William E. Mann, God, Modality, and Morality

Vallicella, William F. (2016) "William E. Mann, GOD, MODALITY, AND MORALITY," Faith and Philosophy: Journal of the Society of Christian Philosophers: Vol. 33 : Iss. 3 , Article 8. DOI: 10.5840/faithphil201633368

Available here. A long and meaty review article including a discussion of divine simplicity and Mann's approach thereto.

Weyl’s Tiles: An Argument against Discrete Space

Is physical space, the space of the natural world, continuous or discrete? If composed of space atoms, then discrete. The Weyl Tile argument (WTA), however, seems to show that physical space cannot be discrete or 'quantized' and therefore must be continuous. This is relevant to our ongoing debate about potential versus actual infinities. For if physical space cannot be discrete, then it must be at least compact (the lowest grade of continuity), where "A series is called compact when no two terms are consecutive, but between any two there are others." (Bertrand Russell, Our Knowledge of the External World, Norton, 1929, p. 144.) But if between any two points in space there are others, then there are infinitely many others, so that any line segment will be composed of an actual infinity of points.

But before we return to the question of actual infinities we need to get clear about the WTA itself. The nervus probandi lies in the following quotation from Hermann Weyl, Philosophy of Mathematics and Natural Science, Princeton UP, 1949, p. 43:

If a square is built up of miniature tiles, there are as many tiles along the diagonal as along the side; thus the diagonal should be equal in length to the side.

Take a gander at the chess board below. Consider the right triangle the sides of which are a1-a8 and a1-h1, and the hypotenuse of which is the diagonal a8-h1.  The sides and the diagonal are each eight squares long.  Count 'em and see. But this flies in the face of the theorem of Pythagoras.  If the sides are each eight units in length, then the hypotenuse is equal to the square root of  (82 + 82 =128), which is not 8, but the irrational 11.313 . . .  

Chess boardThe question this curious fact raises is whether physical space can be quantized, i.e., whether there are space atoms. If so, space is discrete as opposed to continuous. It may help to bear in mind that the above array is a mere model in continuous space of discrete space.  So it will do no good to object that if space atoms are squares, then the theorem of Pythagoras hold for them.  Space atoms are not squares: they have no shape at all. But I am getting ahead of my story.

We need to define our terms. Space is discrete just in case every finite extended spatial region is composed of finitely many atomic spatial regions. That amounts to saying that every finite extended region of space is composed of finitely many space atoms, where 'atom,' as its etymology suggests, implies indivisibility.  You cannot 'split' a space atom because such atoms are inherently 'unsplittable.'  A space atom is thus an individual that has no proper parts: it is  a mereological atom. A non-atomic region of space is then a mereological sum of space atoms. Note that every space atom, precisely because it is an atom, is an unextended region of space. It's an itty-bitty unextended bit of space itself, not of something in space. Space atoms are not in space; they compose space.  

Now for the argument:

1) The theorem of Pythagoras is not true (or even approximately true) of discrete space.

2) The theorem of Pythagoras is true (or approximately true) of actual space. Therefore:

3) Actual space is not discrete.  

To understand this argument, you have to understand that nothing rides on how small the tiles/squares are. Glance back at the chessboard. Consider the small right triangle in the bottom left corner of the board. Opposing sides and hypotenuse all have a length of two units.  So it doesn't matter how small the space atoms are. No matter how small the squares, the hypotenuse remains equal in length to the other two sides.

You will be tempted to think of the array of tiles/squares against the backdrop of continuous Euclidean space for which the Pythagorean theorem holds.  Thinking in this way, you will imagine that no matter how small you make the tiles, the diagonal will be longer than the sides. You have to resist this temptation to understand the 'Weyl tile' (vile tile?) argument. For if there are space atoms,  then they have no shape and hence no different dimensions in different directions. As Wesley C. Salmon puts, "In discrete space, a space atom constitutes one unit, and that is all there is to it. It cannot be regarded as properly having a shape, for we cannot ascribe sizes to parts of it — it has no parts." (Space, Time, and Motion, U of Minnesota Press, 1980, p. 66) 

I have found K. McDaniel, "Distance and Discrete Space," Synthese (2007) 155: 157-162, very helpful. He has an argument against the WTA which I may discuss in a subsequent post.

Masculinity

Out and about yesterday, I caught a bit of Dennis Prager's radio show. He defended Daniel Penny's behavior in his confrontation with Jordan Neely as masculine, using the word correctly. In our infantilized, feminized, and left-dominated and therefore crime-tolerant society, Penny's behavior will be called toxically masculine by our political enemies. But to anyone who can think straight, there is a difference between the masculine and the toxically masculine.

On the other hand, there are people to my right, politically speaking, who deny that there is any toxic masculinity.  I must oppose them too.  I say to them: Are you seriously going to maintain that there are no instances of machismo that are not reasonably described as 'toxic'?

Consider the sad case of Cynthia Garcia. This foolish middle-aged woman and mother thought it would be fun to party with the Hells (no apostrophe!) Angels in their Mesa, Arizona clubhouse of a Saturday night. The 'Angels' of course demanded sex; she showed disrespect, even after they stomped her, and so they brutally murdered her. There are differing accounts of the exact details.  But the upshot was indeed brutal. Two of them stabbed her to death and attempted to cut her head off,  dumping her remains in the desert proximal to the Rio Salado shooting range.
 
Of course, normal masculine behavior such as that displayed by Penny is not toxic, and the feminization of boys is a serious threat to social stability and the survival of the Republic. But just as a Nazi is no cure for a commie, a biker brute is no cure for a feminized boy.
 
The subversion of language is the mother of all subversion. 
 
You should no more allow the Left's theft of perfectly good English words than you should allow their question-begging and question-burying coinages such as 'Islamophobia' and 'homophobia' and 'transphobia.' I have gone over this many times and I am not in the mood to repeat myself.  Enough compromising with our political enemies; resist them on every front.
 
Addendum
 
William Voegli weighs in on the Penny-Neely encounter at City Journal: 

Are New York’s subways safer, its homeless population less dangerous, than is generally believed? Than Tarannum and, perhaps, Daniel Penny seemed to think? The Times pointed out in February that the rate of violent felonies on the subway system was twice as high in 2022 as it had been in 2019. The system saw ten people murdered in 2022, compared with an average of two per year from 2015 through 2019. On the other hand, the Times pointed out that even after this increase, there were 1.2 violent crimes for every 1 million subway rides, which works out to about the likelihood of being injured during a two-mile automobile trip. Readers deliberating how much reassurance to derive from such statistics may reflect on the Times’s utter lack of such restraint and sobriety following the death of George Floyd in 2020, when the paper made no attempt to caution against sweeping generalizations based on the anomalous death of an unarmed black man in police custody.

You might want to bear in mind that truth is not a leftist value, and that leftists have a strange propensity to celebrate the dysfunctional, the transgressive, the grotesque, and the socially worthless as part of their nihilist drive to normalize deviant behavior, all the while attacking the sane, the decent, the socially useful, including the subway commuters on their way to work.  

This brings up a second point raised by Rahnuma Tarannum, about how the authorities not doing their job puts civilians in a position where they either do it themselves or suffer the consequences of no one doing it. 

Abdication of authority has dire consequences. Leftists unwittingly (or is it wittingly?) promote vigilantism. Remember Bernie Goetz, the subway gunman? In the same way, leftists unwittingly (or is it wittingly?) promote increased gun ownership among civilians. Either unable or unwilling to distinguish weapon from wielder, lefties unrelentingly repeat that guns cause crime. But then demonstrating their lack of common sense, they agitate for the defunding of police, the ratcheting down of criminal penalties, etc. So the people arm themselves. Surprise! How stupid can a 'liberal' be?

I am a staunch supported of 2A rights, but being sane and reasonable I don't want more and more untrained civilians packing heat.

It is true, as Bouie says, that no one on Jordan Neely’s subway car had any way to know that he had been arrested 42 times, including at least four times for punching people, two of which occurred in the subway system. Nor could they have known that Neely was on “the ‘Top 50’ list,” which, the Times explained, is a “roster maintained by the city of . . . people living on the street whom officials consider most urgently in need of assistance and treatment.” Lacking such knowledge, Bouie contends, Neely’s fellow passengers were obligated to give him the benefit of the doubt. 

‘Asylum Seekers’

Is a home invader an asylum seeker? Only in very rare cases.  So why are people who immigrate illegally called asylum seekers? A few are but most are not. What we have here, once again, is the characteristic 'progressive' abuse of language.  At the same time that so-called progressives abuse 'asylum,' they also abuse 'xenophobic' when they apply this terms to those of us who stand for the rule of law. You are one dumb conservative if you acquiesce in the Left's abuse of language.  He who controls the terms of the debate controls the debate.

The Childless as Anthropological Danglers

Top o' the Stack. 

The Austrian philosopher and Vienna Circle member Herbert Feigl wrote about nomological danglers.  Mental states as the epiphenomenalist conceives them have causes, but no effects. They are caused by physical states of the body and brain, but dangle nomologically in that there are no laws  that relate mental states  to physical states.

The childless are anthropological danglers.  They are life's epiphenomena. They have ancestors (causes) but no descendants (effects). Parents are essential: without  them we could not have come into fleshly existence.  But offspring are wholly inessential: the individual, though not the species, can exist quite well without them.

I mention pros and cons of dangling anthropologically.