Why does 7+5=12 is considered "synthetic a priori" by Kant?
"7," "5," "+" is not
According to Kant, analytic statements really tell us nothing new about the world.
All triangles have three sides.
You can see that this is simply a structural relationship between subject and predicate. They are "analytic" in the sense that the predicate can be found by analyzing the meaning of the subject.
All bodies are extended.
Again, analytic because part of the definition of a body is that it occupies space (which is what "extended" means here).
Synthetic statements, on the other hand, assert more of a thing than is already contained in the definition of that thing.
They "synthesize" one concept with another, and tell us that they are found together in some specific thing.
All bodies are heavy.
Is "ampliative," in that it conveys new information about bodies that is not contained in the very concept of that thing. "Having weight" is not part of the definition of "occupying space."
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