Is 50 + 50 = 100 a necessary or self-evident truth?

Question

Certain philosophers say that math constructs like 2 + 2 = 4 or 50 + 50 = 100 are examples of self-evident truths. They are true in any possible world or any counterfactual situation. But I wonder if there is a counterfactual situation in which 50 + 50 does not = 100. Could such a counterfactual situation obtain?

Answer 1

Not quite self-evident, but its truth is semantically necessary. That means it is made true by the meaning of the symbols.

There is another sort of necessary truth, logically necessary truth. But 2 + 2 = 4 is not a logically necessary truth, because it is the form, not the content, of a true expression that makes its truth logically necessary. The form a + a = b is not a logical truth. When it is given the content 2 + 2 = 4, then it becomes true according to the meaning of those symbols. Contrastingly, "If a and b, then a" is a logically necessary truth.

If it were the case that 2 + 2 did not equal 4, then it would be because those symbols had different meanings than they in fact have been given. It's the meanings that count. But those meanings are *not* human inventions, they are human discoveries - they were here before us and will be here after us.

Answer 2

Short answer:
Of course.
Say we use base-8 counting system[1].
Then 50+50=120.

Long answer:
In fact there are a lot of problems with "self evident" mathematical truths. First of all mathematics require some basic axioms that are accepted without proof.[2]
Furthermore it is known that any axiomatizing that is complex enough to define natural numbers will contain statements that are neither provable nor disprovable![3]
IN nature however everything is either true or false. Thus the obvious conclusion is that mathematics are not obvious truths, but are human constructs that APPROXIMATE the world.

Thus More generally surely i can come up with a counter-factual where 50+50 is not 100. All these counter-factual could begin with "let's accept the following axioms without proof" and then depending on the axioms 50+50 could be just about anything.

Answer 3

well...if you were to add 50 soldiers form an army to 50 enemies on a battlefield, you might have a counterfactual situation in which the outcome could be less than 100. Even less than 50.But I'm not sure if this is a very philosophical approach...

Answer 4

Well, according to Pathagoras I'm sure he'd try really, REALLY hard to prove it as a self-evident truth, which is why he led many many people into believing the basis of all things, in truth, are numbers.

However, I think that the ONLY reason we have numbers to begin with is because someone came up with the idea. Ok..so what makes THAT guy right? What IS "1" anyway? Who or what said "I'm going to come up with this "formula" to represent how things go together or how they separate or how they multiply" and so forth? What if the basis of numbers are in and of themselves an illusion? What really IS a number? What really IS a plus sign or an equal? Hmmm....

Answer 5

No. It depends on definitions and rules, so it is not self-evident nor necessary, except in the framework of its definitions and rules. The definition starts with the meaning of "1" and the rule that "1+1=2". Any multiple of 1 added to any other multiple of 1 gives you the answer.

If you define "1" as in computer language, i.e., "on," there is no 2, 3, 4, etc. and 1+1 does not equal 2.

Answer 6

50 + 50 = 100 because that is what you were taught. That is what you believe to be true. For that reason only .. 50 + 50 = 100 .

Answer 7

The answer is that as humans we have innate a priori knowledge that is intuitively known. Further, as universals exist beyond human awareness in themselves there is no reason to think that there would be place where your example of 50+50 does not equal 100.

Answer 8

So If some one is 50 and 9 months and some one is 50 and 7 months and you add their ages together you infact have 101 years and four months. forgive me a long time since i left school and work with words, i would like to know. Email me. maths is of interest to me

Answer 9

u can use 50 pens and 50 books and start to count
1 2 3 4 5 6 7 8 9 10 11 12 13 14 ................................

Answer 10

if you assume base 10 then yes.
however in base 16 hexadecimal
50 + 50 is A0 which is 160 in octal it is 240
so the answer is unattainable if we are left to our own assumptions regardless of unknown factors.