Absolute Truth--split from Is it Rational to believe in Induction

[John Page]

Nice topic. I've spewed forth on this one before, but here goes again..... quoting from Hugo's link.
Originally posted by Hugo Holbling
To look at this further, let’s lay out the information we have in a logical form using what we learned in the last thread from Clutch:

Premise 1: The first sheep was white.
P2: The second sheep was white.
…
P501: The five hundredth and first sheep was white.
(And so on.)

Conclusion: All sheep are white.

The problem is that none of the premises contain the conclusion and all of them are moreover the same in form, so we’re relying on a kind of brute force of numbers. Suppose we saw another thousand sheep, all of which were also white. Are we justified then? Again, apparently we aren’t because in fact some sheep aren’t white? Is there any way around this difficulty?

My views is as follows:

1. There are no absolute truths, a truth is in relation to the truth telling system employed.
2. Minds contain archetypes of objects and may update or modify these archetypes.
3. An archetype emerges in the mind inductively when a sufficient number of instances of a form are encountered. (The sufficient number can vary).
4. A person whose only direct experience and other knowledge of all (real) sheep is of white sheep may include the property "white" in the archetype. That is, white is included in the working definition of a sheep.
5. Once the mind has developed its concept of a sheep to stage 4 above, deductive truths can appear because we now have a definition upon which to base "coherent" statements about the world. IOW, we start to assert our definition of a sheep upon the world.
5. Of course, subsequent experience can bring us to a realization that our mental archetypes of the world may be flawed, and there are black sheep. When we learn this, by further induction based on observation we modify our category definition for sheep to include the exceptional case of real black sheep.

In this manner, I see deduction as subsequent to induction. Through induction we observe and modify our conceptions of the world and through deduction we assert our presuppositions upon the same world.

This is intersubjectivity in motion. I believe this approach explains the nature of truths - truths can only arise once we have entered into the deductive stage (5 above) of "concretizing" our concepts in order that we may say things like "(It is true that) a sheep is a four legged mammal that goes bleat and is white, although exceptionally may be black".

Comments welcome.

Cheers, John

[ex-xian]

Originally posted by John Page
1. There are no absolute truths...
Are you absolutely sure this is true? :D

[theophilus]

[QUOTE]Originally posted by John Page
Nice topic. I've spewed forth on this one before, but here goes again..... quoting from Hugo's link.

My views is as follows:

1. There are no absolute truths, a truth is in relation to the truth telling system employed.
2. Minds contain archetypes of objects and may update or modify these archetypes.
3. An archetype emerges in the mind inductively when a sufficient number of instances of a form are encountered. (The sufficient number can vary).
4. A person whose only direct experience and other knowledge of all (real) sheep is of white sheep may include the property "white" in the archetype. That is, white is included in the working definition of a sheep.
5. Once the mind has developed its concept of a sheep to stage 4 above, deductive truths can appear because we now have a definition upon which to base "coherent" statements about the world. IOW, we start to assert our definition of a sheep upon the world.
5. Of course, subsequent experience can bring us to a realization that our mental archetypes of the world may be flawed, and there are black sheep. When we learn this, by further induction based on observation we modify our category definition for sheep to include the exceptional case of real black sheep.

In this manner, I see deduction as subsequent to induction. Through induction we observe and modify our conceptions of the world and through deduction we assert our presuppositions upon the same world.

This is intersubjectivity in motion. I believe this approach explains the nature of truths - truths can only arise once we have entered into the deductive stage (5 above) of "concretizing" our concepts in order that we may say things like "(It is true that) a sheep is a four legged mammal that goes bleat and is white, although exceptionally may be black".

Comments welcome.

Cheers, John

Apart from the obvious problem of incoherence pointed out by ex-xians above (it is the self-destructive foundation of PostModernism), it seems that what your argument boils down to is "there is no absolute truth because there is no premanent reality," or more accurately, there is no reality at all.
"Reality" is only/merely the current state of experience.
The problem with basing "truth" (even truth within a system) on experience is that there is no such thing as common or shared experience, i.e., your experience is not my experience even though we may have the same object in view.
Thus, truth becomes completely personal and, therefore, meaningless (a tautology), knowledge becomes impossible as does meaningful communication.

So, this theory of truth as inductive flux makes this discussion inexplicable.

[John Page]

Originally posted by ex-xian
Are you absolutely sure this is true? :D
Pretty darned sure, but others are not, so its false for them.....

[John Page]

Originally posted by theophilus
Apart from the obvious problem of incoherence pointed out by ex-xians above (it is the self-destructive foundation of PostModernism)...
There is no problem, and I've responded separately to ex-xian's post - the usual rejoinder to a relativistic stance. The fact that you oppose my view strengthens it rather than weakens it - I am merely stating my view and not claiming it is universal.

Your view, which is presumably that absolute truths do exist, is lacking in any examples. Any claim for it to be the rightful or true view is therefore unsupportable.
Originally posted by theophilus
....it seems that what your argument boils down to is "there is no absolute truth because there is no premanent reality," or more accurately, there is no reality at all.
Sorry, you misunderstand my position. There is no fixed reality as far as I'm aware. We only know things in relation to other things. Some of the relations between things seem to be more persistent than others but they are, nevertheless, observed relations.
Originally posted by theophilus
The problem with basing "truth" (even truth within a system) on experience is that there is no such thing as common or shared experience, i.e., your experience is not my experience even though we may have the same object in view.
We do share experience IMO as described in the post of mine that you quote!!! wherein I describe a process by which concepts are share intersubjectively and thence experience.

I think my view can be shown to be valid experimentally. Our minds develop concepts as a result of experience (i.e. they can be taught and learned). Because our concepts differ slightly it then becomes possible for miscommunication to occur. If, however, we know truth about objects through direct experience then a strict objectivist appraoch has no explanation for the difference in understandings.
Originally posted by theophilus
Thus, truth becomes completely personal and, therefore, meaningless (a tautology), knowledge becomes impossible as does meaningful communication.
If there were no communication then yes, we would be trapped inside our personal reality and one's truth would be meaningless to another. IOW your statement supports my view.

Deductive truths are tautologies, self-fulfilling definitions. I don't see how you reach your assertion that knowledge becomes impossible under my schema. Maybe that's to do with a mistaken belief that I don't subscribe to a common external reality (which we refer to as "reality :)) - its only the term objective reality that I reject.
Originally posted by theophilus
So, this theory of truth as inductive flux makes this discussion inexplicable.
Hmmmm. One's inductions are one's own subjective view driven by one's own experience, and not necessarily conscious experience at that. The absolute truth assertion is inexplicable to me - one ends up in a regression or having to believe its "turtles all the way down." Demonstrably truth does differ between us as this debate is witness.

Cheers, John

[ex-xian]

Originally posted by John Page
Pretty darned sure, but others are not, so its false for them.....
This isn't what you asserted, but then my question wasn't a good one. Here's your statement

1. There are no absolute truths, a truth is in relation to the truth telling system employed.
A better question for me to have asked would have been, "Is this statement absolutely true?"

If it is, then it's self-contradictory. If it is not, then the truth value of this statement can change. Thus, there would be situations in which there are absolute truths. Once again, a contradiction. Your "out"...
There is no problem, and I've responded separately to ex-xian's post - the usual rejoinder to a relativistic stance. The fact that you oppose my view strengthens it rather than weakens it - I am merely stating my view and not claiming it is universal.

Doesn't help you. The initial statement is not an assertion of an opinion. It is a statement of fact. If you had said, "It's my opinon that no absolute truths exist" you could have replied with
Pretty darned sure, but others are not, so its false for them.....and it would have been a defensible position.

[John Page]

Originally posted by ex-xian
This isn't what you asserted, but then my question wasn't a good one. Here's your statement
:confused: I thought I was being consistent - asserting there are no absolute truths but being pretty darned sure about it....
Originally posted by ex-xian
A better question for me to have asked would have been, "Is this statement absolutely true?"

If it is, then it's self-contradictory. If it is not, then the truth value of this statement can change. Thus, there would be situations in which there are absolute truths. Once again, a contradiction.
An absolute truth must apply in all situations and the answer to your question is not always yes. I fail to see the contradiction.

I suspect you may think there is a contradiction because of a belief in truth having a "universal" appearance. To the contrary, truths are "local" to the thinker and intersubjective with like-minded folk. Example, if all humans believed that the King of France is bald (or x, whatever) then this typifies the human condition, it does not make x true for bats, aliens.
Originally posted by ex-xian
Doesn't help you. The initial statement is not an assertion of an opinion. It is a statement of fact. If you had said, "It's my opinon that no absolute truths exist" you could have replied with.....
Its all opinion. Facts may have the appearance of universal truths but a claim to know a fact remains a subjective view. Everything that anybody says can be taken as implicitly prefaced by "I think that..." or "I believe that..."

[Amos]

Originally posted by John Page

Your view, which is presumably that absolute truths do exist, is lacking in any examples. Any claim for it to be the rightful or true view is therefore unsupportable.



In science the hypothesis always exists before the experiment is made and this alone proves that an absolute truth exists. The absolute truth is truth in itself and beauty is what maintains this truth wherefore science is beautiful when we can cristalize our concept of truth that existed already before the test was made . . . or science could not be rewarding and beautiful.

[ex-xian]

Originally posted by John Page
:confused: I thought I was being consistent - asserting there are no absolute truths but being pretty darned sure about it....

An absolute truth must apply in all situations and the answer to your question is not always yes. I fail to see the contradiction.
You said, "There are no absolute truths."
I asked, "Is this statement absolutely true?"

If you answer yes, then your statement becomes an absolute.
If you answer no, then the statement "There are no absolute truths" is sometimes not true. Therefore, there would be times when there would be absolute truths. Then if there are sometimes absolute truths, this contradicts your initial position that there are no absolute truths.

I suspect you may think there is a contradiction because of a belief in truth having a "universal" appearance. To the contrary, truths are "local" to the thinker and intersubjective with like-minded folk. Example, if all humans believed that the King of France is bald (or x, whatever) then this typifies the human condition, it does not make x true for bats, aliens.
Are you saying that x is "all humans believe that the King of France is bald" or is x "the King of France is bald?" If the former, then the position of the bats is irrelevent, if the latter, the positon of the bats is likewise irrelevent. Furthermore, as it stands, the statement "the King of France is bald" seems to be undecidable in terms of its truth value for the statement is not well defined.

If you had phrased in the classic way, "The present King of France is bald" then I would agree that this statment has no absolute truth value as the adjective "present" would cause the statement to be in a constant state of flux.

Its all opinion. Facts may have the appearance of universal truths but a claim to know a fact remains a subjective view. Everything that anybody says can be taken as implicitly prefaced by "I think that..." or "I believe that..."
Of course it's all opinion, but you made what was a statement of fact, then equivocated by implying that it was a statement of preference.

[John Page]

Originally posted by Amos
In science the hypothesis always exists before the experiment is made and this alone proves that an absolute truth exists. The absolute truth is truth in itself and beauty is what maintains this truth wherefore science is beautiful when we can cristalize our concept of truth that existed already before the test was made . . . or science could not be rewarding and beautiful.
Amos, this is true for you but not for me and therefore not absolute.

[John Page]

Originally posted by ex-xian
You said, "There are no absolute truths."
I asked, "Is this statement absolutely true?"

If you answer yes, then your statement becomes an absolute.
If you answer no, then the statement "There are no absolute truths" is sometimes not true. Therefore, there would be times when there would be absolute truths. Then if there are sometimes absolute truths, this contradicts your initial position that there are no absolute truths.
:mad: Please read my previous post, if I answer yes, I am answering from my point of view - I am not so presumptive as to claim to have what some call a "God's Eye View".

Also, if a truth is only "sometimes" it cannot be absolute because of the explicit qualification you just made.
Originally posted by ex-xian
Of course it's all opinion, but you made what was a statement of fact, then equivocated by implying that it was a statement of preference.
:confused: Epistemically, that's what facts are, something you accept as true yet at the same time accept that you could be mistaken. If I appear to be equivocating its only because what I accept as a fact is what you are relegating to my opinion. OTOH, you are equivocating the definition of an absolute truth in your argument.

No matter, I'm more interested in why you continue to argue against my position using a form of deductive argument which is fundamentally flawed because it does not apply to my point of view.

Cheers, John

[ex-xian]

Originally posted by John Page
:mad: Please read my previous post, if I answer yes, I am answering from my point of view - I am not so presumptive as to claim to have what some call a "God's Eye View".

Also, if a truth is only "sometimes" it cannot be absolute because of the explicit qualification you just made.
This further illustrates the incoherence of your position. The negation of "It is never the case that x" is "It is sometimes the case that x."

:confused: Epistemically, that's what facts are, something you accept as true yet at the same time accept that you could be mistaken. If I appear to be equivocating its only because what I accept as a fact is what you are relegating to my opinion. OTOH, you are equivocating the definition of an absolute truth in your argument.
Let me try this again, avoiding anything but the initial position, "There are no absolute truths," and let this statement be designated T.

There are three possibilities.
1) T is false. If T is false, then there are absolute truths.
2) T is necessarily true. Then T itself is an absolute truth, a contradiction is reached.
3) T is contingently true. Then T is true given conditions, p1, ..., pn. However, if conditions p1, ..., pk are not fulfilled, then T is false. Then whenever ~(p), ~T. That is, sometimes there are absolute truths. A contradiction.

In every case, absolute truths exist.

The fact that the word "sometimes" is used along with "absolute" is an incoherence resulting from the logical implications of the initial statement, T.

No matter, I'm more interested in why you continue to argue against my position using a form of deductive argument which is fundamentally flawed because it does not apply to my point of view.

Cheers, John
If one isn't allowed to logically deduce the implications of your position, how is rational discourse possible?

[John Page]

Originally posted by ex-xian
This further illustrates the incoherence of your position. The negation of "It is never the case that x" is "It is sometimes the case that x."
No, that would be "It is always the case that x". For x to be an absolute truth then it must always unconditionally be the case that x.

Ergo, x is not an absolute truth if (never x) or (sometimes x).
Originally posted by ex-xian
Let me try this again, avoiding anything but the initial position, "There are no absolute truths," and let this statement be designated T.

There are three possibilities.
1) T is false. If T is false, then there are absolute truths.
2) T is necessarily true. Then T itself is an absolute truth, a contradiction is reached.
3) T is contingently true. Then T is true given conditions, p1, ..., pn. However, if conditions p1, ..., pk are not fulfilled, then T is false. Then whenever ~(p), ~T. That is, sometimes there are absolute truths. A contradiction.

In every case, absolute truths exist.
*sigh*

Let ex-xian's system of logic be represented by E and another system of logic be represented by A. T is the statement "There are no absolute truths"

1. A != E. (The two systems are not equal)
2. A is saying that if you are in system A then ~T
3. A is saying that if you are in system E then T.
4. E is saying that T in both system A and system E.

Given the incompatibility between 2 and 4, which system do you now think is contradictory?
Originally posted by ex-xian
If one isn't allowed to logically deduce the implications of your position, how is rational discourse possible?
You are free to determine what you will under any system you wish to invent, and so am I. I would like to understand how you reach the conclusion that rational discourse is impossible without absolute truths or, if that's not what you're saying, what you mean by the above statement.

Cheers, John

[ex-xian]

Originally posted by John Page
No, that would be "It is always the case that x". For x to be an absolute truth then it must always unconditionally be the case that x.

Ergo, x is not an absolute truth if (never x) or (sometimes x).

The strict negation of a universal is an existential, not another universal.


Let ex-xian's system of logic be represented by E and another system of logic be represented by A. T is the statement "There are no absolute truths"

1. A != E. (The two systems are not equal)
2. A is saying that if you are in system A then ~T
3. A is saying that if you are in system E then T.
4. E is saying that T in both system A and system E.

Given the incompatibility between 2 and 4, which system do you now think is contradictory?
You've misrepresented by position. Under no system (that I can think of) will T be true. You still haven't found a flaw in my argument.

You are free to determine what you will under any system you wish to invent, and so am I. I would like to understand how you reach the conclusion that rational discourse is impossible without absolute truths or, if that's not what you're saying, what you mean by the above statement.
You had said, No matter, I'm more interested in why you continue to argue against my position using a form of deductive argument which is fundamentally flawed because it does not apply to my point of view.
If I can't logically deduce from what you say, how can we continue?

[John Page]

Originally posted by ex-xian
The strict negation of a universal is an existential, not another universal.
Ah! I see, but your claim was existential, there are no absolute universals......which is what we're debating.

You're arguing "Some truths are absolute" and I'm arguing its possible to have a system where "No truths are absolute" (negation of an existential). I don't accept an a priori claim like "It is always the case that...." because its untestable and thus a hypothesis only.
Originally posted by ex-xian
You've misrepresented by position. Under no system (that I can think of) will T be true. You still haven't found a flaw in my argument.

:confused:
Substituting in the above, you just wrote:
"Under no system (that I can think of) will "There are no absolute truths" be true."

That is exactly the position that I attributed to you - see line 4:
"E is saying that T in both system A and E"

I agree I haven't found a flaw within system E, but neither have you found a flaw within system A. However what I think I've shown is that when putting both systems together, A reconciles/explain both A and E whereas E merely claims A is inconsistent. From this reasoning, I suppose relativism is superior because it more accurately portrays the reality that truth is something people think, and is relative to their thoughts, not some god-given (not that you claimed that) universal.
Originally posted by ex-xian
If I can't logically deduce from what you say, how can we continue?
I suggest we proceed using reason and examining the cases available. Logics are fallible systems invented by humans - this is a truth derived by induction - and a claim that "This logic is absolutely true" is an internally consistent deductive claim that does not apply outside the system that spawned it.

Cheers, John

[ex-xian]

Originally posted by John Page
Ah! I see, but your claim was existential, there are no absolute universals......which is what we're debating.
OK, I've not thought about this in a few days, and most of my posts have been late at night, so maybe I've forgotten and/or have missed something important. Let me try again.

Your claim was a negative universal, of the form "Ax~Px," where Px=x is absolutly true If this is negated, it becomes "ExPx."

You claimed there are no absolute truths, and to be consistent, let this be denoted by T.

1) If T is neccisarily true, then it is an absolute...contradiction.
2) If T is contingently true, then there are conditions under which it is false, so its negation is true. The negation is "There is at least one x, such that is true absolutely...a contradiction."
3) If T is false, then there are absolute truths.


You're arguing "Some truths are absolute" and I'm arguing its possible to have a system where "No truths are absolute" (negation of an existential). I don't accept an a priori claim like "It is always the case that...." because its untestable and thus a hypothesis only.
I'll concede that this a bass-ackward to phrase the discussion. Sorry.

:confused:
Substituting in the above, you just wrote:
"Under no system (that I can think of) will "There are no absolute truths" be true."

That is exactly the position that I attributed to you - see line 4:
"E is saying that T in both system A and E"
But what I'm saying is that any system in which T is taken to be true is an incoherent one.

I agree I haven't found a flaw within system E, but neither have you found a flaw within system A. However what I think I've shown is that when putting both systems together, A reconciles/explain both A and E whereas E merely claims A is inconsistent. From this reasoning, I suppose relativism is superior because it more accurately portrays the reality that truth is something people think, and is relative to their thoughts, not some god-given (not that you claimed that) universal.[/b][/quote]
But my position, A, would be that any system in which T is true in an incoherent one.

I suggest we proceed using reason and examining the cases available. Logics are fallible systems invented by humans - this is a truth derived by induction - and a claim that "This logic is absolutely true" is an internally consistent deductive claim that does not apply outside the system that spawned it.

OK, I thought that you were saying that any evaluation of your claim flawed, thus making your claim impossible to refute or defend.

edited to correct one of the many grammar errors that I'm sure are herein, of which I've found only one. :)

[John Page]

Originally posted by ex-xian
Your claim was a negative universal, of the form "Ax~Px," where Px=x is absolutly true If this is negated, it becomes "ExPx."
No, no, no! My claim is not a universal. My claim is that there exists a system (me, A) for which there are no absolute truths. I have no wish or need to impose my belief upon system E to remain coherent.

It is system E that is claiming (a universal) that for system A there are absolute truths. System A does not need to deny that there exists a system E for which there are absolute truths since system A holds that all truhs are subjective. OTOH system E needs to impose that claim on system A in order to remain coherent.
Originally posted by ex-xian
OK, I thought that you were saying that any evaluation of your claim flawed, thus making your claim impossible to refute or defend.
No, if I had said that I would have been making a universal claim..... ;)
Originally posted by ex-xian
edited to correct one of the many grammar errors that I'm sure are herein, of which I've found only one. :)
:), the author paradox, possible due to an absence of a universla syntax!

BTW, would you agree that the universe, reality, is, whether we deem it choherent or not?

Cheers, John

[ex-xian]

Originally posted by John Page
No, no, no! My claim is not a universal. My claim is that there exists a system (me, A) for which there are no absolute truths. I have no wish or need to impose my belief upon system E to remain coherent.

It is system E that is claiming (a universal) that for system A there are absolute truths. System A does not need to deny that there exists a system E for which there are absolute truths since system A holds that all truhs are subjective. OTOH system E needs to impose that claim on system A in order to remain coherent.

But even if you limit you universe of discourse to your system, the claim T is still a universal, isn't it?

:), the author paradox, possible due to an absence of a universla syntax!HA!

BTW, would you agree that the universe, reality, is, whether we deem it choherent or not?
I think I know what I think, but let me think about it for awhile before I post.

[John Page]

Originally posted by ex-xian
But even if you limit you universe of discourse to your system, the claim T is still a universal, isn't it? \
Next Level.....System B.

I am a dynamic system that contains many different possible points of view. T is not a universal within me.

:), John

[ex-xian]

Originally posted by John Page
\
Next Level.....System B.

I am a dynamic system that contains many different possible points of view. T is not a universal within me.

:), John
Ok, I'm starting to have flashbacks of Gödel, Escher, Bach. So is T false in B?

Also, I just bought a book on fuzzy logic. It seems to be dealing with what we've been talking about.

Still thinking about that reality question...

[John Page]

Originally posted by ex-xian
So is T false in B?
B is a multi-POV system. T & ~T in B, see this thread on modal dialetheism (http://www.iidb.org/vbb/showthread.php?s=&threadid=72502) ... there are true contradictions.

Cheers, John

[ex-xian]

Originally posted by John Page
B is a multi-POV system. T & ~T in B, see this thread on modal dialetheism (http://www.iidb.org/vbb/showthread.php?s=&threadid=72502) ... there are true contradictions.

Cheers, John
But doesn't B have to be internally consistent. Consider POVs X and Y in B. If X holds that T and Y hold ~T, if they are both affirmed in B, B is inconsistent. If this is true, then any theorem arising from B is suspect.

[John Page]

Originally posted by ex-xian
But doesn't B have to be internally consistent. Consider POVs X and Y in B. If X holds that T and Y hold ~T, if they are both affirmed in B, B is inconsistent. If this is true, then any theorem arising from B is suspect.
New Territory for me. Let's see...

Consider G, the god's eye view. Let B be an internally inconsistent system. G includes B and therefore becomes internally inconsistent.

I'm wondering what the bottom line is here. For example, how is it that we think there is no requirement for the universe to be internally inconsistent? If I conclude that the universe is necessarily inconsistent, what does that say about my assumptions, since I am not claiming a god's eye view.

:confused:

[ex-xian]

Originally posted by John Page
New Territory for me. Let's see...

Consider G, the god's eye view. Let B be an internally inconsistent system. G includes B and therefore becomes internally inconsistent.
G would be special case that could encompass both consistency and inconsistency and retain its consistency. G would consider B in its entirety, see it as inconistent, label all theorems resulting from B as false, and move on.


I'm wondering what the bottom line is here. For example, how is it that we think there is no requirement for the universe to be internally inconsistent? If I conclude that the universe is necessarily inconsistent, what does that say about my assumptions, since I am not claiming a god's eye view.

I think that the universe has to consistent...I do hold that a fasle propositon implies anything. If the law of the excluded middle were violated, or if you prefer, both 1 and 0 affirmed in a logic of probability or modality, then we would be unable to make coherent judgments or statements about the universe. Also, scientists have been able to successfully apply logical systems to empirical data, which, seems to me, to lend toward believing that the universe is, in some sense, consistent.

[John Page]

Originally posted by ex-xian
G would be special case that could encompass both consistency and inconsistency and retain its consistency. G would consider B in its entirety, see it as inconistent, label all theorems resulting from B as false, and move on.
But we cannot attain G and might as well toss a coin as argue whether it should be taken as consistent/coherent or not.
Originally posted by ex-xian
I think that the universe has to consistent...I do hold that a fasle propositon implies anything. If the law of the excluded middle were violated, or if you prefer, both 1 and 0 affirmed in a logic of probability or modality, then we would be unable to make coherent judgments or statements about the universe. Also, scientists have been able to successfully apply logical systems to empirical data, which, seems to me, to lend toward believing that the universe is, in some sense, consistent.
I think the issue here is knowability rather than the universe being consistent or no.

[ex-xian]

Originally posted by John Page
But we cannot attain G and might as well toss a coin as argue whether it should be taken as consistent/coherent or not.
Hey, you started this G stuff, not me! :P
Actually, my first reaction was to say that G cannot exist, so your question was meaningles. But I decided to answer anyway. In any case, since we're tossing out G, do you have a response to
Originally posted by ex-xian
But doesn't B have to be internally consistent. Consider POVs X and Y in B. If X holds that T and Y hold ~T, if they are both affirmed in B, B is inconsistent. If this is true, then any theorem arising from B is suspect.


I think the issue here is knowability rather than the universe being consistent or no.
Well, once again you brought up consistency. However, I would hold that an inconsistent universe would be unknowable by the same argument I used before.

[John Page]

Originally posted by ex-xian
However, I would hold that an inconsistent universe would be unknowable by the same argument I used before.
Yes, this is possible. However, something that is inconsistent for E could be knowable by system B. (New system = generic bat).

[ex-xian]

Originally posted by John Page
Yes, this is possible. However, something that is inconsistent for E could be knowable by system B. (New system = generic bat).
Only if the axioms are such that the inconsistency is eliminated. In naive set theory, there is nothing wrong with saying that sets are members of themselves. However, Russell's paradox pops up rather quickly (the set of all sets that are not members of themselves), so it is necessary for axiomatic ZFC set theory to include the axiom "No sets are members of themselves" which is for the purpose of avoiding contradiction.

How all this relates to the real world (whatever that means), I'm don't know. It sure seems that the laws of non-contradiction and the excluded middle should apply. Something cannot be totally A and totally not-A at the same time.