Hey M, great post!
My suspicion here is that Psychologist Dean is committing what is called an
Appeal to Plenitude.
The Appeal to Plenitude/Boundary Condition/Semantics
Afford me the miracle of a plea into infinity, and I can prove anything, or render anything absurd.
Bounce your critical logic off of a boundary condition and it will come back in a completely different form.
Love, art, music, consciousness therefore are absurd because I cannot reconcile them with my lexicon discipline.
1)
1 = .99999999... This is true by the nature of mathematical lexicon. But a lexicon is only our artifice approximating the nature of reality. However an infinite number of 9's is what is called 'plenitude' (or possibly a 'boundary condition', depending upon one's philosophy).
Any logical predicate which allows me to appeal into infinity (or boundary condition) as the basis of my argument, is unsound as a line of reasoning. It is pseudo-theory, because I can prove literally anything if you allow me to use infinity as my alternative resource.
2)
1 number + 1 number = 1 number This is called equivocation. Again psychologist Dean is ascribing natural equivalent to our approximating lexicon. Just because I cannot describe love, does not mean that it is absurd and therefore does not exist. The world around us is not enslaved to our (useful but not complete) lexicon.
3)
Zermelo–Fraenkel set theory contradicts itself (by excluding urelements) Again, by making plea into urelements (elements of sets that are not themselves sets - which includes itself - which is plenitude) as a logical critical path, one has to
appeal to plenitude in order to take a philosophical-only set and ascribe to it a literal (and therefore a very useful-as-equivocal) meaning as a Wittgenstein logical object.
Of the seven schools of objective philosophy - Empiricism Logicism Formalism Intuitionism Naturalism Nominalism Structuralism - only one (possibly) regards infinity as a logical object - which could then be employed in a critical path syllogism such as the ZFS contradiction.
4)
Mathematics is not the language of the universe The absurdity of the nature of a boundary condition - absolutely valid. A lexicon cannot comprehensively describe a boundary condition - and furthermore, cannot approach an element which exists outside that boundary condition - nor distinguish the two. This is part of the prison in which we reside. :) Don't drop your soap in the shower.
5)
Mathematics is a lexicon - and a lexicon is never complete. Valid, but since this critique applies to literally EVERYTHING in our realm, it is what is called in philosophy a
pseudo-argument. Our very existence is absurd, and given an appeal to plenitude, I can prove right now, by lexicon and procedure, that neither you nor I exist. This is not useful however.
6)
The SQRT(2) = 1.41421356... is infinite as an identifiable set, yet the boundary of the triangle represented by it is a discrete and finite measure. Again, this is citing the mismatch between lexicon and utility (known as semantics). Math is a lexicon, it is not a comprehensive descriptive. Our universe is discretely bounded by what is called a Planck Interval. Everything is discretely bounded. Math is unbounded appeal to plenitude, i.e. math - reality is discrete and never fully continuous.
Literally every single principle, with the exception of possibly consciousness - will suffer the 'fallacy of meaninglessness' which Mr. Dean has cited here.
All Mr. Dean has done here is to Touch the Sky (plenitude, boundary, absurdity of lexicon) - and to touch that boundary 6 times.
“For the World is Hollow and I have Touched the Sky” was one of my favorite Star Trek episodes (although by this time well into syndication), not only from the perspective that Dr. McCoy got it on with some hott alien chick, but also because this issue was touched. In the plot, a man crawls to the end of the ‘sky’ and touches it, only to find it a tactile boundary, a dome of deception – the sense of which drove him to an insanity of just desserts for violating the strictures of the ‘god’ which ruled their planet and forbade such arrogance – as asking questions.