Footnotes to Plato from the foothills of the Superstition Mountains

  • On Blaming the Victim

    Top o' the Stack.


    2 responses to “On Blaming the Victim”

  • The Demented Dems: Anti-Reality and Anti-Virtue

    Anti-reality:

    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.

    Anti-virtue:

    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.


    3 responses to “The Demented Dems: Anti-Reality and Anti-Virtue”

  • On Potential and Actual Infinity, and a Puzzle

    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. 

    SalamiSuppose 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?

     

     

     

     

     

     


    7 responses to “On Potential and Actual Infinity, and a Puzzle”

  • The Only Way Out is Through

    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.

    The only way out is through.


  • Vox missa nescit reverti

    Good advice from Horace, Ars Poetica, 390: "A word, having been sent forth, does not know how to return." 


  • A New Budweiser Joke

    One of the old ones goes like this. "Ah had me a coupla Buds, but ahm none the wiser."  I suggest as part of the punch back against the Anheuser-Busch Dylan Mulvaney wokery, the following:

    I had me a couple of Buds and my schlong's no longer a riser.

    But I am sure you can do better than that; combox open.

    The logically prior question, of course, is why anyone of taste and discernment would drink the swill served up by Anheuser-Busch when you can drink some such fine German brew as St. Pauli Girl the poster 'boy' of which is a buxom wench (in sense 1) who is not only unambiguously female but also stacked and packed to the nines and hence in violation of all  canons of wokery known to man.

    If your head is screwed on Right, you will enjoy DeSantis' take on this brew-haha (I'm punning on brouhaha, as I'm sure you've noticed.)

    Time to man up and bone up on your political ponerology the better to punch back against the 'woke' kakistocracy and all its works. Not much is at stake, of course, except the survival of civilization.

    St Pauli Girl

     

     


    4 responses to “A New Budweiser Joke”

  • The Grain Problem

    Ed Buckner writes,

    Here is another problem that needs to be carefully phrased.

    I want to say that the pitch of a musical note is continuous through time. I mean, at any point in continuous time, i.e. time as specified by the real numbers, the pitch of the note (e.g. middle C) is the same.

    However, the “physical” property that grounds the pitch is not continuous, but rather a cycle of different events.

    That strikes me as a problem for the kind of physicalism according to which qualities “as we perceive them” are identical with the properties that ground them. For pitch is temporally continuous, the oscillation that grounds it is not temporally continuous, ergo etc.

    It is a problem indeed, Ed, although I have questions about your formulation of it.

    The problem is known in the trade as the Grain Problem. Whether it surfaces before Sir Arthur Eddington, I don't know, but he raises it, or at least anticipates it with his question about the 'two tables.'  A lot of work was done on the Grain Problem by the great American philosopher Wilfrid Sellars, son of the rather less distinguished Roy Wood Sellars, but nonetheless a quantity to be reckoned with in his day.

    Sellars  Wilfrid IntentionalityHere is Sellars fils  in his seminal essay, "Philosophy and the Scientific Image of Man," reprinted in his Science, Perception, and Reality (Routledge, 1963). The portion I am about to quote is from pp. 35-37. I take the text from Chrucky's online version.

    It is worth noting that we have here a recurrence of the essential features of Eddington's 'two tables' problem — the two tables being, in our terminology, the table of the manifest image and the table of the scientific image. There the problem was to 'fit together' the manifest table with the scientific table. Here the problem is to fit together the manifest sensation with its neurophysiological counterpart. And, interestingly enough, the problem in both cases is essentially the same: how to reconcile the ultimate homogeneity of the manifest image with the ultimate non-homogeneity of the system of scientific objects.

    BV: Whether we are discussing colors with Sellars or sounds with Buckner, it is the same problem, that of reconciling the homogeneity of the manifest or phenomenal sensory quality with the non-homogeneity of the underlying  scientific explanatory posits. For Sellars, of course, these posits are not mere posits but ultimately real, as you will see if you read below the fold.

    Buckner's formulation above leaves something to be desired, however. He cites the continuous perception over time of the same note, middle C, let us say. But then in the very next sentence he reverts to a rarefied mathematical concept of continuity, thereby mixing phenomenological description with a mathematico-scientific construct.   He thereby conflates phenomenal continuity with mathematical continuity.  When I hear middle C sounding from an organ, say, over a non-zero interval of time, five seconds say, do I hear a series of points of time — a series of temporally extension-less moments — the cardinality of which is 2-to-the-aleph-nought? No. (The cardinality of the set of real numbers (cardinality of the continuum) is

    And then Ed goes on to say that "the 'physical' property that grounds the pitch is not continuous, but rather a cycle of different events." But that is not right either. Middle C depicted on an oscilloscope shows up as a sine wave:

    Middle_C _or_262_hertz _on_a_virtual_oscilloscope

    Obviously the sine wave is continuous. What Ed wants to say, of course, is that the heard sound, the phenomenal sound, does not fluctuate as does the physical reality does, the physical reality that "grounds the pitch." Ed is equivocating on 'continuous.'

    But I know what he is getting at, and it is a genuine problem. I am merely complaining about his  formulation of it. Now back to Sellars, whose solution to the problem is not clear to me.

     

    (more…)


    14 responses to “The Grain Problem”

  • Why are People so Easy to Swindle?

    My answer at Substack.


  • De-Dox Your Glove Box!

    And what might I mean by that?

    I mean remove documents from your glove compartment or other easily accessible areas in your vehicle wherein it would be unwise to carry them given the spike in crime of all sorts caused by such Democrat policies as defunding the police and eliminating cash bail. I count four levels of foolishness in decreasing levels of inadvisability:

    1) Carrying your driver's license in the glove box.

    2) Carrying the title to the vehicle in the glove box.

    3) Carrying the vehicle registration in the glove box.

    4) Carrying insurance cards in the glove box.

    Since smash and grab is quick and easy and on the rise, the wise do not leave personal information easy of access in their vehicles. (You might want to look into installing a serious console or under-seat lock box.) One scenario goes like this: the thug learns your address and swipes your garage door opener. Now they have easy access to your garage and its contents,  and if you are foolish enough to leave the door to your domicile unlocked, access to your house and its contents including wife and children.


    One response to “De-Dox Your Glove Box!”

  • Tongue and Pen

    Top o' the Stack.

    Christ has harsh words for those who misuse the power of speech at Matthew 12:36: "But I say unto you, that every idle word that men shall speak, they shall give account thereof in the day of judgment."  But what about every idle word that bloggers blog and Substackers stack?  Must not the discipline of the tongue extend to the pen?


    8 responses to “Tongue and Pen”

  • The Pragmatic and the Evidential

    Substack latest.

    On believing beyond the evidence. Immoral? Irrational?


    2 responses to “The Pragmatic and the Evidential”

  • The Biden Maladministration is Placing Us in Grave Danger

    No, you useful idiots, white supremacy is not the greatest threat we face: it is no threat at all since it doesn't exist. A real threat we face, and a very serious one, is posed by an EMP directed against our unprotected grid.  HT to JSO for the following two videos. 

    How would a nuclear EMP affect the power grid?

    How long would society last during a total grid collapse?

    Addendum 4/12:

    A reader refers us to Are Aircraft Carriers Unsinkable? and comments, 

    The whole article is hair-raising, but this jumped out at me:

    About the same time that tensions were rising over Nancy Pelosi’s visit to Taiwan, reposts of a 2020 article by Major General Ed Thomas, the Commander of the Air Force’s Recruiting Service, began to pop up in the media.  The headline?  “Eighty-six percent of Air Force pilots are white men. Here’s why this needs to change.” Too many white men? Is that what our generals worry about? Like many other military top-brass, Major General Thomas seems to think that diversity wins wars.  That’s why he put “improving diversity” on “the top of my to-do-list.”

    What if, in the meritocracy the armed services are supposed to be, not enough nonwhites cut the mustard? Promote them anyway?
     
    BV: This goes to the heart of the matter, namely the assault on merit in favor of 'diversity,' 'equity,' and 'inclusion'  which in practice amount to governmentally enforced proportional  representation, equality of outcome, and exclusion of 'racists' and 'white supremacists.'  The destructive DEI agenda is predicated upon reality denial, in particular, the denial of the reality that we are not equal either as individuals or as groups in those empirically measurable respects  that bear upon qualification for jobs and positions.   The DEI agenda is dangerous and destructive because it allows the physically feeble and disabled, the mentally incompetent, the morally defective, and the factually ignorant and untrained to occupy high positions in government and industry. But 'allow' is too weak a word in this context; 'promote' is more to the point.  
     
    One reason this is dangerous is that our geopolitical adversaries do not subscribe to the destructive DEI ideology. While we self-enstupidate, they salivate. 
     
    How explain the popularity of DEI among the useful idiots?  I suggest that it is due, at least in part, to the 'feel-good' nature of the DEI 'reforms.' They are found very appealing in this, the Age of Feeling.
     
    How explain the popularity of DEI among the drivers of the demented doctrine? In the case of Major General Ed Thomas and his ilk it is probably sheer careerism. They go along not just to get along but to advance themselves career-wise, and the nation and the world be damned. It strains credulity to think that they actually believe the rubbish.
     
    There's a bad moon rising, and trouble's on the way. 

    8 responses to “The Biden Maladministration is Placing Us in Grave Danger”

  • Globalist-Capitalist Woke Leftism II

    On 26 January I wrote:

    The new global-capitalist woke leftism (GCWL) is very different from the old socialist-humanist leftism (SHL, which I take to include both the Old Left and the New Left). I want to understand the similarities and the differences.

    GCWL versus SHL

    1) Both are secular and anti-religion.  Since 1789 the Left has been virulently anti-clerical and anti-religious. Nota bene: an ersatz religion is not a religion! So stop calling leftism a religion, Dennis Prager.

    2) Both target the middle class.

    3) Both are internationalist  and anti-nationalist.

    4) The main difference seems to be that SHL is humanist while GCWL tends toward the erasure of humanity and humanism via anti-natalism, paganism, nature-idolatrous environmentalism, misanthropy, Orwellian subversion of language, and leukophobic ethno-masochism and much else besides.

    So that's a start. Inadequate, no doubt.

    James Soriano responded this morning:

    I liked your January 26 post on the Globalist-Capitalist Woke Leftism, as well as the comments.

    Here are a couple of points on the dissimilarities of the “Woke” compared to the “Old” and “New.” 

    (1)  Both the Old Left and the New Left were hostile to capitalism, whereas the Woke Left finds it a useful tool.  Today corporations big and small have become “woke” and are friendly to the Woke agenda.  Any corporation insufficiently sympathetic to the Woke agenda is bullied until it wakes up.

    (2)  The Old Left got a Russian assist.  After WWI, Russia secretly supported Communist parties and allied organizations in Europe and elsewhere.  These subversive activities continued after WWII and into the New Left period.  By contrast, the Woke Left gets an American assist.  It is not secretive in any way.  It’s in the open.

    (3)  The Old Left and the New Left thought of  “revolution” as something that originates in society and then goes on to take over the state.  But “woke” attitudes have already penetrated into the state.  To a “woke” leftist, a revolution can also be something that moves from the state back into society for the purpose of stomping out pockets of resistance.

    ——

    On this last point, we can make a distinction between a revolution BEFORE power and a revolution AFTER power.  

    Revolutions taking place before the revolutionaries consolidate power:  Americans in 1776, Mao in China, Castro in Cuba, and Khomeini in Iran.

    Revolutions taking place after the revolutionaries consolidate power:  

    — 1917.  A small group of Bolsheviks take over the seat of government in St. Petersburg.  The Russian Revolution took place after that event; there was no Bolshevik uprising prior to it.  

    — 1932.   The National Socialist German Workers' Party came to power by democratic means.  The Nazi transformation of Germany took place after that event; there was no Nazi uprising prior to it. [It was 1933 — BV]

    — Historian Martin Kramer makes this revolution-before-and-after distinction regarding “moderate” Islamists.  Many people in the Arab World fear that “moderates” like the Muslim Brotherhood would use democratic means to take over the state.  They would then go on to Islamize society after they take power.  Wokesters are like that, too.

     


    7 responses to “Globalist-Capitalist Woke Leftism II”

  • Bars Philosophers Opened after being Denied Tenure

    HT: Allan Jackson:
    Beer and Trembling
    Gin and Platonic
    Phenomenology of Spirits
    Martini Heidegger
    Bellini and Nothingness
    Jean-Jacques & Coke
    Vodka on the Lockes
    Maker’s Marx Old Fashioned.
    To this list I add:
     
    Rusty Nagel's. (If you got that, I will buy you the cocktail to which I am alluding.)
     
    Continuing in the humorous vein, Allan offers:
     
    Heraclitus walks into a bar.
    Bartender: Oh…You again?
     
    I counteroffer:
     
    Zeno tries to walk into a bar.
     
    Russell never walks into bars, he is only on occasion at bar-proximal places at bar-open times.
     
    McTaggart, however, has no time for bars at all.
     
    Van Inwagen doesn't believe in bars, but only in bottles and bricks arranged barwise.
     
    Jon Barwise was not available for comment.

  • Amerika, the Police State

    Have you been paying attention, or are you a useful idiot?

    America, No Turning Back

    The Catholic Case for Guns

    A Maoist Cultural Revolution?


    2 responses to “Amerika, the Police State”


Latest Comments


  1. https://www.thefp.com/p/charles-fain-lehman-dont-tolerate-disorder-charlie-kirk-iryna-zarutska?utm_source=substack&utm_medium=email

  2. Hey Bill, Got it now, thanks for clarifying. I hope you have a nice Sunday. May God bless you!

  3. Vini, Good comments. Your command of the English language is impressive. In my penultimate paragraph I wrote, “Hence their hatred…

  4. Just a little correction, since I wrote somewhat hastily. I meant to say enemies of the truth (not from the…

  5. You touched on very, very important points, Bill. First, I agree that people nowadays simply want to believe whatever the…

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