Logical Limitation of the Logic

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GrayArea
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Re: Logical Limitation of the Logic

Post by GrayArea »

aliskermani wrote: April 29th, 2022, 6:37 am Couldn't agree more! That was my point. No know knows the truth and yet everybody insists on their on version of it. Or their story.
By the way, this is off topic but you can click the quotation button on the right end of the message in order to "reply" to the person who wrote it. That way you actually get to notify people that you've replied to their messages, and it makes for a quicker communication. It took me a while to find out that you've responded, haha.

Hope this helps!
People perceive gray and argue about whether it's black or white.
Magnus Anderson
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Re: Logical Limitation of the Logic

Post by Magnus Anderson »

heracleitos wrote:The correspondentist theory of truth works indeed like a charm for empirical knowledge but it generally fails for a coherentist domain such as mathematics.
Hello there.

Just a tiny remark before I address your comment about mathematics. I don't think that the so-called "correspondence theory of truth" is a theory. It's a definition. I don't think that definitions are theories. A definition is merely a statement about what meaning is assigned by some people to some word. What I'm saying is that the meaning assigned to the word "truth" by pretty much everyone -- literally everyone, whether they are aware of it or not -- is best captured by the statement "a belief that corresponds to the portion of reality that it refers to". That might be wrong, of course, but I wouldn't say it's a theory.
One typical reason why a logic sentence is true in math, is not because it corresponds to anything in the physical universe but because it necessarily follows from the construction of its theory. According to the theorem of soundness, a logic sentence is true because it is provable from its theory.
I would actually go so far as to say that any given mathematical statement is true precisely because it matches the portion of reality it refers to. It's merely not evident to a lot of people and the reason it is not evident is because it is difficult to identify what portions of reality mathematical statements refer to.

Let's take a very simple mathematical statement as an example e.g. "2 + 2 = 4". What is this statement actually saying? That's the question that seems to paralyze most people. What that statement is saying is that the symbol on the left side of the equation (which is "2 + 2") has the exact same meaning as the symbol on the right side of the equation (which is "4".) To answer that question, one actually has to look at what meanings were assigned by those who made that statement and whether or not they are in truth equal. It's a linguistic statement, i.e. a statement about language, fundamentally no different from statements such as "The English word "train" has the same exact meaning as the Spanish word "tren"".
aliskermani wrote:Truth and reality are not the same.
That's true.
heracleitos
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Re: Logical Limitation of the Logic

Post by heracleitos »

Magnus Anderson wrote: April 30th, 2022, 7:04 am I don't think that the so-called "correspondence theory of truth" is a theory. It's a definition. I don't think that definitions are theories. A definition is merely a statement about what meaning is assigned by some people to some word. What I'm saying is that the meaning assigned to the word "truth" by pretty much everyone -- literally everyone, whether they are aware of it or not -- is best captured by the statement "a belief that corresponds to the portion of reality that it refers to". That might be wrong, of course, but I wouldn't say it's a theory.
This is certainly a possible view.

The reason why I refer to it as the "correspondence theory of truth" is because it seems to be somehow the standard way of naming it:

https://en.m.wikipedia.org/wiki/Correspondence_theory_of_truth
Wikipedia on "Correspondence theory of truth" wrote: In metaphysics and philosophy of language, the correspondence theory of truth states that the truth or falsity of a statement is determined only by how it relates to the world and whether it accurately describes (i.e., corresponds with) that world.
Magnus Anderson wrote: April 30th, 2022, 7:04 am I would actually go so far as to say that any given mathematical statement is true precisely because it matches the portion of reality it refers to.
It matches a portion of the abstract universe constructed by its theory ("which interprets it's theory"). The term "reality" may be confusing in this context. A logic sentence does not seek to match a portion of physical reality.
Magnus Anderson wrote: April 30th, 2022, 7:04 am Let's take a very simple mathematical statement as an example e.g. "2 + 2 = 4". What is this statement actually saying? That's the question that seems to paralyze most people. What that statement is saying is that the symbol on the left side of the equation (which is "2 + 2") has the exact same meaning as the symbol on the right side of the equation (which is "4".) To answer that question, one actually has to look at what meanings were assigned by those who made that statement and whether or not they are in truth equal. It's a linguistic statement, i.e. a statement about language, fundamentally no different from statements such as "The English word "train" has the same exact meaning as the Spanish word "tren"".
Yes, agreed that it is about language, but disagreed that it would have meaning.

In the case of "2+2=4", we can prove from Peano Arithmetic Theory, by using the axiomatic recurrence relation a+S(b)=S(a+b), that:

S(1) + S(1)
= S(S(1)+1)
= S(S(S(1)))
= S(S(S(S(0))))
= the fourth successor to zero

When we look up the fourth successor of zero, we find the symbol "4".

Since "2+2=4" is therefore provable from arithmetic theory, and in application of the theorem of soundness, this logic sentence is true in all interpretations, i.e. models or universes, of Peano Arithmetic Theory, the intended standard of which are the natural numbers.

In that sense, the truth of this logic sentence is not really a consequence of its meaning but a mechanical (synctactic) consequence of the rules that construct arithmetic theory.

That is why a machine can trivially verify the provability of this logic sentence. It is still all about (formal) language, because verification rests entirely on meaningless symbol manipulation.
Wikipedia on "mathematical formalism" wrote: In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings (alphanumeric sequences of symbols, usually as equations) using established manipulation rules.

According to formalism, the truths expressed in logic and mathematics are not about numbers, sets, or triangles or any other coextensive subject matter — in fact, they aren't "about" anything at all.
Therefore, according to mathematical formalism, the logic sentence "2+2=4" is true but is deemed to mean nothing at all.
Magnus Anderson
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Re: Logical Limitation of the Logic

Post by Magnus Anderson »

heracleitos wrote: April 30th, 2022, 8:41 pmThis is certainly a possible view.

The reason why I refer to it as the "correspondence theory of truth" is because it seems to be somehow the standard way of naming it:

https://en.m.wikipedia.org/wiki/Correspondence_theory_of_truth
Wikipedia on "Correspondence theory of truth" wrote: In metaphysics and philosophy of language, the correspondence theory of truth states that the truth or falsity of a statement is determined only by how it relates to the world and whether it accurately describes (i.e., corresponds with) that world.
I am aware why you used that term. I just wanted to say that I'm not a fan of it (:
It matches a portion of the abstract universe constructed by its theory ("which interprets it's theory"). The term "reality" may be confusing in this context. A logic sentence does not seek to match a portion of physical reality.
I would say that it seeks to match a portion of reality in the same exact way that all other statements do.
Yes, agreed that it is about language, but disagreed that it would have meaning.
Well, maybe we should first agree on the definition of the word "meaning". If you ask me, the meaning of a symbol is the set of all things that can be represented by that symbol. The meaning of the word "dog", for example, is the set of all physical objects that can be represented by that word. The purpose of symbols is to represent what is real and what can be real. If symbols have no meaning, then you cannot use them to represent anything (real or imaginary), so their usefulness is close to nil. Contradictions, for example, are like that. If mathematical statements are meaningless in this sense of the word, then they are pretty much useless. But it's not to difficult to see that they aren't meaningless.
heracleitos
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Re: Logical Limitation of the Logic

Post by heracleitos »

Magnus Anderson wrote: April 30th, 2022, 9:08 pm
heracleitos wrote: April 30th, 2022, 8:41 pmThis is certainly a possible view.

The reason why I refer to it as the "correspondence theory of truth" is because it seems to be somehow the standard way of naming it:

https://en.m.wikipedia.org/wiki/Correspondence_theory_of_truth
Wikipedia on "Correspondence theory of truth" wrote: In metaphysics and philosophy of language, the correspondence theory of truth states that the truth or falsity of a statement is determined only by how it relates to the world and whether it accurately describes (i.e., corresponds with) that world.
I am aware why you used that term. I just wanted to say that I'm not a fan of it (:
It matches a portion of the abstract universe constructed by its theory ("which interprets it's theory"). The term "reality" may be confusing in this context. A logic sentence does not seek to match a portion of physical reality.
I would say that it seeks to match a portion of reality in the same exact way that all other statements do.
Yes, agreed that it is about language, but disagreed that it would have meaning.
Well, maybe we should first agree on the definition of the word "meaning". If you ask me, the meaning of a symbol is the set of all things that can be represented by that symbol. The meaning of the word "dog", for example, is the set of all physical objects that can be represented by that word. The purpose of symbols is to represent what is real and what can be real. If symbols have no meaning, then you cannot use them to represent anything (real or imaginary), so their usefulness is close to nil. Contradictions, for example, are like that. If mathematical statements are meaningless in this sense of the word, then they are pretty much useless. But it's not to difficult to see that they aren't meaningless.
I do not want to hijack this thread. That is why I have given an elaborate answer to your concerns In a new thread:

viewtopic.php?t=17970

You could possibly find my answer somewhat problematic.
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Re: Logical Limitation of the Logic

Post by Belindi »

Mathematics is a system for codifying quantities. Within the standard code which is known to people who have learned the standard code 2+2=4. Otherwise for people who have not learned the standard code possibly 2+2 =22.

Symbolic systems are man made.

Symbols are abstractions from empirical observations for instance the Border collie is frequently adopted as the symbol for canine intelligence.If, among all of our symbols and symbolic systems, there lurks a Platonic Form we can never know.
aliskermani
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Re: Logical Limitation of the Logic

Post by aliskermani »

Infinity is an abstract concept. We can define a set:
Infinity of Infinities which its elements are all sets of infinities within the domain of mathematics. Such a set is not an abstraction of empirical observations. This belongs to the the realm of pure abstraction. Absolutely imaginary.
snt
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Re: Logical Limitation of the Logic

Post by snt »

aliskermani wrote: February 7th, 2022, 5:11 am Logic is the Methodology for relating thoughts in order to make decisions and reach conclusions (reasoning). Logic has helped us a great deal to reach where we are in Philosophy, Mathematics, and Science.

The Ultimate Methodology


Let’s define the Ultimate Methodology as the Ultimate Logical Tool for creating all other methodologies. Since it is a methodology itself, it needs to use itself to create itself, therefore a Paradox. Before solving this paradox, there is no absolute logical premise to drive absolute conclusions from, and all methodologies including logic and science will remain relative and their use in answering the Ultimate Questions (Consciousness and Infinity) will be misleading.

Conclusion
By its nature, Logic can create Dogma and any type of dogmatism; Logical, Philosophical, Political, Religious, Scientific, …; is a hindrance in the pursuit of the truth.
As you mentioned in your post, logic involves a relational context which implies plurality which is finite (limiting) of nature. The potential for reason and logic itself would be at question and that question is equal to the question into the origin of the cosmos.

Chinese philosopher Laozi (Lao Tzu) has attempted it in book Tao Te Ching. The book starts with the following:

"The tao that can be told is not the eternal Tao. The name that can be named is not the eternal Name."

What is the meaning of an insight that logic would attempt to unlock (an insight into the origin of reason itself) when the insight that it unlocks cannot be said?

One would enter the field of poetry that attempts to use language to transfer insight into experience that would then need to function as an addition to supplement logical reasoning to provide it with a ground to venture beyond the limit of its own origin.

The book Tao Te Ching is written as a poem for that purpose. Perhaps it provides an insight for overcoming presumed limits of logic.
aliskermani
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Re: Logical Limitation of the Logic

Post by aliskermani »

Yes, I think intuition should play a bigger part. It will be a big mess for another 6 to 7 hundred years for humans to use both logic and HEART as the sources for knowledge properly. I think we are still in infancy. Wisdom maybe a good way to put it. We still don't know what it is.

It is all awareness trying to understand awareness or itself. and always behind. When just being, time is zero and the Ultimate Methodology works. When trying to do, we get into the trap of time.

Lets' define a set. Infinity of infinities. meaning every member of the set is an infinite set. To me this seems to be how the universe is. infinity of infinite.

I have better visions but cant explain them properly.
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Re: Logical Limitation of the Logic

Post by Pattern-chaser »

aliskermani wrote: April 29th, 2022, 6:37 am Couldn't agree more! That was my point. No know knows the truth and yet everybody insists on their on version of it. Or their story.
...and yet, the uncertainty you correctly (IMO) identify is not an excuse for 'anything goes'. Everyone insists on their own beliefs, their right to their own opinion, which is fair enough. But some of them also demand the right for their opinions to be accepted as right and correct. This is the nonsense it appears to be.
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Re: Logical Limitation of the Logic

Post by Pattern-chaser »

Belindi wrote: May 6th, 2022, 5:17 am Mathematics is a system for codifying quantities. Within the standard code which is known to people who have learned the standard code 2+2=4. Otherwise for people who have not learned the standard code possibly 2+2 =22.
Yes. Such things as "1 + 1 = 2" are only true if we accept the necessary axioms from set and number theory. Even then, they are true because they're defined to be true, which isn't what I would call 'true-in-a-useful-way'.
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