When Logic Equates to Knowledge

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kennethamy
 
Reply Fri 26 Feb, 2010 09:29 am
@jgweed,
jgweed;132828 wrote:
What do we mean when we say that something is true by definition, or that this kind of truth is not contingent?

If we take Rome or Sparta as examples, then the truth of the definition is historically dependent. Sparta may always have been "Hellenic" in opposition to bar-barians, but it was not always a part of Greece (in the sense of a modern state). When Romulus and Remus established Rome (Ab urbe condita, 753 BC), it was as a city-state at most, and it would make no sense at that time to say it was the capital of Italy (the Sabines would have made a very strong protest).

Definitions obviously change with time, so something is true by definition when the definition itself is true, and if the meanings of words are contingent, one presumes that whether or not something is true by definition is equally so.


Yes, of course, whether a truth is true by definition is a contingent matter. But that does not mean that there are no truths by definition. (I don't know whether you think that there are no truths by definiton, though).

---------- Post added 02-26-2010 at 10:39 AM ----------

Zetherin;132827 wrote:
You're confusing things. Reconstructo posted a good article on the analytic and synthetic distinction.

Here's an easy way, according to Kant, to show you are wrong:

The concept "Italian" is not contained within the concept "Roman". Therefore "Every Roman is an Italian" is a synthetic proposition. Also, not all Italians are Roman (someone could be Sicilian, for instance). Something like, "All bachelors are unmarried men" would be an analytic proposition, true by definition. All unmarried men are bachelors, and all bachelors are unmarried men.


Trouble is that "contains" is a metaphor, and it is no clearer than what it is meant to explain. Is "unmarried" contained in "bachelors"? Search me.
He did not say that all Italians are Romans. He said that all Romans are Italians. Of course, a German may be a Roman, but not be Italian.

It might very well be that all Romans are Italians. The question at hand is not that, but whether necessarily, all Romans are Italians. Whether is is impossible for X to be a Roman and not an Italian. It might be true that all X is Y, but not necessarily true that all X is Y. If all X is Y is analytic, it has to be necessarily true, not just true.
 
hue-man
 
Reply Fri 26 Feb, 2010 05:09 pm
@Zetherin,
Zetherin;132827 wrote:
The concept "Italian" is not contained within the concept "Roman". Therefore "Every Roman is an Italian" is a synthetic proposition.


I agree now. If we're defining Roman as simply being a citizen of the city of Rome then that would make the sentence "every Roman is an Italian" a synthetic proposition because you would first have to discover that Rome is indeed in the country of Italy.

Zetherin;132827 wrote:
Also, not all Italians are Roman (someone could be Sicilian, for instance). Something like, "All bachelors are unmarried men" would be an analytic proposition, true by definition. All unmarried men are bachelors, and all bachelors are unmarried men.


Well of course not all Italians are Romans because Rome is a city in Italy but Italy is not a country in Rome. I'm aware of the "all bachelors are unmarried" example. It's a very simple one.
 
HexHammer
 
Reply Fri 26 Feb, 2010 07:08 pm
@jgweed,
jgweed;132828 wrote:
What do we mean when we say that something is true by definition, or that this kind of truth is not contingent?
When the premises of the defined claims are forfilled, then it's true?

jgweed;132828 wrote:
If we take Rome or Sparta as examples, then the truth of the definition is historically dependent. Sparta may always have been "Hellenic" in opposition to bar-barians, but it was not always a part of Greece (in the sense of a modern state). When Romulus and Remus established Rome (Ab urbe condita, 753 BC), it was as a city-state at most, and it would make no sense at that time to say it was the capital of Italy (the Sabines would have made a very strong protest).
Exorbiant bloat of details, but yes.
 
prothero
 
Reply Sat 27 Feb, 2010 12:53 am
@kennethamy,
kennethamy;132343 wrote:
A logical conclusion from what? What is desperately needed here are some examples of what you are thinking of. That will concentrate your mind, and ours too. I don't think your question is specific enough to be answerable. I don't know what you have in mind. To repeat, what is needed is an example or two.
So he gave an example and that started a discussion but it did not seem to clarify things at all?
I quess when I read the OP, my first thought was mathematics is a form of logic and that most of our hard predictive scientific knowledge is only expressible in the form of mathematical equations, so yes some forms of logic do equate to knowledge. On the other hand some forms of logic are mere tautologies or mere definitions and I am not sure they represent useful or practical knowledge at all.
 
kennethamy
 
Reply Sat 27 Feb, 2010 02:41 am
@prothero,
prothero;133130 wrote:
So he gave an example and that started a discussion but it did not seem to clarify things at all?
I quess when I read the OP, my first thought was mathematics is a form of logic and that most of our hard predictive scientific knowledge is only expressible in the form of mathematical equations, so yes some forms of logic do equate to knowledge. On the other hand some forms of logic are mere tautologies or mere definitions and I am not sure they represent useful or practical knowledge at all.


What are called, logical truths, like, all dogs are dogs, or what are reducible to logical truths, like all bachelors are unmarried, are, of course, true. But it does not follow from that, that they are knowledge, because not all truths are known to be true. Of course, the examples above are so simple that everyone knows them. But there are logical truths that are more complicated, and, although they are also true, they need not be known to be true. And there are some logical truths that no one knows are true. Godel's theorem proved that. The point is that knowledge and truth are not the same thing. There is no knowledge that is not true, but there are truths that are not known. And, some truths of logic are not known to be true.
 
 

 
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