Are Infinity and Finity Reconcilable?

PSI Blog 20251222 Are Infinity and Finity Reconcilable?

 

No.

 

            Credit: philosophynews.com.

Thanks to Doug Gill for this comment on the definition of infinity:

 

“Glenn, thanks for this detailed summary and position on the problem. As you point out, infinity introduces the problem of infinite regression (or extension) in logic and mathematics. Another proposal on resolving the issue is paraconsistent logic.[1] I am not sure how this would tie with your approach, but I would be interested to hear. It posits the counterintuitive view that things can be both true and false at the fundamental level. In that regard, Russell’s paradox is the key theoretical argument that defines the property found in all logical paradoxes (including the infinity of the Universe). The Institute of Art and Ideas (iai) is a valuable resource for discussions on this topic (and of all topics) and is worth the fee to join. Every “A-list” physicist and philosopher has appeared in their presentations. Graham Priest (at iai seminars) and Jc Beall argue for the paraconsistent logic approach and have YouTube videos and online seminars.”

 

[GB: Sounds to me like paralogistics (i.e., illogic). These folks must all be paralogists.^[2] For instance, the Liar Paradox[3] is simply nonsense. Many paradoxes have at least one false assumption. An example is Olbers’ Paradox, which states that if the universe was infinite the night sky would be entirely lit up by the infinite number of stars.

 

Here is AI’s regressive explanation:

 

“Olbers' Paradox asks why the night sky is dark, when a universe infinite in size and age, filled uniformly with stars, should have every line-of-sight end on a star, making the sky blaze brightly. This conflict with observation is resolved by the reality of a dynamic, expanding universe that is also finite in age, meaning light from extremely distant sources hasn't reached us yet, and the light that does arrive from far away galaxies is stretched Olbers' Paradox asks why the night sky is dark, when a universe infinite in size and age, filled uniformly with stars, should have every line of sight end on a star, making the sky blaze brightly. This conflict with observation is resolved by the reality of a dynamic, expanding universe that is also finite in age, meaning light from extremely distant sources hasn't reached us yet, and the light that does arrive from far away galaxies is stretched (redshifted) out of the visible spectrum by expansion.”

 

Of course, the false assumption is that light could travel an infinite distance without being scattered or losing energy (e.g., your flashlight would be seen on Mars). But even as admitted in their explanation “light is redshifted out of the visible spectrum” and so is no evidence for finity or expansion. The Infinite Universe has the same property. The ideal replication of each subsequent wave is impossible in the imperfect Infinite Universe. The cosmological redshift is simply a function of distance. It is not a result of the assumed recession of all galaxies due to universal expansion. The calculated recession assumed due to the Doppler effect broke down when it exceeded the velocity of light. Cosmogonists had to invent yet another ad hoc: the magical expansion of perfectly empty space and the inflationary universe. The Big Bang paralogists keep grasping at straws that are irrational, but durable. Twenty-five falsifications have not fazed the “Last Creation Myth.”

 

I suspect the logicians and the techniques you mention are doing the same thing. They are faced with contradictions all the time while attempting to straddle the science-religion fence in the interest of popularity and book sales. "The Ten Assumptions of Science" and their opposites “The Ten Assumptions of Religion” don’t do that. Each set forms a constellation in which all ten “fundamental assumptions” are consupponible, that is, none of the ten contradict one another. The beauty of these two constellations is that if one is true, then its opposite is false.

 

Thus the universe is either infinite or finite. It is not possible for it to be a little bit infinite. It is just like pregnancy: You is or you ain’t. Religious scientists might favor paraconsistent logic, cherry picking among fundamental assumptions. A popular one is the Second Assumption of Religion, acausality (Some effects have no material causes). Although false, that one allows for freewill, making threats of hellfire and damnation profitable.]

 

 

PSI Blog 20251222

 

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[1] In classical logic, if you accept "It is raining" (\(A\)) and "It is not raining" (\(\neg A\)), you can logically derive anything, including "The moon is made of cheese" (\(B\)), because the premise is contradictory. In a paraconsistent logic, you can have \(A\) and \(\neg A\) as true, but still conclude that \(B\) is false, preserving the meaning of \(\neg A\). 

 

[2] Google AI “A paralogist is a person who makes unintentional logical errors or fallacious arguments, reaching incorrect conclusions without intending to deceive (unlike a sophist), often described as using faulty reasoning or paralogism.”

 

[3] Google AI: “The Liar Paradox is a self-referential statement, most famously "This sentence is false," that creates a logical contradiction: if it's true, it must be false, and if it's false, it must be true, leading to an endless loop where it can't be consistently assigned a truth value. It challenges classical logic and reveals issues with truth, reference, and language, with solutions ranging from defining it as meaningless "nonsense" to complex theories in formal logic that restrict self-reference or allow for “truth-value gaps.”