Archive for the ‘metaphysics’ Category

Basic Ontology

Thursday, 2 September 2021

When natural languages first had need to refer to concepts as such, this need was so limited and so vaguely understood that the very same term would refer both to a concept and to that to which the concept pointed. A horse is a mammal. and A horse is on my lawn. seem superficially to be statements of the same sort. Some people, sensing a difference, declare that the first statement is essential, while the second is accidental, but this way of speaking and of writing seems to treat a horse as referring in both cases to the same thing, and embroils us in conflicts over which attributes are essential, which are accidental, and by what methods we all ought to agree on a resolution. The primary difference between the two statements is that in A horse is a mammal. the term a horse typically refers to a concept, whereäs in A horse is on my lawn. the term a horse usually refers to something to which the concept corresponds, which we may call an instantiation of the concept.

I say usually because in theory someone might use a horse only for creatures who were, amongst other things, found on her lawn; but we understand that this practice is not usual, and can find the difference between concept and instantiation by considering usual practice. At the same time, we can see that struggles about essential and accidental attributes are largely rooted in different people simply using related but different concepts.

Even people who are careful to indicate a distinction between some Y and the concept of Y when Y is not itself a concept may fail to do so when it is. But the concept of the concept of X is not the concept of X unless we can find some X which is no more or less than the idea of itself.

From this point, we should see that, to believe that instantiations depend upon their concepts, we must accept an infinite regress. The alternative is not to accept that concepts depend upon that which instantiates them — some concepts are not instantiated — but to understand that concepts must be constructed by employing some thing or things that are not concepts.

In any case, always marking the distinction between concept and instantiation can become a very great burden as we begin to ponder ideas as such, part of which burden would fall upon a reader dealing with compounding of expressions such as the concept of; but, one way or another, we should remember what we are contemplating or discussing.

The confusion in using the same term for concept and instantiation is most acute in existence statements.

The subject in Unicorns do not exist. is the concept of unicorns, not any instantiation of that concept. Grammatically we treat nothing as a something and grammatically we treat non-existence as a property of nothing-as-something. But, underlying this practice, statements about non-existence are really statements that some concepts have no instantiations; if claims about non-existence refer to properties of somethings, then these somethings are concepts. Unicorns do not exist. is not really about unicorns; it is about the idea of unicorns. We can only speak or write of the idea of unicorns.

And, when we speak or write of existence, we are speaking and writing of concepts. The claim Horses exist. is really about the concept, that it is instantiated. Coherent existential claims are no more or less than claims that concepts are instantiated.

That statements of form X exists. unpack to form The concept of X is instantiated. should lead one to recognize that a proper reading of The concept of X exists. unpacks to The concept of the concept of X is instantiated. We don't generally need a concept before we use something that would instantiate it — otherwise the infinite regress of concepts would be needed — but anything that we use is at least potentially an instantiation of multiple concepts. Some might be tempted to conclude that, thus, X exists. needn't refer to the concept of X, and can be unpacked as X is potentially an instantiation of some concept. It may seem doubtful that anyone has ever previously intended such a thing with an existential claim, and certainly existential claims are not usually claims about the ability to find or to construct an idea of a thing said to exist. However, to be potentially an instantiation of some concept is no more or less than to possess properties, so this notion would treat existence as something like a generalization of the concept of property. Still, the formula cannot be adapted to X does not exist. as unpacking it to X is not potentially an instantiation of some concept. is always incoherent when not false, whereäs declarations such as Unicorns do not exist. may be coherent and true. And we are incoherent if by a horse we mean the same thing in A horse has no properties. as in A horse is on the lawn.

I don't propose that we try to reshape our speech and writing nor our work-a-day thinking to distinguish overtly-and-always concept from instantiation. I don't even propose to do so in all philosophic discourse. But, when discussion of existence seems troubling or profound or both, then we may need to bring that distinction to bear.


Some people, encountering a discussion such as the foregoing, will not much attend to it, because they feel certain that they clearly see a truth that contradicts it. I'm going to address propositions of two sorts, mistaken for such truth.

One sort, in which X is something like what is meant by a horse in A horse is on the lawn. says X V because it exists. where the variable V takes the value of a verb. For example, A hot stove burns you because it exists. The first thing to note is that specific values of V that supposedly prove existence aren't universally applicable; we don't say A horse burns you because it exists. Generally, existence is intended to be seen as a necessary but not sufficient condition for X to V. But, when we add conditions to achieve sufficiency, we find that the added conditions (eg, being at a temperature at or above 118°F) are by themselves sufficient, without a mysterious complementary property of existence possessed by X; the notion of such a property results from thoughtlessly confusing a way in which a concept of X may be said to have properties with the way in which X has properties. What we call the horn of a unicorn is itself a concept of a horn.

Though I have encountered at least one would-be follower of Ayn Rand who mistook the tack of because it exists for hers, she made a different mistake. She declared the concept of existence to be irreducible but axiomatic, and that we were to see that it were found and proven in-so-far as a self-contradiction would result from denying Existence exists. However, because we can show that a self-contradiction indeed obtains while interpretting existence and its coördinate terms as in the prior discussion, her attempt to prove the existence of some other concept (profound or otherwise) is a failure.

If we unpack Existence exists. as we can, it is The concept of being an instantiated concept is instantiated. The source of self-contradiction in denial of this proposition is that the concept of a concept being instantiated must have been instantiated for the proposition to be formed, though this proposition could not hold before formation of the concept of existence. And its subjects are not of the sort that Rand and her followers imagined or imagine.

For whatever it's worth, if we grab for potential instantiation then the unpacking is to The concept of potential instantiation is potentially instantiated. that is, more simply put, to A concept can be formed of being the subject of a concept. Again, self-contradiction ensues if we attempt to deny the claim, but in neither expression is the subject that for which Rand reached.

Checked against What?

Sunday, 4 July 2021

Recently, I encountered a bizarre claim about deaths from two different causes, and a link to a supposèd fact-check at Lead Stories, which unequivocally called the claim false. However, when I read the rest of the report, the alleged fact-checker had only failed to find substantiation for the claim. So I sent an inquiry to Alan Duke, the Editor-in-Chief:

Date: Sun, 27 Jun 2021 05:12:03 -0700
To: alan@leadstories.com
Subject: Method?

How do you get from your not knowing of any substantiation of a claim to a declaration that the claim is false?

Merely not knowing that a claim is true is equivalent to merely not know that it is false. Declaring it to be unproven would be perfectly reasonable, but that's not always what you do (though it may sometimes be what you do).

When declaring an unproven claim to be false, or its unproven contradiction to be false, do you flip a coin? or do you decide by some other method?

I've not received a reply.

Now, some people will declare You can't prove a negative! But the mathematic form of the claim being checked was x > y . Accepting that x and y correspond to real numbers, the contradiction of the claim is yx . I don't know that one of these claims should be regarded as positive and the other as negative.

Of course, all but the most terribly gullible understand that what is now-a-days called fact-checking is primarily concerned to protect some narrative or to attack some narrative, and will disregard even basic logic if that concern seems best served by doing so.

Rôles of Prescriptive Models in Economics

Sunday, 30 May 2021

In introductory treatments of economics, one often encounters a distinction drawn between what is called positive economics and what is called normative economics. In these names — and in typical discussion — there are problems.

The meaning of positive here is restricted to fact, as opposed to speculation. Now, on the one hand, supposedly positive economics, like all attempts by human beings to understand the world, is permeated by speculations, which in scientific effort are hypotheses. (The philosophic movement called positivism arose with incompetent aspirations.) On the other hand, contrasting the normative with something called positive entails an implication, insinuation, or declaration that the normative cannot be placed on as solid a foundation as the rest of our understanding. Sometimes a lack of present agreement is treated as if proof that there is no objective ethical truth; sometimes the question is just begged. In any case, the distinction is irrational.

Instead using the terms descriptive and prescriptive steps away from the worst aspect of using positive, though it would be less corrosive to refer to non-prescriptive economics as, well, non-prescriptive or as non-normative.

However, in behavioral science, elements drawn from prescriptive theory are often useful non-prescriptively, either as approximations or as bounding cases. Economic rationality and expected-utility maximization (the latter sometimes conflated with the former) are such elements.

Some economists would not even recognize economic rationality or expected-utility maximization as prescriptive in any case, because they are meta-preferential — they express a preference for structures of preference that have ordering properties such as transitivity and acyclicity, but say nothing about ultimate objectives and thus, in themselves, say nothing about whether one should prefer tomatoes to apples or life over death.

The prescriptive arguments for economic rationality and for expected-utility maximization are to the effect that those who conform realize more of their objectives — regardless of what those objectives might be — than those who do not, with it usually treated as tautologic that one desires such maximization.[1]

The non-prescriptive arguments for economic rationality and for expected-utility maximization as approximations note that these are relatively tractable models of behavior for which evolutionary dynamics will select. Because the models are taken from prescriptive work, some people mistake or misrepresent any use of them as necessarily prescriptive, but the claim is neither that social or other biologic evolution ought to select for something approximated by such behavior nor that agents ought to engage in the behavior for which evolution selects. (If anything, what is illuminated is that evolution selects for a propensity to such prescriptions!)

I endorse use of these models as tractable approximations in many cases, but I also embrace use of a weaker notion of economic rationality as a bounding case. A boundary of economic outcomes is given by considering what those outcomes would be were agents economically rational.

Behavioral economics concerns itself with when-and-how people actually behave, and especially with failures of the aforementioned models. Although this research is not what I do, I acknowledge its value. However, a great deal of what passes for behavioral economics involves an inferential leap from identifying a real or apparent deviation of behavior from one of these models to a conclusion that this-or-that result could be obtained by state intervention, with the researcher looking away from any proper examination of the behavior of agents determining practices of the state. Behavioral economics is thus used as the motte for a statist bailey. Additionally, even behavioral researchers with no apparent statist agenda often fail to recognize when behavior that seems at odds with these models is or may be instead at odds with some presumption of the researcher.[2]


[1] The main-stream of economic theory treats completeness of preferences as a feature of economic rationality but I've never seen a prescriptive argument even attempted for this feature. The prescriptive cases for transitivity and for acyclicity seem to presume an absence of conflicting, prior meta-preferences. The prescriptive argument for expected-utility maximization is especially problematic.

[2] While I have problems with some of the work and with much of the rhetoric of Gerd Gigerenzer, he has ably identified important cases of such failure on the part of researchers.

Nick Hudson on SARS-CoV-2 and the Policy Response

Thursday, 1 April 2021

Alphabet has removed this video from YouTube:

The Paradox of Shadows

Friday, 5 March 2021

For many years, one of the projects on a back-burner in my mind has been the writing of a novel, A Paradox of Shadows, in which the principal character is attempting to reconstruct or to otherwise recover an ancient work, the title of which might have been περὶ τοῦ ἀτόπου τοῦ τῶν σκιῶν, or De [Anomalia de] Obumbratio, or perhaps something else.

Everything about the work is a matter of doubt or of conjecture, including its author and the era and language in which it were originally composed; even that there ever were such a work is uncertain. Its existence is primarily inferred from how parts of it seem to be esoterically embedded in other works; sometimes these passages can be made to fit together like bits of a jigsaw, but different ways of fitting are possible, especially allowing for lacunæ, interpolations, and unintended errors in translation or in transcription. In ancient art and literature are found what may be other references to the work, but these apparent references are subject to alternate interpretation, especially as many of them would be quite oblique if indeed they refer to the work. The search is largely a matter of poring over old manuscripts and documents.

No rational person would look at any one piece of evidence known to the main character and conclude that the work must have existed or just probably existed. Few would take the evidence as jointly establishing such a probability. There is both too much and too little information, so that bold intellectual leaps must be made in chaos or in darkness. A searcher may encounter unscalable cliffs or unbridgable chasms; and, if forced to stop at any point, one is likely to look pathetic. But the evidence, taken jointly, associates a relative plausibility of recovery with each of various possibilities as to the nature of the work. In that context, the possible profundity is enough to drive the search by the principal character, even with likely failure.

Tiny Spaces

Wednesday, 20 January 2021

Famously, the Euclidean axiomata for space seemed necessary to many, so that various philosophers concluded or argued that some knowledge or something playing a rôle like that of knowledge derived from something other than experience. Yet there were doubters of one of these axiomata — that parallel lines would never intersect — and eventually physicists concluded that the universe would be better described were this axiom regarded as incorrect. Once one axiom was abandoned, the presumption of necessity of the others evaporated.

I think that our concept of space is built upon an experience of an object sometimes affecting another in ways that it sometimes does not, with the first being classified as near when it does and not near when it does; which ways are associated in the concept of near-ness are selected by experience. The concept of distance — variability of near-ness — develops from the variability of how one object affects another; and it is experience that selects which variabilities are associated with distance. Our concept of space is that of potential (realized or not) of near-ness.

The axiomata of Euclid were, implicitly, an attempted codification of observed properties of distance; in the adoption of this codification or of another, one might revise which variabilities one associated with distance. One might, in fact, hold onto those axiomata exactly by revising which variabilities are associated with distance. In saying that space is non-Euclidean, one ought to mean that the Euclidean axiomata are not the best suited to physics.

Just as the axiomata of Euclid become ill-suited to physics when distances become very large, they may be ill-suited when distances become very small.

Space might not even be divisible without limit. The mathematical construct of continuity may not apply to the physical world. At least some physical quantities that were once imagined potentially to have measures corresponding to any real number are now regarded as having measures corresponding only to integer multiples of quanta; perhaps distance cannot be reduced below some minimum.

And, at some sub-atomic level, any useable rules of distance might be more complex. On a larger scale, non-Euclidean spaces are sometimes imagined to have worm-holes, which is really to say that some spaces would have near-ness by peculiar paths. Perhaps worm-holes or some discontinuous analogue thereöf are pervasive at a sub-atomic level, making space into something of a rat's nest.

Humpty Dumpty and Commerce

Thursday, 7 January 2021

Fairly inexpensive hair combs made of hard rubber — rubber vulcanized to a state in which it is as about firm as a modern plastic — could be found in most American drugstores at least into the mid-'90s. Now-a-days, they have become something of a premium item. I was looking at listing on Amazon supposedly of hard rubber combs and discovered, to my annoyance, that a careful reading of the descriptions showed that most of the combs explicitly described as hard rubber were made of plastic. To me, the situation seemed to be of pervasive fraud, as it will to many others.

But then I realized that it is more likely to be something else. Fraud, after all, involves deliberate misrepresentation. Whereäs we live in a world in which a great many people believe that no use of a word or phrase is objectively improper — that if they think that hard rubber means a rubbery plastic or a plastic that looks like another substance called hard rubber, then it indeed means just that. (Of course, we cannot trust any verbal explanation from them of these idiosyncratic meanings, as they may be assigning different meanings to any words with which they define other words.)

My defense of linguistic prescriptivism has for the most part been driven by concerns other than those immediate to commercial transactions. And, when I've seen things such on eBay as items described with mint condition for its age or with draped nude, my inclination has been merely to groan or to laugh. But it seems to me that the effects of ignoring or of rejecting linguistic prescription have found their way into commercial transactions beyond the casual.

Well, those who are not prescriptivists are hypocrites if they complain, and they're getting no worse than they deserve.

Perverted Locusts

Wednesday, 9 December 2020

Those who support locking-down in response to SARS-CoV-2 are like weird locusts. Instead of eating the crops; these locusts prevent growth and harvest. That is to say that they prevent economic activity, which is an implicit consumption of an especially perverse sort. In any case, they leave despair and literal starvation in their wake.

Transcription Error

Monday, 23 November 2020

To my chagrin, I find that I made a transcription error for an axiom in Formal Qualitative Probability. More specifically, I placed a quantification in the wrong place. Axiom (A6) should read [image of formula] I've corrected this error in the working version.

Lack of Infrastructure

Saturday, 26 September 2020
[panel from Kirakira • Sutadī — Zettai Gokaku Sengen by Hanabana Tsubomi in which three students react with dismay at something given to them by a fourth student.  One dismayed student declares 'What is this…?!  This is absolutely filled with symbols I've never seen before…'  Another cries 'I don't even understand what the questions are asking…!!']
(from KiraKira★Study by Hanabana Tsubomi, v 2 ch 18)

My work and the problems that most interest me are difficult to discuss with friends and even with colleagues because so much infrastructure is unfamiliar to them.