Plato's "Hidden Theorem on Distribution of Primes"

While I was trying to remember where Aristotle says the thing about primes that Parmenides said, I came across this paper. It argues that the 5,040 number in Plato's Laws (which you will remember from the long series on the Laws here over the winter) hides a secret theorem. 

I'm not sure about that, but read it for yourself if you like. The full text is there, and it's short.

Against Karl Popper

I've always liked Popper's answer, but hear them out. First, what is the answer?

Popper was struck by Einstein’s prediction. “Now the impressive thing about this case,” he wrote decades later, “is the risk involved in a prediction of this kind.” Had the measurements found Einstein in error, Popper said, the physicist would have been forced to abandon his theory. Popper built his demarcation criterion around the bravado of wagering against refutation: “One can sum up all this by saying that the criterion of the scientific status of a theory is its falsifiability, or refutability, or testability.”

Second, what was the answer meant to contrast?

All demarcation criteria are designed to exclude something. What Popper really wanted to do was to show why psychoanalysis and Marxism were not scientific. Those theories had been widely understood as “scientific” in his Viennese milieu because of a logical empiricist theory called verificationism. According to this view, a theory is scientific if it is verified by empirical data.

From my perspective, successfully excluding Marxism and psychoanalysis from science justifies the project. However, others have disagreed, and not only Marxists and psychoanalysts. 

First, it is difficult to determine whether you have actually falsified a theory....  Not so fast. How do you know that your experimental result was accurate?

That's a terrible objection. Falsification is about whether or not the theory could in principle be falsified. The fact that it may be hard to do is quite different from the objection to Freud's theories, wherein a man who e.g. didn't appear to have any Oedipal concerns would just be said to be suppressing or projecting them or whatever. Marxism, too: Lenin wrote a book about how Marx's theory's failure to materialize was just a further proof of how right he was about the evils of capitalism. These theories aren't falsifiable because they let you just tell another story about how they were right all along. 

Yes, the instrument could be wrong; do it again. But if there's not a fact of the matter that could falsify a theory if known, it's not science.

The second problem with Popper’s proposal has to do with the actual demarcations it gives us. The very minimum we should expect from a demarcation criterion is that it slices the sciences in the right places. We want our criterion to recognize as scientific those theories that are very generally accepted as hallmarks of contemporary science, such as quantum physics, natural selection, and plate tectonics. At the same time, we want our criterion to rule out doctrines such as astrology and dowsing. Popper’s falsifiability standard is not especially helpful in this regard. For starters, it is difficult to present the “historical” natural sciences, such as evolutionary biology, geology, or cosmology—those fields where we cannot “run the tape again” in the laboratory—exclusively in terms of falsifiable claims. Those sciences provide persuasive explanations of nature through the totality of a narrative chain of causal inference rather than a series of empirical yes-no votes. Popper thus inadvertently excludes important domains of contemporary science.

I would argue that this is also a terrible objection. To say that you want to "slice the sciences in the right places" indicates that you think you already know where the slices should be made. Actually, Popper raises an important objection to theories even from these widely recognized fields: they aren't doing quite the same thing as the sciences that can provide replicable testing, and their theories remain rather more theoretical as a consequence. They're not in the same category as Marxism, but maybe that only means that there is Hard Science, and then degrees of distance from it. I'm inclined to score this Popper 2, objections 0 so far.

The situation with inclusion is even worse. The difficulty was sharply expressed by philosopher of science Larry Laudan in an influential article from 1983. Popper’s criterion, he wrote,

has the untoward consequence of countenancing as “scientific” every crank claim that makes ascertainably false assertions. Thus flat Earthers, biblical creationists, proponents of laetrile or orgone boxes, Uri Geller devotees, Bermuda Triangulators, circle squarers, Lysenkoists, charioteers of the gods, perpetuum mobile builders, Big Foot searchers, Loch Nessians, faith healers, polywater dabblers, Rosicrucians, the-world-is-about-to-enders, primal screamers, water diviners, magicians, and astrologers all turn out to be scientific on Popper’s criterion—just so long as they are prepared to indicate some observation, however improbable, which (if it came to pass) would cause them to change their minds.

OK, that one's better. Popper's criterion may not be sufficient to exclude fields that are easily falsifiable because they are crazy. We might need to address that objection to have a proper definition of hard science. That seems to be the evolving position, and it's not that hostile to Popper: he said something important, but he may have mistaken that something for everything.

Other approaches might prove more successful. Philosopher and former professor of biology Massimo Pigliucci, for example, has suggested that the problem with falsicationism is its one-dimensionality, not its effort to establish clear criteria. Perhaps we could add more dimensions that correspond to the heterogeneity of scientific practice. 

You Don't Say

Theroux gets that readers might perceive him as cranky, but he thinks the problem might be with the readers. 

Paul Theroux gets older.

His new novel tells the story of Joe Sharkey, an aging North Shore surfer... Sharkey feels acutely that he is being overtaken by younger surfers with big endorsements. For him, surfing was a way of life, an existence centered on catching waves, a commitment to the ocean.

Theroux sees surfing as a metaphor for his own life.... like the surfer past his prime, he is not immune to feeling forgotten, to the sense that the world has become hostile to the pure joy of the waves. There’s a fear of being overlooked, unread.

“I was once a hot shot, I was once the punk,” Theroux said. “And anyone who has once been a punk, eventually you’re older, and you see the turning of the years as it is."

Well, he has had more attention than most; and more wealth and success, too. But there is still a kind of universality to the experience of growing older.  

This looks like fun

"Conservatism" is No Longer Enough

A provocative and worthy piece at The American Mind, by Glenn Ellmers.

Fewer are willing to take the next step and accept that most people living in the United States today—certainly more than half—are not Americans in any meaningful sense of the term.

I don’t just mean the millions of illegal immigrants. Obviously, those foreigners who have bypassed the regular process for entering our country, and probably will never assimilate to our language and culture, are—politically as well as legally—aliens. I’m really referring to the many native-born people—some of whose families have been here since the Mayflower—who may technically be citizens of the United States but are no longer (if they ever were) Americans. They do not believe in, live by, or even like the principles, traditions, and ideals that until recently defined America as a nation and as a people. It is not obvious what we should call these citizen-aliens, these non-American Americans; but they are something else.

That's a very grave problem statement. Is it just? I wonder about the percentage -- "certainly more than half" may be overstating the numbers -- but it is certainly true of some percentage. Percentages aside, too, it seems to be true especially of the part that occupies all the seats of power: in government, both elected and the bureaucracy; in corporations; in the media, to include news, social media, and entertainment; and, at the moment at least, even in top positions of the military. 

Sad times for MIT

I kept reading aloud Townhall excerpts from this extraordinary MIT paper to my husband, who kept insisting that it was a hoax. It does sound as though someone were auditioning for the Bee, and sailing very close to the wind.

[C]alling for increased media literacy can often backfire: the instruction to ‘question more’ can lead to a weaponization of critical thinking and increased distrust of media and government institutions . . . . [C]alls for media literacy can often frame problems like fake news as ones of personal responsibility rather than a crisis of collective action. . . . [Anti-maskers] value unmediated access to information and privilege personal research and direct reading over "expert" interpretations. . . . As a subculture, anti-masking amplifies anti-establishment currents pervasive in U.S. political culture. . . . Data literacy, for anti-maskers, exemplifies distinctly American ideals of intellectual self-reliance, which historically takes the form of rejecting experts and other elites. The counter-visualizations that they produce and circulate not only challenge scientific consensus, but they also assert the value of independence in a society that they believe promotes an overall de-skilling and dumbing-down of the population for the sake of more effective social control. As they see it, to counter-visualize is to engage in an act of resistance against the stifling influence of central government, big business, and liberal academia . . . . Most fundamentally, the groups we studied believe that science is a process, and not an institution.

The solution?

Convincing anti-maskers to support public health measures in the age of COVID-19 will require more than ‘better’ visualizations, data literacy campaigns, or increased public access to data. Rather, it requires a sustained engagement with the social world of visualizations and the people who make or interpret them.

"Social," posited as an alternative to data literacy and explained as a "sustained engagement with the social world," remains a little fuzzy to me. Shaming? Censorship? Police raids? How I hope this turns out to be a Sokal hoax.

Holy Week

If any of you are Jews, Passover was I understand yesterday; I hope your holiday was satisfying. For Christians, of course today is Palm Sunday and the start of Holy Week. (If we have any Muslim readers, I note with surprise that Ramadan will also fall at nearly the same time this year, beginning on the 12th of April. A sacred spring for us all, this year.)

This is the occasion of one of my favorite stories from scripture. Probably I am guilty, like many, of focusing too much on the parts that appeal to me personally. I love the story of Jesus riding an unbroken colt, though. This is Luke 19:28-36:

28 After Jesus had said this, he went on ahead, going up to Jerusalem. 29 As he approached Bethphage and Bethany at the hill called the Mount of Olives, he sent two of his disciples, saying to them, 30 “Go to the village ahead of you, and as you enter it, you will find a colt tied there, which no one has ever ridden. Untie it and bring it here. 31 If anyone asks you, ‘Why are you untying it?’ say, ‘The Lord needs it.’ ” 32 Those who were sent ahead went and found it just as he had told them. 33 As they were untying the colt, its owners asked them, “Why are you untying the colt?” 34 They replied, “The Lord needs it.” 35 They brought it to Jesus, threw their cloaks on the colt and put Jesus on it. 36 As he went along, people spread their cloaks on the road. 

You try riding an unbroken colt sometime, and see if it's as easy as that for you.  

A Good Day for Strongmen

At the Central Georgia’s Strongest Man competition today, resumed after COVID, a man named Shannon Willits finished his courses and then perished. The best of us can hope for no better. He died in competition after finishing a set of heavy farmer’s walks carries and an immediate heavy bag carry. Most people couldn’t do either, given all the time in the world. 

A fit and worthy death. God send us each such when our time comes. 

Plato's Parmenides VIII, The One III: Time

This is a long section, so I'm going to put it beyond a jump. It's important to note at the beginning that this dialogue was written before almost any of the philosophy of time. Aristotle wrote one of the most important pieces on time in the ancient world, Plotinus another, and St. Augustine wrote another one. None of that thinking was available to Plato or to Parmenides. We saw in the preface to this series that Zeno appears to have believed that time, like space, was atomic in nature; Aristotle rejected both, but his rejection has not yet appeared. 

There are a lot of philosophical problems about time. One of them is the status of things (like ourselves) that seem to be extended in time. I can remember existing yesterday. Does that me still exist somewhere? For Zeno, the answer might be yes: there might be a 'time atom' (or rather a whole series of them) in which yesterday me still exists, and permanently (and changelessly). Or it might be 'no,' just as easily: that only the present time atom exists, neither one before nor one after. Both views admit of his apparent theory that change is impossible: the first view for the reasons we've already seen, as about the arrow that must be frozen in time because at any atom of time it is frozen; the second because, if only the current time atom actually exists, there is nowhere to move from or to move towards. 

Lacking a built-out philosophy of time this bit is quite difficult to follow. It is at odds with the way that we tend to think about time. The basic problem is that the one cannot be many, but if it exists through time there will be a part of it that is younger than itself (i.e., the part that existed yesterday) and a part that is older (i.e., the part that will exist tomorrow). The One cannot, then, be in time. This is another reason it can neither 'come to be' nor perish.

You Don’t Say

NCO: Most soldiers thought extremist training was a waste of time. 

Sweden

Preliminary data from EU statistics agency Eurostat compiled by Reuters showed Sweden had 7.7% more deaths in 2020 than its average for the preceding four years. Countries that opted for several periods of strict lockdowns, such as Spain and Belgium, had so-called excess mortality of 18.1% and 16.2% respectively.

UPDATE: Sorry about that; I posted this from my phone, and the mobile version of the Hall didn't show me the formatting error.  

Neighborhood Ordinance: No Whining

Austin immigrants versus “toxic masculinity,” plus an awesome Caddy.

In honor of our heroes, some Tejano music you can blare as loudly as you wish. 

9th Circuit: "What Do You Mean, 'Bear' Arms?"

Hawaii has a law that permits you to carry firearms, provided you obtain a license from the state that requires you to establish that you have an "urgent need" for such a firearm. A man named George Young applied for such a license, but the state was not satisfied that he proved the urgency of his need to carry one. He just wanted to carry a gun in case he needed to defend himself, but had established no reason to believe that it was likely he would need to do so. They thus turned him down, and he sued. 

The 9th Circuit Court of Appeals has upheld them in doing so, but gone rather farther. They assert that Americans have no right to carry weapons in public at all. 

“There is no right to carry arms openly in public; nor is any such right within the scope of the Second Amendment,” the court ruled in an “en banc” decision that involved all the panel’s judges.

“We can find no general right to carry arms into the public square for self-defense,” the majority wrote, claiming that the Second Amendment applies to the “defense of hearth and home.”

“The power of the government to regulate carrying arms in the public square does not infringe in any way on the right of an individual to defend his home or business,” the judges wrote.

This seems to be the evolving position on the Second Amendment from the statists in response to Heller. 'Ok, maybe you have a right to own a gun that we can't completely reject,' they say, 'but only at home.' The District of Columbia will now let you own a gun, to be kept at home, registered with the police; you may not even possess ammunition for it without that permit. You may also not carry it anywhere without an additional license that they are under no obligation to provide you. (They also have a list of handguns you're allowed to buy if approved to buy them, which is called the "List of Handguns Not Determined to be Unsafe," and a list of guns you're definitely not, which they call an "Assault Weapons" ban though it appears to have been constructed largely based on scary appearances.)

So they are responding to the "right to keep and bear arms" somewhat like Ms. Clinton asking whether she was being asked if she had wiped her server with a cloth. "Yes, you can keep it at home; but bear it? What on earth could that mean? Like ride around on a bear with it? That sounds horribly unsafe."

Addendum to Part VII

Though I'm going to leave the discussion of whether our approach to relations is better than the Greeks for another day, I would like to say some things about how we handle it in logic.

There are different ways that contemporary symbolic logic tends to handle relations like the kinds Parmenides was discussing in the previous post. I'll walk through just one. Let's say that we wanted to express a likeness relation such as "All crows are black." It would look like this:

∀x(Cx⊃Bx)

That is read, "For every x, if x is a crow then x is black."

Notice that this relationship does not include any actual crows, only a variable x. It is a statement that describes every object in the universe, most of which will fail to be crows. Those things that satisfy the crow condition will, if the statement is true, also satisfy the black condition.

It is possible to talk about an actual crow. Let's say object a is a crow. (Variables are from the end of the alphabet, whereas letters taken from the beginning of the alphabet are constants. That is to say that x or y could be anything, but a is a particular something.) Now you can test the proposition, because if Ca is true and Ba is false, then the proposition is false. It only takes one counterexample to falsify a universally quantified statement like the one above (the upside-down A is the universal quantifier).

So one way we can talk about relations between objects is to use the capital letter to indicate a class of things. All of those things are automatically related to each other by being members of the class. 

That doesn't actually solve the problem Parmenides is raising, though, because you still need two things at work to express the relation. Let us say that a is not a crow, but the One or really any Form that is a unitary idea. Being a pure unity, it is just a and not Fa. A genuinely pure unity cannot admit of likeness in this way either.

It also, it turns out, can't admit of unlikeness on this model because you'd have to say that a was not a crow, and that requires three concepts working together: the constant, the class, and the negative operator. (¬ Ca). The pure unity does not admit of either the ¬  or the C, because if it did, it would no longer be just one idea but multiple ideas.

It actually seems like the Form of a Crow would be C, though, not a. After all, it is x's participation in C that makes it a crow. Now you might say that the One is "O," and any x might participate in it without changing it. So you could have Oa and Ob, where a and b each participate in the One without being the One. This addresses Parmenides' concerns somewhat, because whether any x does or doesn't participate in O, O remains singular and unchanged by the participation or lack thereof. 

Viewed that way, contemporary symbolic logic depends upon Platonic forms. So too does mathematical logic, and therefore math itself. 

Plato's Parmenides VII, The One II

We continue from yesterday.

Neither will [the One] be the same with itself or other; nor again, other
than itself or other.

How is that?

If other than itself it would be other than one, and would not be
one.

True.

And if the same with other, it would be that other, and not itself;
so that upon this supposition too, it would not have the nature of
one, but would be other than one?

It would. 

Then it will not be the same with other, or other than itself?

It will not.

That part was straightforward: the One is not the same as anything else, because it's itself and not the other thing (whatever that thing might be). The next part is trickier. 

Neither will it be other than other, while it remains one; for not

one, but only other, can be other than other, and nothing else.

True.

Then not by virtue of being one will it be other?

Certainly not.

But if not by virtue of being one, not by virtue of itself; and if
not by virtue of itself, not itself, and itself not being other at
all, will not be other than anything?

Right.

Neither will one be the same with itself.

How not?

Surely the nature of the one is not the nature of the same.

Why not?

It is not when anything becomes the same with anything that it becomes
one.

What of that?

Anything which becomes the same with the many, necessarily becomes
many and not one.
True.

But, if there were no difference between the one and the same, when
a thing became the same, it would always become one; and when it became
one, the same?

Certainly.

And, therefore, if one be the same with itself, it is not one with
itself, and will therefore be one and also not one.

Surely that is impossible.

This argument that pure unity cannot admit of 'sameness' is going to end up being a problem for Plato and even for Socrates, because the unity he is seeking is supposed to explain something else. The idea was that largeness was supposed to have a Form, and that Form was the thing that somehow produces the sameness by virtue of which all large things are large; or all good things are good. If the kind of unity Parmenides is describing cannot even admit of 'sameness' to the degree that it can be said to be 'the same as itself' the whole concept is going to be unworkable. This is sort of the third man problem in reverse: instead of producing an infinite number of additional forms, it can't even produce one additional thing. If that's true, it can't do what Socrates proposed it should do. 

The One cannot be the same in part, also, because the concept of sameness requires a concept of difference; and that is two things (in addition to itself). Once again, the idea of a unity produces a trinity. (See the comments to yesterday's post for further discussion). If the One is a kind of mind, this realization is itself productive: of that which is different, and sameness, and then a space between them for similarity and difference. The Neoplatonists will explain creation -- including the creation of the Platonic Forms -- in terms of the way that the thinking of the One ends up producing everything else. 

Parmenides is not going to make that move; he's going to block it by trying to show that the One not only cannot be the same as another, it cannot even be like another. 

And therefore the one can neither be other than other, nor the same

with itself.

Impossible.

And thus the one can neither be the same, nor other, either in relation
to itself or other?

No.

Neither will the one be like anything or unlike itself or other.

Why not?

Because likeness is sameness of affections.

Yes.

And sameness has been shown to be of a nature distinct from oneness?

That has been shown.

But if the one had any other affection than that of being one, it
would be affected in such a way as to be more than one; which is impossible.

Why is it impossible? Because motion and therefore change in the unity have already been shown to be impossible.

True.

Then the one can never be so affected as to be the same either with
another or with itself?

Clearly not.

Then it cannot be like another, or like itself?

No.

Nor can it be affected so as to be other, for then it would be affected
in such a way as to be more than one.

It would.

That which is affected otherwise than itself or another, will be unlike
itself or another, for sameness of affections is likeness.

True.

But the one, as appears, never being affected otherwise, is never
unlike itself or other?

Never.

Then the one will never be either like or unlike itself or other?

Plainly not.

The Archangel Michael's name is translated in a way that captures the Judeo-Christian-Islamic sense of this difficulty. "In art St. Michael is often represented as an angelic warrior, fully armed with helmet, sword, and shield, as he overcomes Satan, sometimes represented as a dragon and sometimes as a man-like figure. The shield at times bears the inscription: Quis ut Deus, the translation of the archangel's name, but capable also of being seen as his rhetorical and scornful question to Satan." The difference between God (or the One) and everything else is so categorical that it does not admit of likeness. 

It seems stranger to say that it does not, then, admit of unlikeness: it seems as if everything is unlike God, both categorically and in degree. Partly that is because we think differently than the Greeks here. Aristotle will divide the world into substances and the attributes they have. A relation, then, is a kind of attribute of a substance. If X and Y are related, X has attribute a which is 'is like Y,' and Y has attribute b which is 'is like X.' Xa and Yb thus produce the relationship, which is not 'real' in itself (i.e., it is not a substance); it is a product of their similar but distinct attributes.

Thus, you can see how from the Greek perspective it makes sense that the One, being a pure unity, cannot admit of a relation such as 'is unlike Z.' Being a pure unity, it cannot carry any attributes -- not sameness, not difference, not like nor unlike, neither red nor blue.

Our metaphysical approach to relations is different, such that it seems illogical to say that A is not like B, and also not unlike B. Whether or not our approach is better is a topic for another day. For now, keep it in mind as Parmenides runs through several more apparent paradoxes. 

Again, being of this nature, it can neither be equal nor unequal either

to itself or to other.

How is that?

Why, because the one if equal must be of the same measures as that
to which it is equal.

True.

And if greater or less than things which are commensurable with it,
the one will have more measures than that which is less, and fewer
than that which is greater?

Yes.

And so of things which are not commensurate with it, the one will
have greater measures than that which is less and smaller than that
which is greater.

Certainly.

But how can that which does not partake of sameness, have either the
same measures or have anything else the same?

Impossible.

And not having the same measures, the one cannot be equal either with
itself or with another?

It appears so.

But again, whether it have fewer or more measures, it will have as
many parts as it has measures; and thus again the one will be no longer
one but will have as many parts as measures.

Right.

And if it were of one measure, it would be equal to that measure;
yet it has been shown to be incapable of equality.

It has.

Then it will neither partake of one measure, nor of many, nor of few,
nor of the same at all, nor be equal to itself or another; nor be
greater or less than itself, or other?

Certainly.

Well, and do we suppose that one can be older, or younger than anything,
or of the same age with it?

Why not?

Why, because that which is of the same age with itself or other, must
partake of equality or likeness of time; and we said that the one
did not partake either of equality or of likeness?

We did say so.

And we also said, that it did not partake of inequality or unlikeness.

Very true.

How then can one, being of this nature, be either older or younger
than anything, or have the same age with it?

In no way.

The next argument changes grounds from the previous series, so we'll proceed with it in the next post. 

The Devil “Gender Neutrality” Dealt Fatal Blow

The Army admits that it has to score women differently from men if it wants women to be able to pass. It also eliminates the requirements for job specific roles, or that you pass the parts of the test women had trouble with. 

And you will only be ranked according to sex: “The new scoring system will ‘place everyone that passes the ACFT into an individual performance category based off of how well they score relative to their gender,’ tweeted Michael Grinston, sergeant major of the Army.”

Plato's Parmenides VI: The One I

Ok, so let's go through Parmenides' argument in a few stages. It is done in a dialogue, with Aristoteles answering him. I see no alternative but to quote the whole long thing, breaking in at points for discussion. 

Parmenides proceeded: If one is, he said, the one cannot be many?
Impossible.
Then the one cannot have parts, and cannot be a whole?
Why not?
Because every part is part of a whole; is it not?
Yes.
And what is a whole? would not that of which no part is wanting be a whole?

Certainly.
Then, in either case, the one would be made up of parts; both as being a whole, and also as having parts?

To be sure.
And in either case, the one would be many, and not one?
True.
But, surely, it ought to be one and not many?
It ought.
Then, if the one is to remain one, it will not be a whole, and will not have parts?

No.

Now the first difficulty for me is Parmenides' decision to 'cash out' (as philosophers love to say) wholeness in terms of having parts. That seems circular: a part is a part of a whole, but a whole is that which has all its parts together. I would have preferred at least one of these terms to be defined independently of the other.

However, I spoke with a friend of mine who is a mereologist, and he thought it was a reasonable thing to do under the circumstances. His problem was that Parmenides might be confusing spatiotemporal wholes with the kinds of wholes that Socrates' ideas are meant to be. A thought can have parts, even though it has no spatiotemporal parts; if you think through a remembered psalm (to borrow an example from St. Augustine), you think through the first part before the last part. It's divisible without being spatial.

Socrates wants to get from discursive thinking to grasping a unitary idea, though; and Parmenides is exploring whether the idea of a unity like that has sense. What would it be like? Well, it wouldn't have parts; and therefore, it wouldn't be a whole.

But if it has no parts, it will have neither beginning, middle, nor end; for these would of course be parts of it.

Right.
But then, again, a beginning and an end are the limits of everything?

Certainly.
Then the one, having neither beginning nor end, is unlimited?

Yes, unlimited.
And therefore formless; for it cannot partake either of round or straight.

But why?
Why, because the round is that of which all the extreme points are equidistant from the centre?

Yes.
And the straight is that of which the centre intercepts the view of the extremes?

True.
Then the one would have parts and would be many, if it partook either of a straight or of a circular form?

Assuredly.
But having no parts, it will be neither straight nor round?

Right.

These are fairly straightforward consequences of what it is to be a unity like they are exploring, but it is useful because it ends up dismissing several analogies and metaphors. Later philosophers often speak as a circle as a kind of unity, for example; but it isn't this kind of unity. A circle has parts, is a whole, and has features that are definable. The Form of the Good ultimately will not have any of those things.

And, being of such a nature, it cannot be in any place, for it cannot be either in another or in itself.

How so?
Because if it were in another, it would be encircled by that in which it was, and would touch it at many places and with many parts; but that which is one and indivisible, and does not partake of a circular nature, cannot be touched all round in many places.

Certainly not.
But if, on the other hand, one were in itself, it would also be contained by nothing else but itself; that is to say, if it were really in itself; for nothing can be in anything which does not contain it.

Impossible.
But then, that which contains must be other than that which is contained? for the same whole cannot do and suffer both at once; and if so, one will be no longer one, but two?

True.
Then one cannot be anywhere, either in itself or in another?

No.

Where is an idea? We might say "in my mind." Materialists will want us to 'cash that out' as "in my brain." But the brain is a place that occupies physical space; and Parmenides is proving that an idea like a Form, at least, can't be in any place. It therefore can't be contained, neither by a brain nor by anything else material.

That's not a problem for ideas like Augustine's psalm, but it is definitely a problem for any kind of Greek Form -- and especially for Aristotle's, which is supposed to somehow be 'in the thing.' Where is the form of a table? It's in the table, somehow. If the parts of the table are laying on the ground in a heap, you don't have a table. It's when the right order comes to be that the thing becomes a table. For Aristotle, form is a kind of order or structure; and thus it must be in the thing. Yet, as Parmenides is showing, a form can't be.

You can say something here that is quasi-material about the table: the 'form' is a way of speaking about a bunch of relations between the material objects, so that a properly formed table will have electromagnetic force relations between the proper atoms that make it up, such that they allow other objects to be placed upon it at "our level" of organization; the atoms of the book placed onto the table interact with the atoms of the table, etc. Form ends up being supremely complex, but explicable in terms of material relations.

Yet even in that case form is immaterial; the table and book interact as they do only because they've been put in that order, and they were put there for a reason. There's a purpose, a telos, in the construction of the table; and the form of the organization is defined by that. That form isn't in the thing; it is an idea in the mind of the creator of the artifact. If it is a form in that sense, it is closer to Plato/Socrates/Parmenides' sense of a Form; and if so, it can't really 'be in the brain,' either, because it can't really exist in a physical place. It can perhaps be in a mind, but where then is the mind?

Further consider, whether that which is of such a nature can have either rest or motion.

Why not?
Why, because the one, if it were moved, would be either moved in place or changed in nature; for these are the only kinds of motion.

Yes.
And the one, when it changes and ceases to be itself, cannot be any longer one.

It cannot.
It cannot therefore experience the sort of motion which is change of nature?

Clearly not.
Then can the motion of the one be in place?
Perhaps.
But if the one moved in place, must it not either move round and round in the same place, or from one place to another?

It must.
And that which moves in a circle must rest upon a centre; and that which goes round upon a centre must have parts which are different from the centre; but that which has no centre and no parts cannot possibly be carried round upon a centre?

Impossible.
But perhaps the motion of the one consists in change of place?

Perhaps so, if it moves at all.
And have we not already shown that it cannot be in anything?

Yes.
Then its coming into being in anything is still more impossible; is it not?

I do not see why.
Why, because anything which comes into being in anything, can neither as yet be in that other thing while still coming into being, nor be altogether out of it, if already coming into being in it.

Certainly not.
And therefore whatever comes into being in another must have parts, and then one part may be in, and another part out of that other; but that which has no parts can never be at one and the same time neither wholly within nor wholly without anything.

True.
And is there not a still greater impossibility in that which has no parts, and is not a whole, coming into being anywhere, since it cannot come into being either as a part or as a whole?

Clearly.

This is a huge challenge: if a Form is a kind of unity, and such a unity cannot have parts, then it cannot come to be in anything. Really, the conclusion here is that it cannot come to be at all. 'Coming to be' is a kind of motion, and Parmenides is going through all the kinds of motion and showing that a unity cannot experience any of them. 

The conclusion is that Forms, if they exist, are eternal; they do not come to be, and they do not perish. They aren't in anything that we encounter in the world. The Forms, thus, belong to another world -- one that interacts with our material, spatiotemporal world in some way, but that is not itself material or spatiotemporal.

Then it does not change place by revolving in the same spot, not by going somewhere and coming into being in something; nor again, by change in itself?

Very true.
Then in respect of any kind of motion the one is immoveable?

Immoveable.
But neither can the one be in anything, as we affirm.
Yes, we said so.
Then it is never in the same?
Why not?
Because if it were in the same it would be in something.

Certainly.
And we said that it could not be in itself, and could not be in other?

True.
Then one is never in the same place?
It would seem not.
But that which is never in the same place is never quiet or at rest?

Never.
One then, as would seem, is neither rest nor in motion?
It certainly appears so.

Questions? Discussion?

A Shopkeeper Remembered

An older lady who ran a shop out on a rural highway out this way died last week. Some of the neighbors were talking about her, telling stories about how she ran the place. I guess she was about 85.

One fellow was on a construction crew that was working in the winter time, and they staged up about her store before going out to work. One of the workers had bought a cup of coffee, and after finishing it decided he wanted another. Now while outside he'd pulled his ski mask down to keep his face farm, at first halfway so he could drink the coffee, and then all the way. He went in to the store without removing it, and this fellow went with him for something he wanted. No sooner had they walked through the door than the old woman intercepted them, shoved a .357 Magnum right between the one guy's eyes, and demanded that he immediately remove his mask. His hands were full, so in order to free them up to do it he handed her the empty coffee cup and the other guy his money.

Another time one of them went in and she had filled these hard candy hoppers she had with a new kind of green jawbreaker. She told him to try one, and when he did it nearly knocked him down. "What is this?" he asked.

"Wasabi candy," she said.

Apparently some of the migrant laborers who'd been coming in to her store had been stealing candy out of her hoppers when they came in. She decided to put a stop to it. It reportedly worked, although I'll bet she put a stop to her candy sales, too. 

America's Disinformation Source of Record

"We know it can't be satire, because it's NOT FUNNY."

Trail Songs

Marty Robbins apparently did this album in a single take, I hear. He is said to have convinced the studio that they had to let him do it because he'd done so many things that they wanted done. Neither they nor he thought it would be a big success, but he wanted to do an Old West album.

The song "El Paso" alone went to #1 on the country chart... and also on the pop chart. That one day's work paid for his whole life, and probably is still supporting his grandkids. It's one of the few dozen songs I can sing from memory, and do, much to the annoyance of everyone but my wife who finds it charming.

Johnny Cash did an experimental 'true West' album too, but it wasn't nearly as successful. Fortunately, he had other songs that did well. I've always liked this piece from it, though.

Also this one, even more, about the old "Wilderness Road." "Boone recommended three essentials for a pioneer: 'A good gun, a good horse, and a good wife.'" 

And this one, which I quote from time to time. "I saw him one day, but I ain't seen him since."

 Appropriately, I did come across a loose horse along a mountain road today. I returned him to his owners.