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[virtual_anima]

Often in philosophy, 1 + 1 = 2 is used as evidence that there are absolute truths. i.e things that are absolutely true. If you have one thing and one thing, and you put it together you have two things

Comments

[virtual_anima]

but that would make it... the opposite of what you said....

[jeffrock]

2 + 2 doesn't = 5 because we say it doesn't.

This implies that we could have said that 2+2=5, which is silly. I don't see how it's up to us in any way.

[virtual_anima]

Why is that silly?

[xiota]

An a priori truth is a thing that "could not have been otherwise." (philosophy 101... ding ding)

If this is because it's so obvious (space and time are necessary for objects to exist) or because we have defined it thus (math) or because we intuitively know it's true (laws of logic) - that's an entirely different question.

That's of course ignoring that math has been able to be founded on logic and is thus less "artificial" than once thought by philosophers (thanks Russell, Whitehead).

So I don't see what the problem is.

[virtual_anima]

I think, what do we assume is logic, what do we assume is "reality" and what is logic, what is "reality"?

[virtual_anima]

Is it true that it's a meter long or that we all agree our senses tell us that it's one metre long? Could "one meter" be actually a bit longer? etc.

basically... are these a priori truths things that we experience and claim them to be true. How would they be otherwise?

[unnamed525]

Mereology isn't mathematics. Mereologically, when we sum two objects, we still have the two objects as well as having a third object that is the mereological sum of the objects. Mathematically, when we add measurements, for instance, we go from having two distinct lengths of 1 inch (for instance) to a third length of 2 inches. Mereologically, the lengths could be considered as distinct things, but I think your problem comes from confusing mathematics and mereology, to be honest.

[virtual_anima]

mereology sounds like an arbitrary invention more than the idea of a priori mathematical truths does. There is no third object, it's not an object, it's a concept.

[unnamed525]

I don't see how it is. I can have a rock, a stick, and a piece of sinew; these are three distinct things. I can combine them to create a fourth thing, a stone hammer; the rock, stick, and piece of sinew are still three distinct things, both from each other and from the stone hammer itself. How do I know their distinct from the stone hammer? It has properties which none of the three possess individually ... and I can decompose the stone hammer into its constituent parts.

[virtual_anima]

I guess this shows that the idea of 'object' is a concept as well. Maybe the fundamental concept that the idea of 'math' relies on.

[iheartfeijoas]

for example,

1+1=2
you have 1 teaspoon of baking soda
you have 1 pound of flour

and the baking soda makes it rise and then you have much much more than 2, perhaps.

or is that just a silly sort of idea?

[unnamed525]

By abstracting away from the units, it's presumed that the units are the same for all the numerical values.

[virtual_anima]

when dealing with math, discreet units for measurement is only one area.

[unnamed525]

Right ... there are continuous quantities of measurement ... and set of measurements with cardinalities even greater than aleph_one ... and, actually, I can't think of one area of mathematics except the foundations of mathematics and number theory (although that seems like measuring numbers themselves) that doesn't deal with measuring something; just different types of things.

[jeffrock]

You can talk of "1+1" equalling "2" without referring to any "things" other than the integers "1" and "2".

You can count me among those who feel that mathematical truths are absolute, that is to say they are neither arbitrary nor relative in any way.