Archive for the ‘philosophy’ Category

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.

Judging the Past in the Present

Monday, 28 December 2020

I often hear or read someone objecting to judging an historical person or act by present moral standards. Although there seems to be some element of reasonableness entangled in this objection, it's very problematic.

It is especially problematic as expressed. Technically, we cannot judge anyone or anything at all, except by whatever may be our present standards. If we judge historical people and acts differently from how we do present-day people and acts, it is exactly because our present standards incorporate a recognition of historical context.

I don't see that the real issue is historical context as such, but context more generally. If we are to make allowances for historical person or acts, it is because of what informed them and what did not inform them; and, similarly, acts by persons in some present-day contexts are very differently informed from acts by other persons in other present-day cultures. As L.P. Hartley usefully noted, The past is a foreign country: they do things differently there.

Cultural relativism, in application to other places or to other times, is sensible when it warns one against presumption that one's own culture is doing things the only right way. (One's culture may be doing things a wrong way, or there may be other ways that are just as good.) But a cultural relativism that instead claims that something is automatically acceptable simply because it prevails in the culture of that place or prevailed in the culture of that time dissolves into nihilism because each person at each time and at each place is him- or herself a subculture.

And I think that some allowances should be made; but I think that too much allowance is often made.

For example, is the case against slavery now available really all that much better than the case that was available in America a few hundred years ago? Inverting that question, was the case against slavery available a few hundred years ago really much worse than the case available now? There is a sound argument, even to-day, for not waging war against slavery in the territories ruled by other states; and there may be a case for making treaties or even forming alliances with such states; but those are different practices from engaging in slavery or actively enabling slavery. Is there really a meaningfully better defense of the slavery of two hundred years ago than there would be of slavery now?

I   don't   think   so.

Nor do I think so for a great deal else that I am told not to judge by modern standards.

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.

Tasers

Sunday, 6 December 2020

State officials should not use tasers as devices to compel positive acts. I have made and explained this point elsewhere, but I believe that I have failed to do so previously in this 'blog.

When tasers were introduced to policing, they were presented to the public as devices to stop attackers, without potentially lethal force. It would take some contrivance to present a situation in which such use of a taser would not be preferable to lethal force.

But tasers also inflict pain. And police officers quickly began using them to hurt people until those people complied, even when compliance was a positive act, such as moving one's body in some way. The pain inflicted by a taser is sufficiently severe that it will cause people to act in ways that will lead to their convictions, as when a taser was used to induce a suspect to produce a urine sample. Used to motivate behavior, a taser is a device of torture. Judges have acquiesced to this use of torture to compel positive acts. Almost no one speaks out against it. The taser has become a socially accepted device of torture.

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.

Science and the Humanities

Saturday, 7 November 2020

Reading a book first published in 1951, I am reminded that, at one time, the definition of humanities included sciences of human behavior within its scope. Now, one seldom encounters that inclusion in contemporary use, and the Merriam-Webster Dictionary explicitly excludes the study of social relations (though it says nothing explicit about that part of behavior outside of the social).

In the earlier period, there was a question of whether the study of human behavior were fundamentally different from the study of the properties of other things. Those who insisted upon such a difference would speak and write of science and the humanities as if of two separate things.

But the tools by which the physical, biological, and behavioral science were studied were increasingly shared. The physical and biological sciences took-up probability and statistics; the biological sciences have taken-up chemistry, mechanics, and game theory; the behavioral science have taken-up biological explanation and mathematical modelling. All have been affected by the same philosophic theories of method. A dichotomy of science and the humanities cannot prevail so long as the behavioral sciences are included amongst what are called humanities.

Apparently that dichotomy was so dear to some of those who insisted upon it that they attempted its preservation by implicitly changing what they intended with humanities in order to hold fast to it. Of course, the newer definition doesn't maintain the original dichotomy; but replaces it with a new one.

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.

Libertine Bayesianism

Thursday, 24 September 2020

As repeatedly noted by me and by many others, there are multiple theories about the fundamental notion of probability, including (though not restricted to) the notion of probabilities as objective, logical relationships amongst propositions and that of probabilities as degrees of belief.

Though those two notions are distinct, subscribers to each typically agree with subscribers to the other upon a great deal of the axiomatic structure of the logic of probability. Further, in practice the main-stream of the first group and that of the second group both arrive at their estimates of measures of probability by adjusting initial values through repeated application, as observations accumulate, of a principle known as Bayes' theorem. Indeed, the main-stream of one group are called objective Bayesian and the mainstream of the other are often called subjective Bayesian.[1] Where the two main-streams differ in practice is in the source of those initial values.

The objective Bayesians believe that, in the absence of information, one begins with what are called non-informative priors. This notion is evolved from the classical idea of a principle of insufficient reason, which said that one should assign equal probabilities to events or to propositions, in the absence of a reason for assigning different probabilities. (For example, begin by assume that a die is fair.) The objective Bayesians attempt to be more shrewd than the classical theorists, but will often admit that in some cases non-informative priors cannot be found because of a lack of understanding of how to divide the possibilities (in some cases because of complexity).

The subjective Bayesians believe that one may use as a prior whatever initial degree of belief one has, measured on an interval from 0 through 1. As measures of probability are taken to be degrees of belief, any application of Bayes' theorem that results in a new value is supposed to result in a new degree of belief.

I want to suggest what I think to be a new school of thought, with a Bayesian sub-school, not-withstanding that I have no intention of joining this school.

If a set of things is completely ranked, it's possible to proxy that ranking with a quantification, such that if one thing has a higher rank than another then it is assigned a greater quantification, and that if two things have the same rank then they are assigned the same quantification. If all that we have is a ranking, with no further stipulations, then there will be infinitely many possible quantifications that will work as proxies. Often, we may want to tighten-up the rules of quantification (for example, by requiring that all quantities be in the interval from 0 through 1), and yet still it may be the case that infinitely many quantifications would work equally well as proxies.

Sets of measures of probability may be considered as proxies for underlying rankings of propositions or of events by probability. The principles to which most theorists agree when they consider probability rankings as such constrain the sets of possible measures, but so long as only a finite set of propositions or of events is under consideration, there are infinitely many sets of measures that will work as proxies.

A subjectivist feels free to use his or her degrees of belief so long as they fit the constraints, even though someone else may have a different set of degrees of belief that also fit the constraints. However, the argument for the admissibility of the subjectivist's own set of degrees of belief is not that it is believed; the argument is that one's own set of degrees of belief fits the constraints. Belief as such is irrelevant. It might be that one's own belief is colored by private information, but then the argument is not that one believes the private information, but that the information as such is relevant (as indeed it might be); and there would always be some other sets of measures that also conformed to the private information.

Perhaps one might as well use one's own set of degrees of belief, but one also might every bit as well use any conforming set of measures.

So what I now suggest is what I call a libertine school, which regards measures of probability as proxies for probability rankings and which accepts any set of measures that conform to what is known of the probability ranking of propositions or of events, regardless of whether these measures are thought to be the degrees of belief of anyone, and without any concern that these should become the degrees of belief of anyone; and in particular I suggest libertine Bayesianism, which accepts the analytic principles common to the objective Bayesians and to the subjective Bayesians, but which will allow any set of priors that conforms to those principles.


[1] So great a share of subjectivists subscribe to a Bayesian principle of updating that often the subjective Bayesians are simply called subjectivists as if there were no need to distinguish amongst subjectivists. And, until relatively recently, so little recognition was given to the objective Bayesians that Bayesian was often taken as synonymous with subjectivist.

Making Your Vote (or Non-Vote) Count

Sunday, 14 June 2020

In nearly every election of a state official, even those in which only a few hundred voters participate, the margin of victory is more than one vote. What that means is that, if any one voter had refrained from voting, or if any one abstaining voter had not abstained, the candidate who won would still have won. Some people — even some very intelligent people — conclude that the vote of an individual has no efficacy beyond that of other acts of expression. Those people are missing something.

Indeed, one's vote or refusal to vote has absolutely no effect on the election at hand. There are various things that one can do prior to the election which may help one candidate to achieve a margin of victory, or prevent another from achieving such a margin. But one's own vote isn't going to make any difference in that election.

However, as potential candidates and parties decide what to do with future elections in mind, they look at margins of victory in past elections. Potential candidates decide whether to run and, if they choose to run, how to position themselves, informed by those margins. Parties decide their platforms and whom to nominate, informed by those margins. With large margins in their favor, they feel free to alienate a greater number of potential voters; with small margins or losing margins, they consider what to do differently in order to pull voters who previously voted for another, or who didn't vote at all.

Thus, an individual vote or the decision not to vote has a small effect — but its only effect — on later elections and on behavior of those who are acting with concern for later election.

The least effective thing that a potential voter can do is to vote for a candidate whom he or she dislikes. People in America who have held their noses to vote for the Democratic or Republican nominee in order to stop the nominee of the other party did worse than to throw-away their votes; they have helped to ensure that the next pair of choices would likewise be disagreeable, and that the behavior of officials in the mean time would likewise be disagreeable. It is only if one genuinely thought that one of these candidates were worthwhile that one should have voted for him or for her, and then still only to affect the next election and interim behavior of officials.

The most effective thing that a potential voter as such can do is to vote for a candidate of whom that voter approves, even if that candidate has no chance of winning, or to submit a ballot from which no candidate receives a vote. An increasing number of people are doing the latter, either in expression that no candidate is worthy, or to challenge the legitimacy of the process in a way that makes it difficult for these people to be dismissed as apathetic by apologists for the process.