Relax the burden of deductive proof

So, as shown in the previous section, we can't use deductive reasoning and pure logic (a priori) to prove the existence of "noumena" or "things in themselves" in an external reality. Most philosophers start off with the premise that they exist, and then focus more on our ability to experience them. This is descriptive of Kant, who spent much of his effort exploring how we only have access to noumena through the "phenomena" presented to us through our senses. For him, and for others, the question of the independent status of the noumena was not nearly as interesting a problem. He assumed that the noumenal world existed, but was completely unknowable to humans.

"Though we cannot know these objects as "things-in-themselves" (i.e., noumena), we must yet be in a position at least to think them as things in themselves; otherwise we should be landed in the absurd conclusion that there can be appearance without anything that appears."

He conceded, as did Scottish 18th century philosopher David Hume and others that:

"the reality of external objects does not admit of strict proof."

But that is exactly what we are talking about here. We are considering whether the noumenal world does or does not really exist - is there something behind the phenomena that we experience? As suggested previously, a significant problem is the application of deductive reasoning to the question. We should admit and concede that using the strict rules required for deductive logic can’t be applied to questions of this sort, nor can a priori reasoning be applied to the entire process of Inductive reasoning (you can't deduce that induction is a valid way to reason). Or, as Hume also said, in Dialogues Concerning Natural Religion:

...there is an evident absurdity in pretending to demonstrate a matter of fact, or to prove it by any arguments a priori. Nothing is demonstrable, unless the contrary implies a contradiction. Nothing, that is distinctly conceivable, implies a contradiction. Whatever we conceive as existent, we can also conceive as non-existent. There is no being, therefore, whose non-existence implies a contradiction. Consequently there is no being, whose existence is demonstrable.

Induction (proceeding from the specific to the general - as in "the sun has come up every day, so it will continue to come up) is a fundamentally different and looser form of reasoning than deduction. The truth-preserving nature of deductive reasoning doesn’t work when used to justify a reasoning process in which the conclusions are, by definition, not certain. The conclusions of inductive arguments exceed the content of their premises – individual cases when used to construct a general rule necessarily go beyond themselves. However, with deductive arguments the premises contain everything necessary to systematically arrive at a definitive conclusion – the conclusion is inescapable. For this reason, it is simply impossible and inappropriate to impose the tough standards of deduction on the fuzzier process of inductive logic, so we are left with inductive logic to "prove" the existence of a physical universe.

As we have seen, inability to disprove a proposition does not render it true. For example:

• Although the Omphalos and Solipsistic positions are immune to disproof, all reasonable people agree they are beneath consideration, mere philosophical novelties and parlor tricks.
• Russell's celestial teapot and the Flying Spaghetti Monster (blessed be his name) cannot be successfully defeated through argument. But, all satire aside, they are not really out there.
• The many varieties of supernatural mythologies all create beings or histories or forces that are beyond the means of science to disprove. This doesn't make them real.
• There is an astronomical number of other incredible claims that bear similar logical structures to the above examples that also are unsusceptible to the power of logic. They are not, therefore, all true.
• Likewise, no one can disprove this claim: "Reliance on induction is unwarranted". That does not automatically render this proposition true. If we can't disprove that "induction is groundless", reliance on induction is not, therefore, groundless. In fact, it is "probably true".

All assertions about the existence or lack of existence of the external world are beyond positive proof.