MONDAY, MAY 17, 2021
Commitment to our ongoing task: Over the weekend, strange as it seems, we dug out our copy of The Principles of Mathematics, Bertrand Russell's famous text.
We dug out our copy of the book and briefly applied ourselves to it. Our book had been priced at $2.95. We'd purchased the book while in college!
Why would we dig out our copy of Russell's book?. You're asking an excellent question. It's a question we'll address as the week proceeds.
For today, we'd like to give you a quick look at some of what we found.
As some may know, The Principles of Mathematics (1903) is a separate text from Principia Mathematica, the three-volume work published by Russell and Alfred North Whitehead starting in 1910.
The Principles of Mathematics is the shorter, simpler text. But because it's difficult, at first glance, to know what Lord Russell is, or could be, talking about, we turned to the leading authority on the book for a stab at a quick overview.
We flung ourselves on that account. It started off like this:
The Principles of Mathematics is a 1903 book by Bertrand Russell, in which the author presented his famous paradox and argued his thesis that mathematics and logic are identical.
The book presents a view of the foundations of mathematics and Meinongianism and has become a classic reference. It reported on developments by Giuseppe Peano, Mario Pieri, Richard Dedekind, Georg Cantor, and others.
As we've noted in the past, Russell's "famous paradox" grew out of his tortured ruminations concerning "the set of all sets not members of themselves." For today, we're going to leave that right there.
Meanwhile, is Russell's thesis actually true? Is it true that mathematics and logic are identical?
Full disclosure: We don't have the slightest idea. In truth, don't even know what that statement might mean.
We wouldn't even necessarily swear that the statement means anything at all in the end. We've been in this maze too long!
That said, "Meinongianism!" We'll admit we'd never heard the term, but there it was in print: According to the leading authority, Russell's text "presents a view of the foundations of mathematics and Meinongianism and has become a classic reference."
Meinongianism! Inevitably, we we clicked the link which had been provided. When we did, here's the start of what we found:
Alexius Meinong Ritter von Handschuchsheim (1853 – 1920) was an Austrian philosopher, a realist known for his unique ontology. He also made contributions to philosophy of mind and theory of value.
Meinong wrote two early essays on David Hume, the first dealing with his theory of abstraction, the second with his theory of relations, and was relatively strongly influenced by British empiricism. He is most noted, however, for his edited book Theory of Objects (full title: Investigations in Theory of Objects and Psychology, 1904), which grew out of his work on intentionality and his belief in the possibility of intending nonexistent objects. Whatever can be the target of a mental act, Meinong calls an "object."
Perhaps as part of his unique ontology, Meinong believed in "the possibility of intending nonexistent objects." Inevitably, we found ourselves being drawn in at this point.
Still, there may have been a bit of fuzz in what we had read so far. Hungry for knowledge, we continue to read—and this is what we found:
His theory of objects, now known as "Meinongian object theory," is based around the purported empirical observation that it is possible to think about something, such as a golden mountain, even though that object does not exist. Since we can refer to such things, they must have some sort of being. Meinong thus distinguishes the "being" of a thing, in virtue of which it may be an object of thought, from a thing's "existence", which is the substantive ontological status ascribed to—for example—horses but not to unicorns.
Let's start at the beginning of that passage, using slightly simpler language:
According to a "purported empirical observation" which was part of Meinong's "theory of objects," it's possible to think about something—for example, a unicorn—even though it doesn't exist!
That struck us as a somewhat underwhelming "observation." Still though, we were initially intrigued by this:
"Since we can refer to such [imaginary] things, they must have some sort of being!"
At this point, we still felt fairly sure that we were following Meinong's chain of thought. According to Meinong's theory of objects, imaginary entities have some sort of "being" even though they don't exactly "exist!"
To us, it sounded like good, solid stuff! Then we stole a glance at the faces of the youthful analysts who assist, aid and help us in everything we do.
By now, the youngsters were delivering their frozen, thousand-yard stares. They said they'd been through this sort of thing in their college "philosophy" course—various courses which were imposed on them by various "professors."
The youngsters were recalling the pain of those earlier days. We didn't want them to know the worst, but the leading authority on Meinongianism proceeded to bring it back home::
Historically, Meinong has been treated, especially by Gilbert Ryle, as an eccentric whose theory of objects was allegedly dealt a severe blow in Bertrand Russell's essay "On Denoting" (1905). However, Russell himself thought highly of the vast majority of Meinong's work and, until formulating his theory of descriptions, held similar views about nonexistent objects.
Instructive! Until formulating his "theory of descriptions," Russell had generally agreed with Meinong's "theory of objects." The young analysts tore at their hair.
As we've noted in the past, our favorite books have always been the ones which don't make sense. With respect to the kinds of theories being discussed in the passages we've quoted, the later Wittgenstein dared to suggest that such theories may not exactly make sense.
These "theories" had come from the very top levels of the western world's intellectual establishment. When we see this kind of work coming from our culture's highest platforms, can we really be surprised by the various forms of incoherence and clatter we encounter even now, every day, in Our Town's most respected top newspapers?
Before the week is done, we'll show you Lord Russell's elaborate proof of the claim that 1 plus 1 equals 2. As our society slides toward the sea, is it possible that work of that type carries a substantial type of anthropological significance?
Major experts say it does. Extending our great anthropological project, we'll examine their claim all week.
He proved that 1 plus 1 equals 2! No, we aren't making that up.
Tomorrow: Whatever may seem to come next