Understanding Infinity and Infinite Regress

Here’s another philosophical problem that has, and will continue to plague us for eternity…

The problem of origin is one that has remained unsolved since the advent of thought. Philosophers throughout history have tried to address the mystery of “the uncaused cause” and “the unmoved mover”. These mysteries are a result of attempts to prevent the problem of infinite regress, in which the search for justification is unending as the question of justification of every next/previous premise keeps arising.

To defend a theory, or prevent it from falling into the problem of infinite regress, an infinite regress argument is used. One example of the use of such an argument is in the argument for the existence of God through The Cosmological Argument given by Thomas Aquinas.

Epistemic Regress and Metaphysical Impossibility

In philosophy, there are two major forms that the infinite regress problem takes.

Epistemic Regress

Knowledge is a true, justified belief. In every chain of logical reasoning, each step depends on the previous one (its justification) for its existence. For the sake of understanding, let’s take a step T1 in a logical argument. T1 relies on T2 for its justification, and similarly, T2 relies on T3, which again would require a justification in the form of T4. T1 will never be supported adequately because the needed series of support would be infinite. Thus the search for rational justification is neverending, as it seems that a starting/ending point can never be reached.

Metaphysical Impossibility

This can be explained by taking an ontological example. Things in the external world are taken to exist because of the parts that they are composed of. These things (parts) must also depend on their own parts for existence. This chain continues till infinity, which many thinkers like Thomas Aquinas claim to be impossible.

There are things in the world (composed of matter). Everything has an origin. Something cannot come from nothing. Yet, something has to come from nothing if there is to be an origin. The idea of an origin-less universe seems absurd, yet an explanation (without contradictions) to escape this has not been obtained so far. The problem of metaphysical impossibility is thought to be the most serious form of viciousness entailed by infinite regress.

Aristotle and Francisco Sanchez on Infinity and Infinite Regress

Aristotle

The Greeks viewed the concept of infinity as being synonymous with chaos. ‘Apeiron’ (Greek for infinity) was a problem for them because it evaded their conception of everything existing in precise and measurable terms.

Aristotle defined infinity as being a potential state. He said that the existence of infinity was necessary because he couldn’t conceive of time as having a beginning or an ending. Nor could he conceive the same when it came to counting numbers, or of the universe. But, at the same time, he said that infinity couldn’t possibly exist. To support this stand, he said that the existence of an infinite object is unimaginable, because by virtue of its infinite nature, it is undefinable, and hence could not be told apart from other objects. To conclude, Aristotle said that as neither of these two stands seems possible, infinity must both exist and not exist in different senses.

Francisco Sanchez

Sanchez took Aristotle’s argument further by giving an argument for skepticism based on an infinite regress. Going against foundationalism, while supporting evidentialism, he pointed out the absurdity of the idea that knowledge rests on something other than knowledge. From this, he concluded that nothing could be reasonably believed. One of his popular quotes is — “Knowledge is fiction.”

The argument he gave is-

Premise 1: Knowledge cannot rest on assumption.

Premise 2: Knowledge requires justification

Premise 3: Knowledge is finite.

Conclusion: Nothing is known.

This is known as the semantic argument. He used it to convey that even though the meaning of knowledge is known, it cannot possibly be obtained. Therefore, we need to substitute the word knowledge with reasonable beliefs.

Food For Thought

There is an interesting question that helps explain the problem that infinity, as a concept, poses. It has no conclusive answer, as of yet. The question is — “If you turn a light bulb on and off an infinite number of times, does it end up on or off?”