. . . looking sad.
Bartender: "What's the matter, pal?"
"My girlfriend says we have nothing in common!"
Bartender: "But you are a nominalist! Isn't that the way it's supposed to be?"
This short video is sloppy, but will give you some idea of what nominalism is if you don't have a clue.
Why present evidence for something so obvious? Because there are a few 'liberals' whose thinking is not entirely emotion-driven and are therefore open to persuasion.
Patrick Flynn over at Substack supplements some thoughts of mine.
Top o' the Stack.
Substack latest.
One day, well over 40 years ago, I was deeply tormented by a swarm of negative thoughts and feelings that had arisen because of a dispute with a certain person. Pacing around my apartment, I suddenly, without any forethought, raised my hands toward the ceiling and said, "Release me!" It was a wholly spontaneous cri de coeur, a prayer if you will, but not intended as such. I emphasize that it was wholly unpremeditated. As soon as I had said the words and made the gesture, a wonderful peace descended upon my mind, and the flood of negativity vanished. I became as calm as a Stoic sage.
I wrote recently that the only way out is through, but Malcolm Pollack's most recent offering is much better; it is indeed brilliant. It divides into three parts. There is first a litany of what ails us. The second part explains why the ills listed are upon us. The general answer is that
. . . an aggressive, secular pseudo-religion, which denies all transcendent order and natural categories, has seized control of the minds of scores of millions of Americans, and of the levers of political power and information dissemination. This ersatz religion holds as its highest principle the flattening of every natural distinction, and all social hierarchies, except of course the hierarchy that places itself in the position of commanding power over every institution, and over all of civil society.
This general answer is then fleshed out with a list of the specific truths that the secular pseudo-religion brands as heresy.
The third part of the essay raises the question of what we can do about the miasmic mess we are in. Pollack rejects as hopeless three ways out that quite naturally suggest themselves: voting, a return to federalism, and armed revolt.
And then comes the startling suggestion:
Perhaps, then, it is best in the long run not to slow this process by incremental and ineffective political resistance. It may be that such an approach, by making the decay more gradual, will also make it somehow more bearable, day by day, and might turn it from an acute and intolerable affliction to a slow and chronic decline — a creeping Brazilification, a great national frog-boiling. Perhaps we would be wiser simply to let the cleansing fire of fever run its course, and burn itself out. It will be painful, and surely debilitating for a while, but then it will be over. And then, at last, we can awaken, blink our eyes, and get back on our feet.
Another term for the Big Guy might be all it takes. Four more years!!
In sum, the only way out is through, and the best way through is pedal-to-the-metal, balls-to-the-wall, lets-go-Brandon! Let Biden finish the job, as he intends to do, and thereby finish us off. After an ignominious death, resurrection, a new Phoenix from the old ashes.
Might I suggest an historical parallel? Germany gone mad had to be destroyed before it could be rebuilt into sanity. It is perhaps a good thing that Hitler, drunk on his initial success, and consumed with hubris, overextended himself, thereby bringing to an end National Socialist totalitarianism. And so it may also be a good thing to allow the totalitarian-globalist-'woke'- race-delusional-culturally Marxist scum now in control of our once-great Republic to bring her to her knees where she will repent, suffer, and die to be reborn.
The resident nominalist comments:
Nominalists say that the conception of an actual infinity of natural numbers depends on there being a set of all such numbers. But Ockhamists do not believe in sets. They say that the term ‘a pair of shoes’ is a collective noun which deceives by the singular expression ‘a pair’. Deceives, because it means no more than ‘two shoes’, and if there is only a pair of shoes, then there are only two things. But if a ‘pair’ of two things is a single thing, there are three things, the two things and the pair. Ergo etc.
I agree that there cannot be an actual infinity of natural numbers unless there is a (mathematical as opposed to commonsense) set of all such numbers. But of course this holds for all numbers, rational, irrational, transcendental, etc. Indeed, it holds for any category of item that is actually infinite. If there is an actual infinity of propositions, for example, then there must be a set of all propositions. I would point out however that there is nothing nominalistic about our friend's opening remark.
Nominalism kicks in with the claim that there are no sets. What there are are plural referring devices such as 'a pair of shoes' which fools us into thinking that in reality, i.e., extralinguistically, there are three things, a left shoe, a right shoe, and the pair, when there are only two things, the two shoes. The same goes for the following seemingly singular but really plural phrases: a gaggle of geese, a pride of lions, a parliament of owls, a coven of witches, etc.
This all makes good sense up to a point. When I put on my shoes, I put on one, then the other. It would be a lame joke were you to say to me, "You put on the left shoe and then the right one; when are you going to put on the pair?" To eat a bunch of grapes is to eat each grape in the bunch; after that task is accomplished there is nothing left to do. The bunch is not something 'over and above' the individual grapes that I still need to eat.
Consider now the Hatfields and the McCoys. These are two famous feuding Appalachian families, and therefore two pluralities. They cannot be (mathematical) sets on the nominalist view. But there is also the two-membered plurality of these pluralities to which we refer with the phrase 'the Hatfields and the McCoys' in a sentence like 'The Hatfields and the McCoys are families feuding with each other.'
If, however, a plurality of pluralities has exactly two members, as in the case of the Hatfields and the McCoys — taking those two collections collectively — then the latter cannot themselves be mere pluralities, but must be single items, albeit single items that have members. They must be both one and many. That is to say: In the sentence, 'The Hatfields and the McCoys are two famous feuding Appalachian families,' 'the Hatfields' and 'the McCoys' must each be taken to be referring to a single item, a family, and not to a plurality of persons. For if each is taken to refer to a plurality of items, then the plurality of pluralities could not have exactly two members but would many more than two members, as many members as there are Hatfields and MCoys all together. Compare the following two sentences:
1. The Hatfields and the McCoys number 100 in toto.
2. The Hatfields and the McCoys are two famous feuding Appalachian families.
In (1),'the Hatfields and the McCoys' can be interpreted as referring to a plurality of persons as opposed to a mathematical set of persons. But in (2), 'the Hatfields and the McCoys' cannot be taken to be referring to a plurality of persons; it must be taken to be referring to a plurality of two single items.
Or consider the following said to someone who mistakenly thinks that the Hatfields and the McCoys are one and the same family under two names:
3. The Hatfields and the McCoys are two, not one.
Clearly, in (3) 'the Hatfields and the McCoys' refers to a two-membered plurality of single items, each of which has many members, and not to a plurality of pluralities. And so we must introduce mathematical sets into our ontology.
My conclusion, contra the resident nominalist, is that we cannot scrape by on pluralities alone. (Man does not live by manifold alone! He needs unity!) We need mathematical sets or something like them: entities that are both one and many. A set, after all, is a one-in-many. It is not a mere many, and it is not a one 'over and above' a many. The nominalist error is to recoil from the latter absurdity and end up embracing the former. The truth is in the middle.
What I have given is an argument from ordinary language to mathematical sets. But there are also mathematical arguments for sets. Here is a very simple one. The decimal expansion of the fraction 1/3 is nonterminating: .33333333 . . . . But if I trisect a line, i.e., divide it into three equal lengths, I divide it into three quite definite actual lengths. This can be the case only if the the decimal expansion is a completed totality, an actual infinity, not a merely potential one. An even better example is that of the irrational number, the square root of 2 — it is irrational because it cannot be expressed as a ratio of two numbers, the numerator and the denominator of a fraction as in the case of of the rational 1/3. If the hypotenuse of a right triangle is units of length, that is a quite definite and determinate length. How could it be if the decimal expansion however protracted did not point to a completed totality, an actual infinity?
REFERENCES
Max Black, "The Elusiveness of Sets," Review of Metaphysics, vol. XXIV, no. 4 (June 1971), 614-636.
Stephen Pollard, Philosophical Introduction to Set Theory, University of Notre Dame Press, 1990.
The RFK [Jr.] Potential for Political Disruption
His main target was the corrupt relationship between large corporations and captured administrative bureaucracies. He has spent his career battling such corruption in the realm of environmental regulation and wants to use his knowledge and experience to expand that battle to the whole of the administrative state. In what might have been the biggest applause line of the night, he said as president he would never be muscled or manipulated by any bureaucrat or lobbyist.
[. . .]
To be sure, he has been on record in being among the climate-change alarmists in even recent history. Have his views on this topic shifted in light of the fake COVID science of the last three years and the lockdown experience? Perhaps so. Many people on the left have begun to rethink this topic and perhaps RFK is among them. He certainly seems to have zero interest in anything like a “great reset” and he is not a member of the World Economic Forum.
[. . .]
His next area was the most satisfying to me personally. He broke the public silence on the critical issue of COVID lockdowns. He chronicled the astonishing expense for which we gained nothing, and blasted companies like Amazon that censored contrary views while driving the competition out of business. He spoke with fire about the shutting down of small business and the violation of people’s property rights and religious liberties and illustrated a profound command of the facts, being how the lockdowns created an even worst public-health crisis.
[. . . ]
Finally, he called for a national conversation about this proxy war that is developing with Russia. The first excuse for U.S. involvement was purely humanitarian but it is mutating into yet another disaster along lines of the Iraq war. He demanded an immediate end to U.S. funding and a push for a diplomatic solution before it is too late. He further called for closing military bases around the world and bringing the troops home, plus a revival of U.S. economic strength. In the course of this discussion, he explained with great competence the threat to the U.S. dollar from the recent moves by BRICS to abandon trade in the dollar.
UPDATE (4/24) RFK, Jr. on why Tucker got the boot.
Here.
Were you draftable during the Vietnam era? What's your story?
UPDATE (4/23)
A correspondent and I both lament the non-inclusion of a certain period piece by Country Joe and the Fish. Said correspondent points out that the CJF tune is based on Louis Armstrong, Muskrat Ramble from 1926.
How might a socialist respond to the meme below?
One way is by committing the No True Scotsman Fallacy.
Another is by adapting the G.K. Chesterton riff: "Christianity hasn't failed; it's never been tried."
Is that the best socialists can do? If you want to weigh in on this, you'd best begin by defining 'socialism.'
DIVERSITY demands that crash dummies be of all sizes, shapes, races, ethnicities, animal species including trans-species hybrids such as the Cat Man, and also 'genders' including trans-dummies, and let's not exclude living humans who 'identify' as crash dummies the better to facilitate their exit from life's freeway.
EQUITY will then be served: an equal outcome will be achieved by all dummies including the dumb-assed Dems who 'identify' as inanimate dummies when they are 'merely' transgressive leftards.
INCLUSION rules out, or excludes, all conservatives from serving as crash dummies, and rules in all fat, ugly, 'vertically challenged,' and 'differently abled' persons especially such politicians as Lori Lightfoot and John Fetterman.
What am I mocking?
Top o' the Stack.
House Republicans voted Thursday to ban transgender female athletes from taking part in girls’ and women’s sports by amending Title IX protections to only apply to biologically female athletes.
The Protection of Women and Girls in Sports Act passed 219-203, with no Democrats supporting the measure.
Homebuyers with good credit scores will soon encounter a costly surprise: a new federal rule forcing them to pay higher mortgage rates and fees to subsidize people with riskier credit ratings who are also in the market to buy houses.
You see, self-control, self-reliance, deferral of gratification, financial responsibility and the like are 'white' virtues, and therefore 'racist.' 'Racists' whether white or black need to be punished with higher mortgage rates. 'Equity' demands it. In fact, credit ratings as such are 'racist' and 'white supremacist' and need to go the way of the SAT.
Consider the natural numbers (0, 1, 2, 3, . . . n, n +1, . . . ). If these numbers form a set, call it N, then N will of course be actually infinite. This because a set in the sense of set theory is a single, definite object, a one-over-many, distinct from each of its members and from all of them. N must be actually infinite because there is no greatest natural number, and because N contains all the natural numbers.
It is worth noting that 'actually infinite set' is a pleonastic expression. It suffices to say 'infinite set.' This is because the phrase 'potentially infinite set' is nonsense. It is nonsense (conceptually incoherent) because a set is a definite object whose definiteness derives from its having exactly the members it has. A set cannot gain or lose members, and a set cannot have a membership other than the membership it actually has. Add a member to a set and the result is a numerically different set. In the case of the natural numbers, if they form a set, then that set will be an actually infinite set with a definite transfinite cardinality. Georg Cantor refers to that cardinality as aleph-zero or aleph-nought.
I grant, however, that it is not obvious that the natural numbers form a set. Suppose they don't. Then the natural number series, though infinite, will be merely potentially infinite. What 'potentially infinite' means here is that one can go on adding endlessly without ever reaching an upper bound of the series. No matter how large the number counted up to, one can add 1 to reach a still higher number. The numbers are thus created by the counting, not labeled by the counting. The numbers are not 'out there' in Plato's topos ouranios waiting to be counted; they are created by the counting. In that sense, their infinity is merely potential. But if the naturals are an actual infinity, then they are not created but labeled.
Moving now from arithmetic to geometry, consider a line segment in a plane. One can bisect it, i.e., divide or cut it into two smaller segments of equal length. Thus the segment AB whose end points are A and B splits into the congruent sub-segments AC and CB, where C is the point of bisection. The operation of bisection is indefinitely ('infinitely') iterable in principle. The term 'in principle' needs a bit of commentary.
Suppose I am slicing a salami using a state-of-the-art meat slicer. I cannot go on slicing thinner and thinner indefinitely. The operation of bisecting a salami is not indefinitely iterable in principle. The operation is iterable only up to a point, and this for the reason that a slice must have a certain minimal thickness T such that if the slice were thinner than T it would no longer be a slice. But if we consider the space the salami occupies — assuming that space is something like a container that can be occupied — then a longitudinal (non-transversal) line segment running from one end of the salami to the other is bisectable indefinitely in principle.
For each bisecting of a line segment, there is a point of bisection. The question can now be put as follows: Are these points of bisection only potentially infinite, or are they actually infinite?
A Puzzle
I want to say that from the mere fact that the operation of bisecting a line segment is indefinitely ('infinitely') iterable in principle, it does not follow that the line segment is composed of an actual infinity of points. That is, it is logically consistent to maintain all three of the following: (i) one can always make another cut; (ii) the number of actual cuts will always be finite; and that therefore (iii) the number of points in a line will always be finite, and therefore 'infinite' only in the sense that there is no finite cardinal n such that n is the upper bound of the number of cuts.
At this 'point,' however, I fall into perplexity which, according to Plato, is the characteristic state of the philosopher. If one can always make another cut, then the number of possible cuts cannot be finite. For if the number of possible cuts is finite, then it can longer be said that the line segment has a potentially infinite number of points of bisection. It seems that a potential infinity of actual cuts logically requires an actual infinity of possible cuts.
But then actual infinity, kicked out the front door, returns through the back door.
I have just posed a problem for those who are friends of the potentially infinite but foes of the actual infinite. How might they respond?
The urge to retreat is tempting, but the only way out is through. To float above the fray in the manner of a Rod Dreher is not the way; the only way out is through.
Minervic flights and the consolations of philosophy cannot be enjoyed when the barbarians are at the gates of one's stoa.
Now you know why I mix the abstruse and theoretical with the political and practical.
Conservatives, especially those of them given to contemplative pursuits, need to make their peace with activism in order to secure and defend the spaces of their quietism. And this with blood and iron if need be.
The owl of Minerva is a tough old bird, but no phoenix capable of rising from its ashes.
When the world and its hopelessness are too much with us, one can and must beat a retreat into the private life and the pleasures and pursuits thereof: body culture, mind culture, hobbies, family life, the various escapes (which are not necessarily escapes from reality) into chess, fiction, prayer, meditation, history, pure mathematics and science, one's own biography and the pleasant particulars of one's past, music, gardening, homemaking . . . . But all this by way of recuperation for the battle.
I pity the poor activist for whom the real is exhausted by the political. But I detest these totalitarians as well since they seek to elide the boundary between the private and the public.
So we need to battle the bastards in the very sphere they think exhausts the real. But it is and must be a part-time fight, lest we become like them. Most of life for us conservatives must be given over to the enjoyment and appreciation, in private, of the apolitical: nature, for example, and nature's God.
units of length, that is a quite definite and determinate length. How could it be if the decimal expansion however protracted did not point to a completed totality, an actual infinity?