Is LOGIC the same as MATH?

Is LOGIC the same as MATH?

Here's a test for you:
1. BIRD is to NEST just as _______ is to __.
a) DOG : LEASH c) BEAVER : DAM
b) SQUIRREL : NUTd) CAT : LITTER BOX
2. 4 is to 2 just as _______is to__.
a)3:7c)20:10
b) 7:3d)10:13
These are analogy problems. The answer to question one is (C), since the relationship between bird and nest is "the first builds the second." The answer to question two is (C), since the relation- ship between 4 and 2 is "the first doubles the second." The first question is logical, the second is mathematical-yet, they are both about relationships between things. Does this mean logic is the same as math?

Nineteenth-century German philosopher GOTTLOB FREGE argued that logic is the same as math. He believed that numbers exist in a place beyond the physical world. We use number symbols (2, 17, 100, for example) to represent numbers, but we can also use other symbols(x, y, z, for example) to represent things in the physical world. He developed a complex system for symbolizing deductive arguments.

Twentieth-century German mathematician DAVID HILBERT disagreed with Frege. In his view, math is like a game, not in the sense that you win or lose, but in the sense that the system is self-contained. When we play chess, the pieces are symbols of kings and queens, but they don't stand for any real people
at all-the pieces only represent something inside the game. Likewise, when we use numbers, they do not represent anything existing in a place beyond the physical world.

Present-day American philosopher SHARON BERRY points out that whether logic is the same as math depends on what you mean. If by “logic" you mean general rules of reasoning, then logic is the same as math. Set theory-a type of math that uses circle diagrams-is the link between math and logic.

Eleventh-century Italian philosopher ANSELM OF CANTERBURY developed a proof for the existence of God. A proof is used in math to show that a mathematical idea is true. To prove: A triangle has three sides.
1. A triangle must have three angles.
2.Suppose a triangle does not have three sides.
3. Then we would have a triangle without three angles, which is impossible. Therefore, a triangle must have three sides.
This is what Anselm's proof for God looks like: To prove: That God exists.
1. By definition, God is the greatest being
2. Suppose God does not exist.
3. Then we could imagine an existing god that is greater than the greatest being, which is impossible. Therefore, God must exist.

Eleventh-century French philosopher GAUNILO disagreed with Anselm. He insisted that abstract reasoning can't prove the existence of anything. He wrote a parody, making fun of Anselm's argument. It went like this: To prove: That Blessed Island exists. Suppose the greatest conceivable island does not exist.
1. By definition, Blessed Island is the greatest island.
2.Suppose Blessed Island does not exist.
3. Then we could imagine an existing island that is greater than the greatest island, which is impossible.
Therefore, Blessed Island exists.

THINK ON IT!

1. Write a logical analogy.
2. Write a mathematical analogy.
3. The geometry-style proof we looked at is called "reductio ad absurdum," which means "to shrink your opponent's view to an absurdity." When philosophers use the term"absurd" they don't mean "silly." They mean "impossible" or "contradictory." Write a reductio ad absurdum proof for the conclusion that your birthday only comes one day per year.
4. Write a reductio ad absurdum proof for a conclusion of your own.