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THE QUANTUM of EXPLANATION

~ Science, logic, and ethics, from a Whiteheadian Pragmatist perspective (go figure)

THE QUANTUM of EXPLANATION

Tag Archives: Ontology

The Infinite

22 Thursday Jul 2021

Posted by Gary Herstein in Logic, Mathematics, Ontology

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Logic, mathematics, Ontology

I don’t anticipate any explicitly Whiteheadian considerations this time around, but all my thoughts are informed by my Whitehead scholarship, so you never know. What I want to talk about here is the idea of infinity. I say “idea,” rather than “concept,” because even within the relatively constrained bounds of formal mathematics infinity is not one thing. Outside of the bounds of mathematics matters are significantly worse, little or since no effort is made to constrain such talks, or even render it potentially intelligible, with formally legitimate techniques.

Speaking of “outside the bounds,” the ancient Greek word for the infinite is “apeiron” (ἄπειρον), which translates as “unlimited” – the “a” being the negation (“un”) and “peiron” meaning limited or bounded. Clever as they were, the Greeks lacked our additional 2,300 years of mathematical study, so the idea that one can have something that is infinite (unbounded) – for example, the length of the perimeter of a geometrical figure – i.e. a perimeter that exceeds any possible length, measurable either in practice or the ideal, that is nevertheless bounded by an easily measured finite figure (a circle, for example) would never have occurred to them.i But the figure above, the Koch snowflake, is precisely such a figure. (Details can be found HERE. As is my wont, I skip the technical details which will take up more text than this blog post.)

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Un-Cut

27 Sunday Mar 2016

Posted by Gary Herstein in Logic, Mereology, Ontology

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Critical Thinking, Logic, Ontology

I was reminded again this other day that the varieties of ways that things can be “together” easily exceed the kinds of ways that even smart people will often notice or imagine are possible. The issue I have in mind here is not a matter of relationship advice but rather of logic (although more than a few relationships would profit from even a smattering of basic reasoning.) In this instance, some things can be analyzed into genuine parts that can be separated in fact, while other things can only be analyzed into abstract “parts,” which are not ever separable in reality; there is yet a third type that can only be taken as a whole, even in analysis, without doing violence to the nature and meaning of the thing in question. Failure to recognize what type of thing or idea one is dealing with can lead one into fundamental errors which, while often terribly clever are, for all of that, still just flat wrong. My interest here will be with the first two of the above three.Scissors

Various common phrases are easily recognizable in this context, most especially the old saw about, “the whole is greater than the sum of its parts.” This is especially true of organic unities. For while we’ve achieved a level of surgical finesse that can, under extremely delicate and rigorously right sets of circumstances, permit us to, say, remove an organ from a living being and replace it with another, this generally cannot occur without considerable trauma, frequent enough failures, and extraordinary skill to reassemble the whole that has been torn apart by the procedure. Such holistic entities are what the Greeks referred to as a-tomos, a word that roughly translates as “uncut.” It is from this Greek root that we get our term “atom,” which originally meant an undivided unity. Continue reading →

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“But in the real world it is more important that a proposition be interesting than that it be true. The importance of truth is, that it adds to interest.” – Alfred North Whitehead, Process and Reality

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