A Conclusion Independent Of Premises: Truth

A deductive argument can be proven wrong if one of the premises is proven wrong. If the premises are axiomatic or self-evident, we are standing on thin ice. Something accepted as self-evident may get proven wrong just as easily. For instance, people once observed the Sun to be yellow and the sky to be blue. Now, we know that the Sun releases most of its energy in green wavelength and appears white before its short wavelengths get scattered by Earth's atmosphere and become the sky we see as blue. He who considers the sun to be self-evidently yellow can take a severe beating in debates. Chances are, nothing we observe is true because our tools of observation are limited and biased. All observations are inductive and, hence, subject to the same error. In addition, what has been true for every observation does not have to be true for the next attempt (Russel ch. VI). For instance, an animal with a life span of less than 6 months may never see both shorter and longer days. If it was born on the shortest day, it may always think that days only get longer. And it would be dead wrong.

Consider a basic argument -

If P, then Q

P

Thus, Q.

An argument laid down in such a fashion can be dismantled if you disprove P (you don't even need to destroy P -> Q). This becomes more problematic when the structure is used recursively to derive multiple subsequent conclusions as in syllogism -

P --> Q

Q --> R

R --> S

P

Thus, S

The longer the chain of premises, the more dubious our conclusions. If our worldview is based on P, we are in a precarious situation. Everything we know is wrong if P is wrong. Thus, we can never say that we have arrived at an absolute truth but at a conditional one. The dependency on the veracity of P makes our argument fallible in case P changes with time or location. For example -

Ram eats (Q) what he likes (P).

P - Ram likes apple.

Thus, Q - Ram eats apple.

If we offer Ram an apple, we can reliably predict that he will eat it. But this isn't eternally true. Ram may lose interest in apples someday. Then, our prediction will be wrong not because our logic is wrong but because the first principle was assumed to be true. One way to get around this problem is to prove that Ram eats things he does not like, too. Then, we can say -

If P, then Q.

If not P, then Q. {if we can prove that Q holds for both P and not P}

Thus, Q.

This is the structure of an absolute principle. Q stands true independent of P.

Let's try proving that Ram will absolutely eat an apple if offered. If we can prove that he is not attached to taste, we can make a case that he would eat whatever offered. If Ram was an unattached ascetic, our conclusion may become independent of P, or not. Even though we have freed ourself of P, we have fallen victim to another observational axiom. Our conclusion about Ram remains true only so long our statement about Ram’s detachment from taste is correct at all locations and times. Thus, we still haven’t arrived at an eternal principle. In this situation, we will never do, because human behavior is not driven by fixed laws. This is the nature of pretty much everything we know. Everything we know is bound to be wrong if our most basic axioms are even slightly wrong.

An absolute principle must be true for all values of the premises. Only then can it be said to be absolute. For instance, all moral principles are absolute. Read this post to see how the moral principles I derived are independent of axioms.

Work Cited

Russel, Bertrand. "On Induction". The Problems of Philosophy, edited by Andrew Churley, 1998.

Oxford University Press, 1959. Digital Text International, ditext.com/russell/russell.html.