Semantics and Truth

[bumab]

Given this statement is true:

All statements are either true or false.

 

By which I mean any statement has the property of referring to a truth or a falsehood- an exhaustive list- "Either x has the property a or not, either y has the property z or not, etc." for all properties in the world.

 

Given that:

Are all philisophical arguments merely about the definitions of words? And if so, following the strict rules of logic, can all arguments be distilled to semantics.

 

If that is the case, then all arguments have a logical conclusion, and all philosophers should have the same, inetivable view.

 

Agree? Disagree?

[Biochemist]

... Are all philisophical arguments merely about the definitions of words?...

I don't think so. Clearly, word denotation clouds many arguments. But is I argue that God is male and you argue that God is female, it does not seem like semantics. Anyone could argue pro, con or a mixed position (e.g., God is a hermaphrodite) but the core argument is not semantic.

[bumab]

You missed the first part of the argument- if all statements are either true or false.

-thus, the statement "God is male" is either true or false

"God is female" is either true or false

"God is some other gender/combo we don't know about" is true or false

 

Thus- one of those statements is irrevocably true (given my first statement). Thus, any argument about them, based on the laws of logic, should arrive at the same conclusion. The fact that we don't have enough information at the moment to draw a conclusion should also be arrived at by all parties, if that is the case. Irregardless, it is not semantic, if my first statement is correct.

 

Can anyone think of a case where a statement is neither true nor false?

[Biochemist]

Ah. Now I understand the question.

 

I think you are correct. However, I have noticed that the conflicts in most of the debates here are elevated becasuet we do not agree on the facts. The semantic elements certainly arise here as well. But the variance of acceptance of fact is pretty high here (and I suspect everywhere).

[Tormod]

Can anyone think of a case where a statement is neither true nor false?

 

Man, this twisted my brain for a few minutes. Extremely good question.

 

But...isn't this just a version of the Liar's paradox? Like "this sentence is false" or "Bumab always lies".

 

The inverse question, can a statement be both true and false, is much easier to solve.

 

Since, according to Gödel, we can never know everything about anything, we need to understand as much as possible about a statement before we evaluate it. Given that statements may appear in different settings, the same statement could be true in one setting and false in another - thus it is neither true nor false yet it is also both, which is a paradox but only until we investigate the semantic association.

 

Simple solutions would be "The punishment was just", which obviously is both true and false depending on who you ask. Others vould be "George Bush is a good politician" and "America is a safe country". It is a matter of relatives, or rather a matter of adjectives.

[Tormod]

the variance of acceptance of fact is pretty high here (and I suspect everywhere).

 

I think this is inevitable. It is the very reason for all intelligent (and non-intelligent) concourse.

[bumab]

Given that statements may appear in different settings, the same statement could be true in one setting and false in another - thus it is neither true nor false yet it is also both, which is a paradox but only until we investigate the semantic association.

 

But one could argue that in different settings a statement is different then it would be in the former setting. This gets horribly messy when talking about conventional, conversational topics, and is prehaps easier thought about in metaphysical terms.

 

The statements "I will eat before noon" and "I will not eat before noon" cover all possible ground. One of those two statements is correct, any arguments would come from a definition of "eat" I suppose. The statement "GW is a good politician" would be much messier, but still follows the same form. You would have to define politician explicitly, but then it could be done... maybe.

 

Perhaps value statements are excempt- but that really brings one back to the definition of "good" etc. Semantic issues, not issues related to wether or not he really is a "good" politician.

[Tormod]

I agree, bumab. Actually my post was merely an attempt to look at the content of a couple of statements to see if I could avoid the ambiguity of created situations. It was not an exhastive attempt. :)

 

I need to simplify your progress here.

 

A) All statements are true or false

:) Thus there must be a logical conclusion for all statements

C) However, can there be case where statements are neither true nor false?

 

If we are to consider only metaphysical statements, and only statements where there is no room for interpretation, then our language falls short of being able to comply with A). I am unable to come up with even a statement that is *always* true or *always* false. "The sun rose this morning" for example: which sun?

 

Or, "I will eat before noon". Noon where?

[Southtown]

I've come to realize that people simply believe what they want to, and any quest for Truth becomes a quest for excuses. This is not to say that there is NOT an ultimate Truth, but that few people are really seeking it as such. Hence the twisting of words and the blurring of perceptions, etc.

[Tormod]

I don't believe in ultimate truth. It will always be biased, whether it is a GUT or a religious idea.

 

I do however believe that there are logical truths. But language and mathematics are different entities. A truth in language will always be susceptible to fallacy due to the richness and ambiguity of words. A truth in math can be rock solid because of the simplicity of numbers. Yet what happens when formulae grow large and difficult? They are wrongly interpreted. Observe for example how Andrew Wiles thought he had solved Fermat's last theorem only to find an error which I believe had semantic connotations:

 

The key reduction of (most cases of) the Taniyama-Shimura conjecture to the calculation of the Selmer group is correct. However the final calculation of a precise upper bound for the Selmer group in the semisquare case (of the symmetric square representation associated to a modular form) is not yet complete as it stands. I believe that I will be able to finish this in the near future using the ideas explained in my Cambridge lectures.

 

From

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Fermat's_last_theorem.html

[bumab]

Or, "I will eat before noon". Noon where?

 

That is an exhaustive statement that is either true or false- it could happen anywhere. Red things are red- and exhaustive statement that is true.

[Southtown]

I don't believe in ultimate truth. It will always be biased, whether it is a GUT or a religious idea.

So is it possible that each person has a different origin? Rather than as a unified species?

[Qfwfq]

Given this statement is true:

All statements are either true or false.

Nope, it ain't true!

 

Even when it is a well formed assert in a given formal system, if that system also represents number theory there will be undecided asserts. (Good ol' Gödel)

 

Let alone if you consider "just the statement". 7 + 9 = 3. True or false?

[bumab]

Let alone if you consider "just the statement". 7 + 9 = 3. True or false?

 

Feel like I'm walkin' into something :), but false.

[Tormod]

So is it possible that each person has a different origin? Rather than as a unified species?

 

This is off-topic and belongs in a different thread.

[UncleAl]

All statements are either true or false.

1) Schroedinger's cat; time-like and space-like events. Empirical reality itself can be maleable. It takes some large amount of effort to diddle.

 

2) Empirical reality (science) is objective. Everything else is arbitrary. Is murder a good thing? Your nation's highest honor is awarded for it (in the US, the Congressional Medal of Honor. A private with a CMH is saluted by generals). Philosophy should be internally self-consistent though it may be real world crap (e.g., scientific socialism). Religion doesn't even have that - in fact, it revels in self-contradiction. Test of faith!

 

3) Philosophy requires a pencil and paper. Science requires a pencil, paper, and a wastebasket. Religion only requires a mob.

 

and all philosophers should have the same, inevitable view.

An axiomatic system depends on its axioms. You can get out any answer you like from pure deduction - everything and its opposite are true.

 

If you have not read this sentence, put an "X" in the box,

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[Qfwfq]

Feel like I'm walkin' into something :), but false.

It's false in Z. It's true in Z_13. It's false in Z_n for n other than 13.

 

How about ab = c, true or false?