specific place and time. It is really quite common for rain to evaporate before reaching the ground. Not only are space and time variable, but what rain means is quite vague as well. Maybe it's only a mist, or its sleet.

But once we choose to ignore linguistic and epistemic issues then the logic is cut and dry. But do we really want to do that? What good is logic without meaning?

You mean that had I been in New Orleans at the height of Katrina I couldn't have told that it was raining? And that if I was in the middle of the Gobi Desert with the Sun shining, I couldn't have told it was not raining?

Why do you say such things?

[comiezapr]

i am curious as to whether the law of non-contradiction of logic which states a statement a cannot be both a and non-a at the same time and true, is merely the result of what the word a and non-a mean. does the word non- imply in itself the law- of contradiction?


Yes and no. I, personally, dont have the expository skill to express what i want to say without technical language so bear with this vague, impressionistic answer. I assume were working only in propositional logic.

"Not" is an operator that maps the truth value of a proposition to the opposite truth value. This assumes that the language has only two truth values. (You can defined the not operator in systems with more than two truth values but they dont seem to be philosophically interesting systems.) This, roughly, is the definition of "not." This definition, along with an adequate expansion of the model theory (truth tables) of the propositional system do imply the law of non contradiction: each statement, when in conjunction with the opposite of the truth value of that statement, is always false.

This, i dont think, was what you are asking. You asked whether, semantically, "not" is intamantly related to the law of non-contradiction. This is not the case in a natural language. When we talk about sentences, where semantics is a live question about the meaning of the terms within the sentence, not can apply to a sentence without the new sentence (the concatanation of not and the original sentence) contradicting the first. This can be due to vagueness in the sentence.

In terms of the semantics of a formal system "not" usually is intamantly related to the law on non contradiction in this way: "not" wouldnt be a semantically interesting term if it did imply the law of non-contradiction so "not" is defined in such a way that it does imply this.

I hope this answers your question. If it doesnt, i can shed more light on the issue but will require a more precise question.

Edit: I had ignored the second part of the OP. What i have to say is breif.

does this law of logic apply equally to all known languages? the spanish language use double negatives to mean a negative "no nunca" literally translates no never but it means not ever.

supposedly the hopi language has no terms for tense and time (perhaps an urban legend?) so another aspect of the law of non-contradiction may not apply in their language.

supposedly in many eastern thought a and non-a can be true (at least that's how ken wilbur explains eastern mysticism)

All languages that have ever been studied have equal expressive power. Where the expressive power lies (within large vocabularies, inflection of words, changing words in different contexts, etc...) varies enormously from language to language. I think that the hopi language expresses tense related things with enormous changes to verbs, changes much larger than the suffixes in english. Dont take my word for this since my knowledge of language taxonomy is very sparse, all i know is from the introductory texts on linguistics. Just because there isnt a term doesnt mean the language cant express it! Just because there isnt a term that exresses something doesnt mean that it cant be expresses in the abstract logical structure set out by propositional logic!

[comiezapr]

But once we choose to ignore linguistic and epistemic issues then the logic is cut and dry. But do we really want to do that? What good is logic without meaning?

Logic is most useful when it is "cut and dry" in your sense. The main purpose of formalizing reasoning processes is so that we can prove things ABOUT those reasoning processes; we abstract from natural language in order to understand natural language better. Its like the idealized models of science that are used to penetrate into the mysteries of nature. Abstraction from the messyness uncovers a world of order that we can work with.

Logic is not an all purpose tool with respect to arguments in natural language; it works only when vagueness is reduced to a minimum. Nor was it designed to work like a magic wand to decifer arguments; it is a tool with which to augment philosophical reasoning skills generally. There are various systems that can acomadate for more vagueness than standard propositional logic but the inferance rules from formula to formula are weaker.

[Foobear]

There are various systems that can acomadate for more vagueness than standard propositional logic but the inferance rules from formula to formula are weaker. Traditional logical transformations (like De Morgan's Law) work in fuzzy logic as well as traditional logic.

As for fuzzy logic systems not being interesting philosophically... I'll have to disagree. They can explain a wider variety of phenomena than classical logic.

[sweetiepie]

i am curious as to whether the law of non-contradiction of logic which states a statement a cannot be both a and non-a at the same time and true, is merely the result of what the word a and non-a mean. does the word non- imply in itself the law- of contradiction?

does this law of logic apply equally to all known languages? the spanish language use double negatives to mean a negative "no nunca" literally translates no never but it means not ever.

supposedly the hopi language has no terms for tense and time (perhaps an urban legend?) so another aspect of the law of non-contradiction may not apply in their language.

supposedly in many eastern thought a and non-a can be true (at least that's how ken wilbur explains eastern mysticism)

P is a pretty dumb thing to say when ~P remains an option. I fail to see how any declarative statement made in any language can stand without the law of noncontradiction and come out having any meaning. To say something is to use the law of non-contradiction.

[y_feldblum]

Since when?

Since its discovery.

[Preno]

P is a pretty dumb thing to say when ~P remains an option. I fail to see how any declarative statement made in any language can stand without the law of noncontradiction and come out having any meaning. To say something is to use the law of non-contradiction.Or more accurately, to mean something is to use the law of non-contradiction. "Contradictions" in what is said do not necessarily reflect contradictions in the meaning of what is said (as in kennethamy's examples, e.g.).