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Analytic-synthetic vs priori/ posteriori

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Analytic-synthetic vs priori/ posteriori

xzJoel
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Posted 07/02/09 - 09:47 AM:	#11
jtoma wrote: 'An object from set Z may be either 5 or 6' and 'An object from set Z may be neither 5 nor 6' are both truth by virtue of the definition of the set. (Negating the predicate does not negate the subject: Saying that neither 5 nor 6 are from set Z does not prohibit their being contained in set Z. Think of them as 5 and 6 as the members of Z not picked up at looked at. If you don't think of 'from set Z' in this way then 'An object from set Z may not be either 5 or 6' is false.) I am unclear on whether you are saying that the sentence is analytic or synthetic. True by definition is not the criteria by which something is judged analytic or synthetic.
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Posted 07/02/09 - 11:01 AM:	#12
I guess to unclarity above is "An", that it may have been interpreted as "Some", when I guess what you really meant was that some randombly or arbitrary object picked out of that set is 5 or 6 is synthetic. That some object is 5 or 6 is analytic, because 5 being in the set, for instance is proof of this.
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jtoma
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Posted 07/02/09 - 11:13 AM:	#13
xzJoel wrote: I am unclear on whether you are saying that the sentence is analytic or synthetic. True by definition is not the criteria by which something is judged analytic or synthetic. Sorry, I substituted 'true by virtue of meaning' for 'true by definition'. I did not want to say that 'An object from set Z may be either 5 or 6' is true by the meaning of set Z because I don't know what the 'meaning' of a set is. But, loosely, I do think that a word relates to its meaning as a set does to its definition. 'Either 5 or 6' or 'Neither 5 nor 6' are predicate concepts both contained in the subject concept of the set you defined. I haven't seen the synthetic a priori in this thread.

yasseford
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Posted 07/02/09 - 11:35 AM:

#14

analytic (df.): an analytic judgment contains nothing in the concept of the predicate not already thought in the concept of the subject (e.g., “Bachelors are unmarried&rdquo wink

synthetic(df.): a synthetic judgment is one which is not analytic (e.g., “Some philosophers are bachelors&rdquo wink

This is a metaphysical distinction between two different types of truth.

a priori (df.): an a priori judgment is one that can be known to be true or false independently of sense experience

a posteriori(df.): an a posteriori judgment is one that can be known to be true or false only by sense experience.

This is an epistemological distinction between two different types of knowledge.

Therefore...

	Analytic	Synthetic
A priori	trivial verbal judgments (“Unmarried males are male”; “Bachelors are unmarried&rdquo	mathematics (e.g., "7 + 5 = 12") & metaphysics (e.g., "Every event has a cause").
A posteriori	empty	natural science, history, commonsense empirical knowledge

Source: http://www.westga.edu/~rlane/analytic/lecture17_meta1.html

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jtoma
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Posted 07/02/09 - 03:44 PM:	#15
As has been covered, it is analytic that 7 + 5 = 12 (it proceeds from the definitions of integers and addition over integers). Not all of mathematics is synthetic, but perhaps new research in math could be considered synthetic: it consists at least somewhat in the relating concepts that have not been before related.

cosscos
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Posted 07/02/09 - 09:04 PM:	#16
As long as I believe, 7+5=12 is known as a priori synthetic proposition probably by certain initiator's experience. As for the proposition, 'Bachelors are unmarried' could be switched into a priori synthetic proposition by by trancendental aesthetic. All in all it depends on presence of intellect, which is the identifying faculty upon subject and object.

jtoma
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Posted 07/03/09 - 12:24 PM:	#17
cosscos wrote: As long as I believe, 7+5=12 is known as a priori synthetic proposition probably by certain initiator's experience. As for the proposition, 'Bachelors are unmarried' could be switched into a priori synthetic proposition by by trancendental aesthetic. All in all it depends on presence of intellect, which is the identifying faculty upon subject and object. Yea, I think I have something like this in mind too. Like '7+5=12' is analytic to me after the concept have been so related. But before I learned to add, thinking '7+5=12' would be learning that '7+5+12' and would be synthetic at that time. Even though the distinction between analytic and synthetic is supposed to be a metaphysical one, between different types of truth, I think it can remain a metaphysical distinction without distinguishing different types of truth, but rather different ways of experiencing that truth. That is just a hunch because I don't know what metaphysics is about. But I remember hearing some guy talk about how pragmatics and the philosophy of language will expand the traditional conception of metaphysics to incorporate an experiential bridge of the type whose specifics could in principle be filled by science. Sounds like a crackpot now that I'm recounting it...

yasseford
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Posted 07/06/09 - 05:11 AM:	#18
The source I've given is actually taken from Kant, who believes that 7+5=12 is synthetic. I personally don't like the distinction between synthetic and analytic.
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jtoma
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Posted 07/07/09 - 12:13 AM:	#19
The first time you perform 7+5+12 you might apply a rule in a way not yet applied, and you might even apply a new rule, but that doesn't change that the concept of '= 12' is contained in the concept of '7+5': twelve is nothing other than the sum of seven and five. Even if twelve appears different than the sum of seven and five that doesn't change the fact that the predicate concept is contained in the subject concept. What knowledge do we have that does not proceed from a rule? Knowledge via a rule is always a case of subject concept containing predicate concept, this being the case with inference. Is knowledge of particulars knowledge? If yes, then that is empirical knowledge, and that need not prevent apriority, recall the contingent a priori, 'if actually p, then p'. That knowledge concerns empirical knowledge that is known without experience. So, is a synthetic knowledge contained by empirical knowledge of particulars? If not, then the definition of synthetic being not analytic is inadequate. Edited by jtoma on 07/09/09 - 10:17 AM

Death Monkey
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1 of 1 people found this post helpful Posted 07/07/09 - 01:23 AM:	#20
I don't see how "7 + 5 = 12" could be considered to be synthetic. We have the following terms in the sentence: '7', '5', '12', '+', and '='. In order for this sentence to constitute a statement to which a truth value can be meaningfully assigned, each of those terms must be defined. Now, in principle we could assign any definitions we wanted, but in the context of this discussion it is pretty clear that what is intended is the definitions given in ordinary artithmetic. That said, the truth value of the statement directly follows from those definitions. It is not possible for the statement to be false without negating one or more of the definitions that establish the meaning of the statement in the first place. Perhaps the dispute here is one of definitions? Maybe the proponents of the statement being synthetic are actually referring to statements about real-world examples of these abstract mathematical operations? For example, "I have 5 apples in a bag. I put 7 more apples in the bag. I then have 12 apples in the bag". This would clearly be synthetic, but it would also be a posteriori. I cannot know independantly of sense experience that my rules of artithmetic will apply to this, or to any other real-world situation. As for the example of metaphysics being a priori and synthetic, I do not think this is correct either. Such statements are neither a priori nor a posteriori, because they cannot be known to be true or false at all. Indeed, I am not even convinced that it is meaningful to try to assign truth values to such statements. DM
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