Socrates believed Truth was ABSOLUTE

[Monte314]

We are always talking about much we INTJ's love logic... so I knew we would enjoy looking at a famous and interesting example.

The following is an exercise I go through when I teach my Logic course. It is Monte's symbolic restatement of a demonstration used by Socrates in a discussion he had with Protagorus of Abdera. Socrates, probably the most logical person who ever lived, believed in ABSOLUTE TRUTH. (You can read an excerpt from this debate in William S. Sahakian's outstanding book, Ideas of the Great Philosphers.)

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John: "I think truth is relative, not absolute. Something can be true for you, and not true for me."
Ann: "You mean, really true AND really not true at the same time, not just different opinions?"
John: "Sure!"

So, let A be any proposition that is both true and not true.
Let B be the proposition "Truth is absolute, not relative."

Then, proceeding according to the rules of logical inference (standard first-order predicate logic, e.g., Copi and Cohen, Introduction to Logic, 8th Edition, Macmillan Publishing, 1990), we have:

1. A (Given)
2. -A (Given)
3. (-A) V B (Law of Addition, using line 2)
4. A --> B (Law of Material Implication, using line 3)
5. Therefore, B (Modus Ponens, lines 4 and 1).

This would seem to suggest that the assertion that truth is truly subjective gives its proponents two alternatives:

1.) admit their position is logically untenable (since it contradicts itself), and abandon it
2.) retain their position, and abandon logic

Thoughts?

[Marcus]

John: "I think truth is relative, not absolute. Something can be true for you, and not true for me."
Ann: "You mean, really true AND really not true at the same time, not just different opinions?"
John: "Sure!"
I don't get why what John says and what Ann says are considered equivalent. 'True for me' means truth in my system, which is not necessarily the same as 'truth for you'. We might start from different axioms and we might use a different logic, (or no logic at all to take a more realistic example :)) .

So, let A be any proposition that is both true and not true.
Let B be the proposition "Truth is absolute, not relative."

Then, proceeding according to the rules of logical inference (standard first-order predicate logic, e.g., Copi and Cohen, Introduction to Logic, 8th Edition, Macmillan Publishing, 1990), we have:

1. A (Given)
[SIZE=4]2. -A (Given)
3. (-A) V B (Law of Addition, using line 2)
4. A --> B (Law of Material Implication, using line 3)
5. Therefore, B (Modus Ponens, lines 4 and 1).

This would seem to suggest that the assertion that truth is truly subjective gives its proponents two alternatives:

1.) admit their position is logically untenable (since it contradicts itself), and abandon it
For me it means that if A and -A are both truth, then any P proposition is true, as you did not use any specificity of B in the derivation.


2.) retain their position, and abandon logic

Thoughts?
That's an option, logic is only one way to derive knowledge.

[Fridays Child]

Feelings are relative. Beliefs are relative. Facts are facts and stats are stats...but they require human interpretation to attain meaning beyond mere existance.


John: "I think truth is relative, not absolute. Something can be true for you, and not true for me."
Ann: "You mean, really true AND really not true at the same time, not just different opinions?"
John: "Sure!"


Logically, I can't go further with this argument until I question John. Is he asserting that facts can be true and not true simultaneously...or is he off on a waffle-y I'm Okay You're Okay road to crash and burn in ignominity?

(Gosh, did I give my ultimate position away with that last line?)

[SShack]

Well, part the issue here is that people cannot agree on what the definition of "true" is. People can't even agree on the definition of "fact."

Knowing this, whether or not there is an absolute truth is rather academic because vast swaths of the public would refuse to accept it. Not that it doesn't make the debate interesting and fun.

[Marcus]

Logic is an abstract system. It does not work with facts. It works with axioms, propositions, and derivation rules. You can relate facts to axioms or propositions, but this relation is outside logic, and is not justified by logic.

[Monte314]

I don't get why what John says and what Ann says are considered equivalent. 'True for me' means truth in my system, which is not necessarily the same as 'truth for you'. We might start from different axioms and we might use a different logic, (or no logic at all to take a more realistic example :)) .


For me it means that if A and -A are both truth, then any P proposition is true, as you did not use any specificity of B in the derivation.


That's an option, logic is only one way to derive knowledge.

Well, if the knowledge you derive doesn't have to be "true", then you are right. I would be interested in seeing an example of untrue knowledge that you have illogically derived.

As to the notion of "systems":

Sorry, but I'm not talking here about your "system". I'm talking about THE system: logical Truth with a capital "T".

The entire point of Ann's comment was to let John make it completely clear that he was not limiting the scope of his claim. We all agree that people have "systems" of belief, but this thread is not about epistemology (what we think we know); it's about ontology (what IS).

Socrates' argument shows that, irrespective of our beliefs, if the universe is logical, then propositions cannot be both really true AND really false.

It is very tempting to formulate "systems" that insulate our beliefs from logic; but it is incorrect to then refer to their content as "true". For the logical mind, that word is reserved for things as they are.

So: I might believe A (that's my "system") and you might believe -A (that's your "system"); but neither of these systems of belief has any necessary connection to truth or logic save this:

EXACTLY ONE OF THEM IS CORRECT.

[Marcus]

For me a system is a set of axioms and derivation rules, if we stay at logic. I was thinking about analogical reasoning as non-logical derivation, but I did not work out the concept fully.

[Monte314]

Logic is an abstract system. It does not work with facts. It works with axioms, propositions, and derivation rules. You can relate facts to axioms or propositions, but this relation is outside logic, and is not justified by logic.

Logic doesn't work with facts?! I'm not quite sure how to respond to such a statement.

What say ye, logical INTJ's? Does logic "not work with facts"? Is it an empty theory, disconnected from what is true?

Do I belong in this Forum, or are you guys misrepresenting yourselves?

[Homini Lupus]

My conclusions since now is that truth is absolte but unknowledgeable in its pure form since it has to pass through a representation process that turns it understandable in our minds (basically, these are ideas I stole from Kant). Since the process of representation is fallible, absolute truth in our mortal life has little meaning.

[Marcus]

Logic doesn't work with facts?! I'm not quite sure how to respond to such a statement.

What say ye, logical INTJ's? Does logic "not work with facts"? Is it an empty theory, disconnected from what is true?

Do I belong in this Forum, or are you guys misrepresenting yourselves?

Maybe we are not on the same page.

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In formal logic, a formal system (also called a logical system,[1] a logistic system,[1] a logical calculus,[2] or simply a logic[1]) consists of a formal language together with a deductive system (also called a deductive apparatus) which consists of a set of inference rules and/or axioms. A formal system is used to derive one expression from one or more other expressions antecedently expressed in the system. These expressions are called axioms, in the case of those previously supposed to be true, or theorems, in the case of those derived. A formal system may be formulated and studied for its intrinsic properties, or it may be intended as a description (i.e. a model) of external phenomena.

For me the bold part means that this intention/description is outside logic. The correspondence between physical phenomena and mathematical objects does not come from the logical system. Also, do perfect circles, spheres, etc., the objects of geometry exist in reality?

Also:
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Logic is concerned with the patterns in reason that can help tell us if a proposition is true or not. However, logic does not deal with truth in the absolute sense, as for instance a metaphysician does. Logicians use formal languages to express the truths which they are concerned with, and as such there is only truth under some interpretation or truth within some logical system.

[Monte314]

Feelings are relative. Beliefs are relative. Facts are facts and stats are stats...but they require human interpretation to attain meaning beyond mere existance.


John: "I think truth is relative, not absolute. Something can be true for you, and not true for me."
Ann: "You mean, really true AND really not true at the same time, not just different opinions?"
John: "Sure!"


Logically, I can't go further with this argument until I question John. Is he asserting that facts can be true and not true simultaneously...or is he off on a waffle-y I'm Okay You're Okay road to crash and burn in ignominity?

(Gosh, did I give my ultimate position away with that last line?)

My intention here is that John is making an assertion that 'A' is both simultaneously true and false; that is, it violates the Law of Contradiction, and is not just a reflection of mere opinion or belief.





Monte314 added to this post, 4 minutes and 6 seconds later...

Maybe we are not on the same page.

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For me the bold part means that this intention/description is outside logic. The correspondence between physical phenomena and mathematical objects does not come from the logical system. Also, do perfect circles, spheres, etc., the objects of geometry exist in reality?

Also:
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OK, mea culpa. I'm so dumb sometimes...

I see what you are saying. I completely misunderstood you. Sorry.

Yes, you are quite right, there are multiple logics ("systems"), each having their own universe of discourse, laws of inference, and hence, their own "truth".

I guess what I want to know is, if the universe of discourse is the physical one that we inhabit, is their a unified system of truth (as Scorates claimed)? Not OPINION, mind you: TRUTH. Or, does our universe contradict itself? Have "laws" that are both true and untrue at the same time?

[Fridays Child]

My intention here is that John is making an assertion that 'A' is both simultaneously true and false; that is, it violates the Law of Contradiction, and is not just a reflection of mere opinion or belief.



Excellent. My next logical move would be to invite John to submit examples to support his assertion...mostly for my future shredding pleasure.

[Marcus]

I guess what I want to know is, if the universe of discourse is the physical one that we inhabit, is their a unified system of truth (as Scorates claimed)?

My problem is the following: How do you know that your logical system reflects the physical universe we inhabit? I think that a logical system can only be a model or approximation of physical reality, so there can be no absolute logical truth about the physical universe.

[Rafael]

You cannot find absolut truth using a relative set of logic. Hence, we cannot find absolut truth because our logic is relative.

So to find absolut truth one had to be
Omniscient
Omnipresent
Omni(insert some thousand words here)
That means one had to be absolut, Socrates was not, he died.

That's what I think...

Oh, and I'll develop this thought further later, in a hurry right now.

[Monte314]

My problem is the following: How do you know that your logical system reflects the physical universe we inhabit? I think that a logical system can only be a model or approximation of physical reality, so there can be no absolute logical truth about the physical universe.

Quite so. The question of "correspondence" is vexing, and was the subject of much debate in the early part of the 20th century. Once again, this is an epistemological question (one treating knowledge); I am asking about the ontological problem (one treating being).

Apart from what we can know about what is true, IS anything true?

[Rafael]

Truth is out there, but no one knows what it is.

[Rei]

There is no way to know absolute truth as we don't have infinitive access to information. There is also no way to know if there are any truths that are universally true.

So unless you say specifically "absolute truth", "truth" is relative truth.
If you say something is "absolute truth" you are making an inaccurate claim (according to above premises).

[Uytuun]

I just want to point out one thing, and that is the way in which you phrased one of the things you mentioned in your first post and in the title and that says a lot IMO:

Socrates, probably the most logical person who ever lived, believed in ABSOLUTE TRUTH

I think it's almost impossible to escape contradiction as a human being, but I know absolutely nothing about formal logic, so I'll leave you guys to it. ;)

[Fridays Child]

John: "I think truth is relative, not absolute. Something can be true for you, and not true for me."
Ann: "You mean, really true AND really not true at the same time, not just different opinions?"
John: "Sure!"


1. A (Given)
2. -A (Given)
3. (-A) V B (Law of Addition, using line 2)
4. A --> B (Law of Material Implication, using line 3)
5. Therefore, B (Modus Ponens, lines 4 and 1).


John is basically screwed here, logically. Once he takes the position that if something is true for him then it is true, it follows that the same applies to me when I state that absolute truth exists. He is forced to acknowledge that absolute truth exists by his own proposition or abandon any pretense of logical argument.

[Rafael]

There is no way to know absolute truth as we don't have infinitive access to information. There is also no way to know if there are any truths that are universally true.

So unless you say specifically "absolute truth", "truth" is relative truth.
If you say something is "absolute truth" you are making an inaccurate claim (according to above premises).

Exactly what I thought, but you explain it way better than I do.

[Noehelia]

So, let A be any proposition that is both true and not true.
Let B be the proposition "Truth is absolute, not relative."

Then, proceeding according to the rules of logical inference (standard first-order predicate logic, e.g., Copi and Cohen, Introduction to Logic, 8th Edition, Macmillan Publishing, 1990), we have:

1. A (Given)
[SIZE=4]2. -A (Given)
3. (-A) V B (Law of Addition, using line 2)
4. A --> B (Law of Material Implication, using line 3)
5. Therefore, B (Modus Ponens, lines 4 and 1).

This would seem to suggest that the assertion that truth is truly subjective gives its proponents two alternatives:

1.) admit their position is logically untenable (since it contradicts itself), and abandon it
2.) retain their position, and abandon logic

Thoughts?

Could you please explain a little more the process? I did not understand points 3 by using law of addition and 4 by law of material implication.

[Ool]

John: "I think truth is relative, not absolute. Something can be true for you, and not true for me."

The statement “I’m Ann” comes to mind as something that is true for Ann but not true for John…

So, by giving one example, I have proven that John is right.

[Marcus]

Apart from what we can know about what is true, IS anything true?

Do you mean: "is there truth outside our knowledge?" If it's outside our knowledge, then the answer seems to be that we don't know.

Or, does our universe contradict itself? Have "laws" that are both true and untrue at the same time?

Take Schrödinger's cat. A=alive, -A=dead. Both are true:

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Schrödinger's Cat: A cat, along with a flask containing a poison, is placed in a sealed box shielded against environmentally induced quantum decoherence. The flask is shattered, releasing the poison if a Geiger counter detects radiation. Quantum mechanics suggests that after a while the cat is simultaneously alive and dead, in a quantum superposition of coexisting alive and dead states. Yet when we look in the box we expect to see the cat either alive or dead, not a mixture of alive and dead.

The statement “I’m Ann” comes to mind as something that is true for Ann but not true for John…

So, by giving one example, I have proven that John is right.

You did not disappoint me, Ool. :)

[Noehelia]

The statement “I’m Ann” comes to mind as something that is true for Ann but not true for John…

So, by giving one example, I have proven that John is right.

Actually, this is a statement not a fact. Ann in this particular moment can be only Ann.

[thod]

The problem of determining truth from propositional logic is that you are bound by the accepted truth of the propositions. No such logical system can prove the truth of its own axioms. Its deductions from those propositions are only true relative to the system defined by them. As an example

All men are immortal
Plato is a man
-> Plato is immortal

The logic makes the last statement true, yet the correspondence with observed reality tells us that the conclusion is false.

You find such errors in argument all the time. "God made all that exists". Therefore if the number 7 exists, God must have made it. Since the number 7 does exist it must have been made by God, QED, God exists.

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[Noehelia]

Take Schrödinger's cat. A=alive, -A=dead. Both are true:

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The same goes here. The cat in a particular moment will be either dead or alive, our knowledge of this however can not be verified.

The problem for me however in the logical reasoning of Monte is whether this line of reasoning can be imposed to other meanings as well besides facts.
What if the givens was what Ool proposed, statements. What would happen?

[Marcus]

The same goes here. The cat in a particular moment will be either dead or alive, our knowledge of this however can not be verified.

I think that according to quantum mechanics it's not decided until measurement.

A simpler example would be A=particle P is at position p at time t. -A=particle P is not at position p at time t. Unless no measurement takes place at time t, the particle can be both at p and not.

[thod]

The same goes here. The cat in a particular moment will be either dead or alive, our knowledge of this however can not be verified.

That is not what is being said. The cat is both dead and alive at the same time. Experimental evidence confirms this.

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[Monte314]

The discussion here is eye-opening.

It seems that while we INTJ's pride ourselves on our logical nature, when push comes to shove we have plenty of arguments to explain why it doesn't actually apply to the "real" world.

Is this what we are saying?

[Noehelia]

That is not what is being said. The cat is both dead and alive at the same time. Experimental evidence confirms this.

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The theory talks about our observance of facts, how we are limited in measurement capacity and how we influence the observed. It is a practical matter of how we comprehend reality.

I do not have a problem to accept that there is an objective truth in facts while we are not able to grasp it. However objective truth does not mean that it holds constantly, it applies only for a moment. A stone is a stone until it is changed.

[cal]

The discussion here is eye-opening.

It seems that while we INTJ's pride ourselves on our logical nature, when push comes to shove we have plenty of arguments to explain why it doesn't actually apply to the "real" world.

Is this what we are saying?

Maybe not accepting traditional logic as a be all, end all, is logical. Example: Another form of logic, called 'water logic':

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[sriv]

My grandpa once said "Truth is an asymptote." and I think he's right. Our attempt at it is the graph to go along with it.

[Beery Swine]

Truth and facts are not subjective. A person's perception of reality, beauty, taste, morality, etc. are.

[Ool]

Actually, this is a statement not a fact.

So? All that John said was, “something can be true for you and not true for me.”

A statement is something.

So he was right.