WJ

Is 1/3 + 2/3 = 1 an objective truth, or is it a subjective truth?

Hint: one way to find an answer philosophically, could be in the so-called distinctions between subjective thinking v. objective thinking. Otherwise, what kind of truth does it represent?

Walrus

Devilnaut

It is objectively true that 1/3 + 2/3 = 1 , assuming that we are utilizing standard rules of mathematics.


In the same way, it is "objectively true" that the word "water" refers to the substance H20, assuming that we are utilizing standard rules/definitions of the english language.

Bluenose

BTW, water is the English name for hydrogen hydroxide, H+(OH)- unless they have changed the earlier change from H2O............. <img src="confused.gif" border="0">

WJ

Devil!

In comparison or contrast (depending on how you look at it), could the decimal equivalent also be considered an objective truth, in your opinion?

Walrus

sotzo

It is objectively true that 1/3 + 2/3 = 1 , assuming that we are utilizing standard rules of mathematics.

As opposed to the non-standard rules

In the same way, it is "objectively true" that the word "water" refers to the substance H20, assuming that we are utilizing standard rules/definitions of the english language.

It is not the same at all. One is a semantic construct and the other is mathematic. Semantic constructs have a large range depending on context. Furthermore, we could decide right now to hold a conversation about water, and henceforth refer to it as "ret". You and I would then be able to carry on a clear conversation knowing that the word "ret" carries the semantic content of the word "water".

Not so with the mathematic construct. For instamce, if you wish to redefine the associative property such that a+b does not equal b+a, then nonsense results.

Cheers,

jkb

[ May 29, 2002: Message edited by: sotzo ]</p>

MaxMainspring

I would extend your answer to say that 1 is *defined* as that which is the additive product of 1/3 and 2/3. Likewise 1/3 is defined as that which, when added to 2/3, gives 1 and so on. Math is a system of definitions and tautologies. However, in that sense any "truth" is illusory. It is not objective or subjectively true except that it is defined to be true.

If, on the other hand, I take 1/3 of a bushel of apples and add it to 2/3 of a bushel of apples then I will have 1 bushel of apples, an outcome which can be objectively verified. So it is an objective fact that the above operation will yield 1 bushel.

But the purely mathematical statement 1/3 + 1/2 has no truth value at all except that it is consistant with at least one of many possible abstract axiomatic systems. (clearly we will often say that it is true that 1/3 + 2/3 = 1, but that is only a shorthand way of avoiding a pendantically rigorous statement of circumstances) The fact is that it is analogous to the operation with the apples and is a convenient way to mentally make an abstract generalization of all such operations regardless of what is being combined, whether apples or some other entities. But this doesn't make it "true" in any immutable sense. What is objectively true is if I add 1/3 ton of bricks to 2/3 tons of bricks I will have 1 ton of bricks.

Like all my possesions, they are for sale to anyone who can meet the price.

[ May 29, 2002: Message edited by: MaxMainspring ]</p>

MaxMainspring

By no strech of the imagination am I a mathematician, but my understanding is that you have defined your abstract mathematical inference system as one in which a+b = b+a and then what is follows is an series of statements (one of which is 1/3 + 2/3 = 1) are demonstrated to be consistent within your axiomatic system. This does not imply any "truth" value to these statements. Only that they are consistent with your axioms.

[ May 29, 2002: Message edited by: MaxMainspring ]</p>

Devilnaut

Thanks for your comments Max, and yeah, that's exactly what I was trying to get at. I don't think that there's anything profound about Mathematics, except that it's been developed and refined over thousands of years, and happens to be extremely useful

I am not a mathematician by any means, criticisms are very welcomed.


devilnaut

NialScorva

It's tautalogical, neither objective nor subjective. It's true because we *define* it to be true, not because it was found to be true after investigation.

snatchbalance

WJ,

Help me out, what might some of these distinctions be?

SB