Is meaning a mystery?

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What is mystery of meaning? To be brief, it is the same mystery as to how it is possible that a string of symbols means what it is in everyday usage. An objection is that the meaning of a word is imply it` s definition, but that cannot possibly be the case. Here is why: If every word has a definition, and definition are made of words. How do children acquire the understand of their very first word? They can` t possible understand the meaning of the words in the definition. The problem reveals itself in a different form in the study of formal systems. For a formal system, the axioms, alphabets are uninterpreted. It is later given a "model", or "interpretation". The illustrate:

The symbol 'O' means zero.
The synbol "=" means equal.
...

..

So, there is mystery. What is these things on the right hand side of the word 'means'?

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@TuringEquivalent,

TuringEquivalent wrote:

The symbol 'O' means zero.
The synbol "=" means equal.
So, there is mystery. What is these things on the right hand side of the word 'means'?

I dont think these examples are mysterious, a child learns the terms for quantities, addition, subtraction and equality, by illustration, armed with these concepts, zero is easily understood.

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@ughaibu,

ughaibu wrote:

TuringEquivalent wrote:
The symbol 'O' means zero.
The synbol "=" means equal.
So, there is mystery. What is these things on the right hand side of the word 'means'?
I dont think these examples are mysterious, a child learns the terms for quantities, addition, subtraction and equality, by illustration, armed with these concepts, zero is easily understood.

Well, intuitively, there seems to be a difference in kind between an 'act'( or algorithm) itself, and a concept, or meaning. There are many instances of kind acts, but those acts all fall under the concept of 'kindness'. There is also what is called "rule following paradox" from Wittgenstein. As the problem goes: A repeated application of a rule don` t seem to imply that rule. Given that sequence " 2, 4, 6, 8...." it is easily to suppose the rule is 2*x, but it could also be something else. My point is that rules don ` t seem to capture semantics.

A more technical example would obvious be Godel ` s theorem where no finite axiomatic system can capture the whole of number theory.

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i don't see what the problem is. to me it is simple, but i can see the conflict. it is like someone trying to ask you to look at your own face without using a mirror or reflective surface. you can't do it yet you don't question weather or not you have a face simply because you can not see it. i think meaning is similar that trying to define it or to pin it down is doing something in which it is not intended to be done. it is designed to be a very lose defined term because of how it applies itself into the context. so when you start to ask about the meaning behind meaning it is a loop just like trying to see your own face.

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@TuringEquivalent,

TuringEquivalent wrote:

A repeated application of a rule don` t seem to imply that rule. Given that sequence " 2, 4, 6, 8...." it is easily to suppose the rule is 2*x, but it could also be something else.

I dont see a real problem. In the application of a rule, the rule is decided by the applier, that one cant be inductively certain of what, if any, rule has been applied, unless it was applied by oneself, is a separate issue.

TuringEquivalent wrote:

My point is that rules don ` t seem to capture semantics.

I'm not sure how this follows. Aren't semantics a matter of agreement?

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@Krumple,

Krumple wrote:

i don't see what the problem is. to me it is simple, but i can see the conflict. it is like someone trying to ask you to look at your own face without using a mirror or reflective surface. you can't do it yet you don't question weather or not you have a face simply because you can not see it. i think meaning is similar that trying to define it or to pin it down is doing something in which it is not intended to be done. it is designed to be a very lose defined term because of how it applies itself into the context. so when you start to ask about the meaning behind meaning it is a loop just like trying to see your own face.

The problem of meaning is really one of the hot topics for professional philosophers. I agree with you that it is not something we are aware, because it feels so unconscious that we normally don` t take much of it. This issue really come at you if you study formal systems, and their interpretations.

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@ughaibu,

ughaibu wrote:

TuringEquivalent wrote:
A repeated application of a rule don` t seem to imply that rule. Given that sequence " 2, 4, 6, 8...." it is easily to suppose the rule is 2*x, but it could also be something else.
I dont see a real problem. In the application of a rule, the rule is decided by the applier, that one cant be inductively certain of what, if any, rule has been applied, unless it was applied by oneself, is a separate issue.
TuringEquivalent wrote:
My point is that rules don ` t seem to capture semantics.
I'm not sure how this follows. Aren't semantics a matter of agreement?

Well, the technical usage of meaning is really semantics.

Of course, we all agree that meaning of the symbol '0' is zero. The concept 'zero' is not in question. What is in question is how we obtain that concept. The attachment of the concept ( eg: 'zero') to the symbol ( eg: 'o') is easy, and not worth much thought. It is a technical matter for logicians, or scientists.

There are many views on how we obtain concepts like zero. Some say we learn a concept by seeing how it works. I think this is wrong, and a rather old view. You can see how things work (ie: what follows what), but there seems to be a conceptual understanding of a concept that cannot be capture by by just seeing how it works.

A technical example would be Godel theorem. One of the version of Godel theorem is that axiomatic system expressive enough to contain number theory would necessary be incomplete. By this, he means that there is a proposition in number theory that is true, but not proviable in the system.
eg: The meaning of say " every even number is the sum of two primes" could be true ( truth values are semantics), but not derived from the formal system.
If we interpret what it means to derive something as "showing it". There seems to be infinite many statements( in number theory) that are true, but not show able. The question then is "why do we know it is true?". The latter question is semantics.

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@TuringEquivalent,

TuringEquivalent wrote:

The question then is "why do we know it is true?"

The presuppositions of the question need to be explicated, as it might not form a legitimate question. If it's the case that why-questions are answered with true statements in algorithmic form, and the question asks 'why do we know an algorithmically inaccessible truth?', then the question has no answer.

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@ughaibu,

ughaibu,

To be clear so that the discussion don` t turn too technical. Godel say that any formal system( say TM) expressive enough to contain number theory would necessary be incomplete. This means there exist a statement in number theory that is true( semantically) that is not derivable by TM. Say that this statement is S. S is not derivable from TM, but S is true.

Godel say we ought to include S as an axiom into TM so that S is derivable.

What godel tell us in not far from the truth. Mathematicians were always compiling axioms that they feel are true, and deriving consequences of those axioms. The mathematicians obvious do know these algorithmically inaccesible truth( ie: Axioms). Otherwise, how else can they write it up, and prove theorems using it? Let` s be clear, mathematicians do know these 'algorithmically inaccessible truth', because they been doing it for the last 2000 years ever since Euclid ` s element. The question about "how they know it?" is part of the theory of meaning, and a hot topic in philosophy. One answer that you give( they see it enough times) is one answer, but there are others. You can say it is not answerable, but many philosophers are trying to answer it anyway.

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@TuringEquivalent,

TuringEquivalent wrote:

You can say it is not answerable, but many philosophers are trying to answer it anyway.

Fair enough, but it seems to me that philosophers aren't especially different from any other group of people, and some of them will spend their careers chasing rainbows. If the question has legitimate presuppositions, then there is a true answer, and that answer will have a logical form. What logical form do you suggest to be the form of a true statement answering the question 'why do we know some algorithmically inaccessible truths?'?

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@TuringEquivalent,

- some are ignorent and must be enlightend.
- some have a difficult with preception and must have it clarifyed.
- some doesn't care about other's silly interpetation and make their own.
- some are so insecure that they need other to find a way for them.
- sometimes it is group think/flok instinct that are dictatorial and must be faught.

...things are what you make of them!

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