Tuesday, January 28, 2014

What is Truth?

I think, therefore I am

“I was especially delighted with the mathematics, on account of the certitude and evidence of their reasonings; but I had not as yet a precise knowledge of their true use; and thinking that they but contributed to the advancement of the mechanical arts, I was astonished that foundations, so strong and solid, should have had no loftier superstructure reared on them.”
René Descartes
A Discourse on Method

Area of Rectangle
A = area
b = length of base
h = height

A triangle of the same height and base length as the rectangle containing it will always take up half the area of the rectangle.  This formula will hold true no matter the shape of the triangle.  In the countless uses of this formula by humans on a human scale there has been no instance where this has proven not to be true.  Thus it can be said that no amount of empirical data has ever contradicted these formulas.  In science that would be a very high probability of truth.

Area of Triangle

Truth is always subjective because the only truth I know is what it is I believe.  This holds true for you, as well.  Ultimately all truth is subjective because it is an inner belief.  You can make the same claim regarding mathematics.  I might say the formula for finding the area of a triangle is one half the base times the height and that this is an objective truth because I read it in a book and it is what is taught at school to kids everywhere.  It is a fact that no one has yet found to have a fault according to what I have been told.  What can be a more objective truth?  Still, I have to believe it for it to be true to me.  Maybe the formula to find the area of a triangle doesn’t make sense to me.  I don’t believe it.  Now the formula is no longer true in my mind.  The formula may, in fact, be true to most everyone else but it is false for me.  Truth is ultimately subjective.  Maybe I am right.  There is possibly a flaw in the formula that makes it true most all the time but not always.  It is possible that if the triangle were large enough that we would have to take into account the curvature of the earth then this simple formula would no longer be true.  If I believe the formula for finding the area of a triangle then I believe something that is objectively false.  But I believe it so it is subjectively true. 

Kierkegaard says that objective truth is an abstraction.  Basically he is saying that objective truth has no meaning unless someone believes something to be true.  He says, “Truth is subjective.”  Does that mean that if I believe the Area of a Triangle formula to be true then it must be objectively true?  Obviously no.  If the object, the formula, is objectively false then my believing it to be true does not make it true.  What is true is my belief that the formula is true.  The truth of the object, the formula, is irrelevant to my truth – my relationship to the object.  So what is true is not the object itself but my relationship to it.  This is Kierkegaard’s subjective truth.  In this regard objective truth is irrelevant to what one believes is true.

Certainly we cannot rely on anyone’s subjective truth to land a man on the moon but for truth to have any meaning, for mathematics to have any meaning, it must first become subjective truth - someone must believe it for it to exist.  This statement would be true for Kierkegaard but not for Descartes because Kierkegaard sees truth in purely human terms.

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