Is the proposition 7 + 5 = 12 analytic or synthetic?

Answer 1

Aaron is right regarding the Kantian view of analytic and synthetic, however it can conversely be argued that 7 + 5= 12 is analytic because all the possible numerical combinations that go to make up 12 are contained within the concept of 12, in relation to its existance within the mathematical and numerical sphere of concepts. In the same way the analytical statement "All bachelors are unmarried men" contains all possible combinations of properties which make up any given man in regards to the statement.

The question with Kant seems to be exactly how much of a concept, and how many variations of definition, are contained within the word used to describe it.

The logical positivist definitions of analytic and synthetic would appear to class this particular statement as both the first and second of the three types of analytical propositions they posited.

1. Analytic proposition: a proposition whose truth depends solely on the meaning of its terms

2. Analytic proposition: a proposition that is true by definition

3. Analytic proposition: a proposition that is made true solely by the conventions of language

It is true solely by virtue of the definition of its terms (5 must mean 5, 7 must mean 7), although this can be demonstrated as a truth inherent in every statement as we what we mean in a word is entirely up to us as individuals. It is also true, with the above statement in mind, in definition, in a manner similar to the above observation that 12 contains all its possible component parts, and that it is inherant to the concepts of 7 and 5, taken together, that they total 12. The third can also be said to be true, but common language is what we make it, so 3 can regress into meaningless as a statement of truth or positive move towards any kind of resolution, and can even be viewed as a tautology.

It depends entirely on whether you go with Kant or the Logical positivists.

Hope that helps, sorry if it was confusing.

Answer 2

7 5 12

Answer 3

you can't just say that all rational and logical propositions are analytic: that's what the whole question is about. most (not all) mathematicians feel that the propositions of math are real in the platonic sense, which would make them synthetic. imagine "reality" before the big bang: does 7+5=12 in that realm? If so, it would seem to be a synthetic reality.

Answer 4

Actually, it is an a priori synthetic proposition, according to Kant. Most philosophers thought that something could be in the realm of experience (synthetic) or a priori (concept given without the need of experience), but that the two were exclusive. Kant's project is to show that there can be both and he gives 7 + 5 = 12 as an example of an a priori synthetic proposition. You can not experience, strictly speaking, the union of seven items and 5 items. In experience they each remain a particular instance of a particular sensation. The union is provided by an axiom of addition which is not given in experience. Hence you have items (synthetic) which combine (a priori).

Answer 5

Synthetic in fact that was Kant's first example of a synthetic proposition in his Critique of Pure Reason.

Because the concept of 12 does not analytically contain the concept of 7, 5, addition, it must be synthetic.

Answer 6

its analytic because analytic means its rational and logical 7 + 5 = 12 makes sense. it isnt synthetic because synthetic means unnatural

Answer 7

analytic

cuz it cant be disruped

5 apples + 7 apples dont make 55 apples(synthetic)

Answer 8

ANALYTIC! Why did you have to ask?

Answer 9

not sure cause i didnt' get t any dumb american scjhool but ....

analisi is when you try to understand so ... you "cut" in piecies...
and sythetic you try to make it smaller so you put all together ...


now use you own neurons ...

Answer 10

Huhh!? Maybe it's both...