In other words: is 2+2=4 a truism independent of human experience, or is it (and all mathematics) a convention created by the human mind? Put another way, is mathematics an objective reality that our mind has uncovered, or is it a set of conventions that have been agreed upon for principally practical purposes: e.g. making the correct calculations so that the bridge does not collapse?
2007-01-02 00:26:04 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
I think that this is true 'a priori' in the following sense.
With a suitable (axiomatic) definition of "2", "4", "+", and "=", the statement is true independent of anything actually existing, provided the usual laws of logic and reasoning hold.
In the world we live in, the purely logical statement "2 + 2 = 4" has a very direct analogue with reality; that is, if I take two objects and two more objects and put them together, there'll be four more objects.
The statement "2 + 2 = 4" might not have a reasonable analogue in reality in all possible worlds (perhaps in some possible world, objects have no reality of their own, but can only be viewed as part of the universe, so the statement "two objects" has no meaning), but "2 + 2 = 4" would still be true as a statement of pure logic.
If you don't believe the laws of logic and reasoning are necessarily true 'a priori'--for example, if you believe it is possible that in some world the propositions "All dogs are mammals," "Fido is a dog," and "Fido is not a mammal" are all true, then I see no reason "2 + 2 = 4" should be true in that world.
It is awfully hard for me to conceive of such a world existing. That doesn't mean it couldn't, but it does mean I would have no idea how to draw any conclusions about that world.
2007-01-02 01:18:50 · answer #1 · answered by Anonymous · 0⤊ 0⤋
I would say 2 + 2 = 4 is a truism independent of human experience, because whether we're sleeping or awake, 2 + 2 WILL equal 4. I can't dream of a square circle, or a four sided triangle.
2007-01-02 08:33:04 · answer #2 · answered by Puggy 7 · 0⤊ 0⤋
if you are counting things , two things plus 2 more things will always be 4 things
If any alien creature knows the semantics it will recgon 2+2=4 as being true.
But it is true yes that knowing the semantics of 2+2=4 let not proof (strangely) you this. YTou have to make "assumtions" , that there is a number 0 , that every number has a successor , and 3 other assumtions i forgot ( google for Peano http://en.wikipedia.org/wiki/Peano_axioms ).
2007-01-02 08:29:48 · answer #3 · answered by gjmb1960 7 · 0⤊ 0⤋
The fact 2 + 2 = 4 is independent of human thought. We may have assigned specific words and symbols to what we think of as "two" and "four" but it's still something we could not change (without mathematical trickery).
2007-01-02 08:30:23 · answer #4 · answered by Tom :: Athier than Thou 6 · 0⤊ 0⤋
it's not 'a priori'. it can be derived from 'euclid's elements' though. and the statement you've given is only true for our 'common use' system of real numbers anyway, if we were living in base 2 then 2 plus 2 would equal 1!
2007-01-02 08:31:36 · answer #5 · answered by ten 2 · 0⤊ 1⤋
hypothesis my friend
2007-01-02 08:33:08 · answer #6 · answered by Anonymous · 0⤊ 0⤋