Four Types of Quantification

Four Types of Quantification

It has been said that there are really two types of quantification not one: “objectual” and “substitutional”. The objectual type may be paraphrased as follows: “There is an object x such that x satisfies F, where F is a predicate” (and similarly for the universal quantifier). The substitutional type may be paraphrased: “There is singular term t such that when t is substituted into the appended open sentence it produces a truth” (similarly for universal quantification). The intent of the distinction is clear enough, though the terminology leaves something to be desired. We might better speak of metalinguistic quantification versus objectual quantification, and admit that the former is a special case of the latter, since bits of language are also “objects”. Also, why is inserting a term into an open sentence a type of “substitution”—isn’t it just occupying an argument place (a blank)? Still, there is no very good terminology to fall back on, so we can stick with the standard formulation, so long as we are clear about what is involved. The question is whether the quantifier is “over” objects or “over” words, i.e., what the “domain” includes.

I think this two-way distinction is too limited. There are (at least) four distinguishable types of quantification; we need to add what I will call conceptual quantification and intentional quantification. Again, the terminology is not pellucid, but the distinctions are real. Intuitively, a conceptual quantifier says something like this: “There is a concept C such that when C occurs in a certain proposition the proposition is true”. For example, “There exists a man” is equivalent to “There is a concept C such that when C is combined with the concept man we get a truth”, where C might be the concept Socrates. This is really the twin of metalinguistic quantification except that we “substitute” concepts into propositions not words into sentences. It proceeds at the level of sense not of reference or signs. What I am calling an intentional quantifier (read “intentional object quantifier”) ranges over existent and nonexistent objects: thus, we can say “Some men fly” meaning to include men like Superman. We no longer require that our range of quantification includes only existent objects; we also quantify “over” nonexistent objects. Obviously, this type of quantifier belongs alongside the usual “objectual” kind. Even if natural languages (or logic texts) don’t include such quantifiers, we can stipulate them: they range over objects of thought as well as objects that exist. Ontologically, there are four kinds of entity to work with—existing objects, objects of thought, concepts, and words—so we have four types of quantification to go with them.

We can construct languages with each type of quantifier and explore their properties. One type may be suitable for some purposes but not for others. If we are discussing fiction, we might want the intentional quantifier (“All of Shakespeare’s tragic figures are flawed”); whereas in the sciences we will limit ourselves to existing things. If we are discussing quantificational thoughts, we might want to keep language out of it. Nonsensical language might invite the substitutional quantifier (“Some mome raths are greedy”). Quantifiers are not logically univocal or ontologically parsimonious. They are flexible and pragmatic, up for anything. They are willing to “range over” anything we can think up. They are not semantically austere or judgmental. They are certainly not the measure of what we take seriously and literally to exist in the world of actual objects.

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Stock and Tuvel

Stock and Tuvel

I was just watching a video of Kathleen Stock and Rebecca Tuvel at Cornell talking about their experiences in academia in recent years. Both women struck me as eminently sensible and decent people with perfectly defensible (and innocuous) views. Yet they have been subjected to vicious persecution and cancellation by assorted idiots. The worst offenders have been other so-called professors, often women. This is really a major scandal in the universities: stemming either from malicious or spineless individuals. How anyone could defend this treatment beats me. It is a sign of a deep sickness in contemporary intellectual culture (sic).

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The Situation Room

The Situation Room

I just read my friend George Stephanopoulos’ book The Situation Room, an account of said room over the last sixty years or so. It is a well-researched, clear, and smoothly written book, full of information, eye-opening. As a window into American politics over the relevant time period, it is exemplary; everyone in government should read it, as well as any responsible citizen. The moral tone is understated but strong. The realities of modern government are vividly evoked. Of course, the author is perfectly placed to provide such an account, given his involvement in front-line politics and political journalism; but I also appreciated the personal qualities of the man, of which I have direct experience. I recommend it. The chapter on Trump alone is worth the price of admission.[1]

[1] An oddity: there isn’t a single semicolon in the whole book, as I pointed out to the author.

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Albert Einstein: Logical Positivist

Albert Einstein: Logical Positivist

In chapter 3 of Relativity (1916) Einstein writes: “We entirely shun the vague word ‘space’, of which we must honestly acknowledge, we cannot form the slightest conception, and replace it by ‘motion relative to a practically rigid body of reference’” (22). Overlooking the use-mention error, Einstein is stating, as if self-evident, that we have no conception of space—not because it exceeds our cognitive powers, but because there is no such thing. We must replace this pseudo-concept with the concept expressed by the quoted words; replace not reduce or identify. Later we read: “The concept [of simultaneity] does not exist for the physicist until he has the possibility of discovering whether or not it is fulfilled in an actual case. We thus require a definition of simultaneity such that this definition supplies us with the method by means of which, in the present case, he can decide by experiment whether or not both the lightning strokes [strikes?] occurred simultaneously.” (37) Does he think physicists are somehow conceptually impoverished compared to the rest of us? Presumably not: he thinks that no one has a concept of simultaneity independent of a method of verifying statements of simultaneity. No method, no concept. He doesn’t argue for this position but takes it as self-evident. Does he think the same thing applies to all concepts or just these two? Apparently, it applies to all. In fact, he thinks these concepts (and maybe all concepts) need what he calls a “physical meaning” in order to be genuine concepts; in so far as they don’t, they are empty. Thus, space comes down to measuring rods and time to clocks. His whole theory rests on these assumptions. But they are straightforward instances of verificationism. Einstein admitted that he was influenced by Hume, and we should take him at his word. One wonders what he thought of mental concepts or ethical concepts or logical concepts.

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Friendship

Friendship

In our society we treat romantic and friend relationships differently. Romantic relationships go through predictable stages, often culminating in marriage: they progress to the point where a legal contract is in order. But friendship does not follow this course: it develops but it doesn’t culminate in a legal contract, or any kind of contract. It remains informal, unregulated. People may have lifelong friends but this is never sanctified by anything like marriage, legal or otherwise. There is no friendship ceremony, exchange of vows, pledge of constancy. Accordingly, there is nothing like divorce, with accompanying protocols. It is possible to terminate a friendship without any legal repercussions or even social stigma. True, people may feel let down, hurt, and betrayed; but there is no legal recourse, no penalty. Nor is there any ritual whereby the friendship is ratified and made public. Everything is left loose and casual. There isn’t even anything corresponding to a “dating” phase, recognized as such; it just meanders along. Would that seem desirable in romantic relationships? Suppose a society treated romance like friendship—wouldn’t that be highly unsatisfactory for all concerned? It carries no commitment, no security. And people like to know where they stand in their interpersonal relations. The institution of marriage, legalized or not, is there for a reason. But friendship is left to its own devices, as if it can take care of itself. The OED defines “friend” thus: “a person with whom one has a bond of mutual affection, typically one exclusive of sexual or family relations”. A bond is defined as “a force or feeling that unites people”. Yes, friendship is a uniting of people in mutual affection—as is marriage—but we don’t treat it correspondingly. It is taken more lightly, as a matter of law and custom. The bonds of friendship can be broken with relative impunity, whether the break is warranted or not. Since this happens with some frequency, people can suffer in consequence, sometimes badly.

What if we changed our practices regarding friendship—would life improve? Suppose we had friendship contracts like marriage contracts: formal ceremonies, document signing, the works. You could be “friended” to X, Y, and Z. This would be the culmination of a kind of trial period and carry serious commitments; it is supposed to be binding. You can’t just a break up a friendship so sanctified without adequate grounds. You have to appear before a judge and specify your reasons for abrogating the friendship contract. We can predict that such separations would be rare, because people would not enter into friendship contracts without serious consideration. This would add structure to human relations: it would produce a degree of stability and assurance, prohibiting the dropping of friends on a whim or because of selfish considerations. It would provide a solidity to friendship that shores it up against human weakness. Moral integrity cannot be relied upon in romantic relations, so we have marriage; similarly for friendship—it needs the backing of custom and law. False friends would be weeded out by such a set-up, or at least minimized. Surely that would be an improvement on the existing arrangements (or lack thereof). People would be happier, less subject to unscrupulous treatment. The system would be entirely voluntary: someone who felt themselves incapable of real friendship need not participate, instead of hiding behind the pretense that they are true friends. Everything would be out in the open. It would take a lot of the uncertainty out of the friendship relation. There would have to be public declarations and promises not just unspoken understandings. You could “propose” friendship to someone and they could accept or decline your proposal. The more one thinks about it the better it sounds; this could substantially improve human relations. It might enhance interpersonal harmony, encourage fellow feeling, prevent conflicts. Not “All you need is love” but “Let’s enter into a friendship agreement”. It would be nice to feel bonded in this way to selected others; not just to one’s spouse but to one’s closest friends. It would introduce a social category that corresponds to a felt human need. You could say, “This is my wife, Claudia, and my friend, Horace”. Ideally, we should have a new term for this category (none exists at present), but pending that we might resort to the description “legal friend” or some such. As things stand, we say things like “dear friend” or “old buddy” or “good mate”, but something semantically like “wife” or “husband” would be desirable. Probably a cap should be put on the number of these permissible in law—say, five. You don’t want to be accused of spreading your friendship too thin. Monogamy is not required, but not unlimited polygamy; we don’t think much of people with twenty “best friends”. It all seems quite doable and potentially beneficial.[1]

We already have something like this set-up with other human relations outside of the romantic. The employer-employee relationship and the teacher-student relationship follow this pattern: obligations and formalization are part of the deal. In both cases there is mutual reliance (if not affection), so that breaches and breaks are frowned upon or worse. There is a kind of contract at work, even if quite loose. If I undertake to teach you something and you agree, it is expected that I follow through, and you too. Teaching, like marriage and friendship, is an investment of time and effort; it needs some sort of institutional backing to keep it on track. Same for employment: hence, employment contracts. These things can’t be left to individual whim or opportunistic opting-out. We recognize this for teaching and employment, so why not for friendship? Indeed, they often both involve friendship. What is not acceptable is violating the trust implicit in friendship without adequate grounds. Here an element of formality is required, given (alas) human nature. The fact is that people need friends—life without them is difficult and dismal—so the social bonds need to be supported by institutional scaffolding. It is really high time in human history that friendship be given its due. It needs all the help it can get.[2]

[1] It would be possible to begin locally: you could ask your friends what they think of the idea and institute a system among yourselves. Verbal declarations would be an obvious starting point (“I hereby promise to act as a friend henceforward”). That way people can’t suddenly turn on you out of the blue.

[2] As a side issue, it might be healthy to view marriage as a special case of a more general type of social bond, along with friendship (also teaching and employing). All of these involve commitments, promises, and obligations. Marriage is not unique in this respect.

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Applause

Applause

I once gave a lecture in Finland on externalism and twin earth cases. At the end there was a very brief burst of applause, lasting no more than two seconds. Afterwards I said to my Finnish friend Esa Saarinen that they must not have liked it much given the brevity of the response. On the contrary, he replied, Finnish academics never applaud at the end of a lecture and this was the first time he had seen it happen in the Helsinki philosophy department; I should be flattered. Funny, I thought. Last night I was watching Bill Maher on HBO and found myself constantly irritated by the applause (from an American audience): it interrupted the flow of the conversation, was too prolonged, and too self-congratulatory. It also reduced a serious discussion to a branch of show business—the audience was enjoying the performance. Surely the expression of a moral position on a serious matter should not be greeted with clapping. No one should be applauded for stating the moral truth as they see it. Of course, in America everything is showbiz, performance, theater: but really! Should I be applauded for expressing my opposition to capital punishment or my belief in animal rights? I am not trying to entertain (that is not the illocutionary force of my speech acts). So, when is it right to applaud, and when is it wrong? The ethics of applause has not, I believe, been explored in moral philosophy, but someone has to do it.

A strict view (call it the Finnish doctrine) is that applause is only proper at theatrical performances–operas, concerts, plays, ballets, and the like. It is not proper at scientific conferences, philosophy talks, political speeches, commencement addresses, and the like. At such events, the intention is to convey truth, impart knowledge, not to entertain or amuse; they are not performances for which the performer should be congratulated. No one thinks that when a doctor gives a diagnosis, or a lawyer a legal opinion, they should be applauded. I think there is a lot to be said for the Finnish doctrine; I also think the Finnish preference for brevity is to be recommended. Nodding is fine in other contexts, or facial expressions of appreciation, but not this wretched clapping of the hands—so loud, so raucous. However, we might make an exception for things like graduation ceremonies and athletic victories—here we might allow some of that “putting your hands together”. Graduating, like singing an aria, is a type of achievement, unlike arguing a philosophical thesis or offering a moral judgement. I like the idea of telling someone you think they gave a good paper, but not slapping your hands together as if he or she just performed a double somersault. It’s debasing, levelling. We must resist the urge to reduce everything to a form of entertainment. The Finnish doctrine embodies this resistance: not all types of appreciation must take the form of that appropriate to an opera or rock concert. My own feeling is that ballet most warrants the response of applause, because of the degree of discipline and achievement that goes into it, closely followed by opera, then drum solos. It should be kept out of intellectual contexts or acceptance speeches or psychotherapy sessions.

One thing about applause that is deeply suspicious is that it is itself a type of performance for which applause might be appropriate. I applaud your applause for its vigor, loudness, sincerity, etc.—and you might in turn applaud my applause for your applause. I suspect this is what is going on with Bill Maher’s audience: they want to be applauded for their good judgment, right-thinking, and sheer loudness. People who applaud at ballet performances for minutes on end, till their palms are red and sore, are like this—look at my excellent taste! I think ten seconds is good enough for a sterling ballet dance. Whooping is the worst: what a dismal performance that is! So, don’t draw attention to yourself when you applaud—don’t perform the act of applauding. And don’t applaud at all if you don’t feel it: when deeply moved by an artistic work (e.g., a Shakespearean tragedy) clapping your hands together may be the last thing you want to do (the noise, the percussive blows). Applause has gotten out of hand; it needs to be handled more discreetly. I actually would like to see Finnish austerity extended across the board, at least for a period of time—no applause for anything, just inner appreciation. The performers could be apprised of this new policy and not take it amiss, relishing those appreciative looks and admiring whispers; there is really no need for all that routine racket and hand spanking. Isn’t it really a paltry substitute for genuine feeling, reflection, thought? Instead of quietly taking in what we have just witnessed, we launch into a frenzied cacophony. Why is that a good idea?[1]

[1] When I used to give papers, I would often be confronted with a wall of applause, quite long-lasting. I would think, “Yes, but did you agree with it?” In earlier years I used to perform drum solos and felt no dissonance at the applause (applause is a bit like drumming).

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Science Without Language

Science Without Language

Clearly, there could not be poems or novels or essays without language: these things consist of words arranged into sentences. Equally clearly, there could be athletic activities without language: football, high jumping, sprinting, badminton. People may talk as they engage in these activities, but they don’t consist in talking. Could there be art (painting, music) without language, or economic activity, or politics, or carpentry? Some may say no, but that is certainly not obvious (I don’t think these activities are necessarily language-dependent). Could there be science without language? That question is much murkier; it is like the question of whether there can be mathematics without language, or logic, or geography, or history. If we ask whether there can be science without thought (knowledge, belief), the answer is quickly returned: no, because science isscientific thought. Science can’t exist without minds for it to exist in, and propositional attitudes are its necessary vehicle. There is no such thing as scientific knowledge if there is no scientific belief. The sciences, as we have them, are bodies of belief or knowledge, so there can’t be the former without the latter.[1] In the same way, there can’t be science (as we have it) without mathematics or logic or observation or inferential reasoning. Viewed as a human cognitive structure, science consists of all these things, but centrally of thought: there is no such thing as thoughtless science. Then the question is whether scientific thought requires scientific language. Can there be science without symbols? Someone might say that there cannot because allthought requires language. Such a person might mean an internal language or an external language—a language of thought or a language of speech. The former view would imply the scientific necessity of language trivially; the latter view would imply it by making inner thought depend upon outer spoken language. I am concerned with the second question: so, we are asking whether science depends on speech. I don’t think all thought depends on speech, for reasons I won’t go into here; I am interested in the question of whether scientific thought in particular depends on speech. Is there anything specific to science that makes it essentially linguistic? Is it like poetry or is it like painting? Is the presence of spoken language necessary or contingent to the existence of scientific thought?

It might be replied, evidently plausibly, that science, as we have it, does essentially involve language because of the existence of scientific communication: conferences, journals, conversations, books, letters, peer review. But that answer is superficial: why shouldn’t there be a Robinson Crusoe figure keenly interested in science and yet cut off from all scientific communication with other scientists? He has scientific thoughts (observational and theoretical) but he never talks about them with anyone. That seems perfectly possible; and isn’t the ordinary scientist in essentially this position when alone in his lab or study? Talking about science is subsequent to thinking about it not a pre-condition of it. Any serious connection between science and language must cut deeper than this. It can’t be just that speech is the externalization of scientific thoughts, if the connection is to be of any significance. Art requires artistic materials in order that anything be made (e.g., pigments and sounds); is there anything about science that makes it require linguistic materials? Does it require, say, the existence of grammar in order to count as science? Granted, not all thought presupposes grammar (say, animal thought), but does scientific thought need the resources provided by grammar? The question is suggestive and appropriate, but the answer to it appears plainly in the negative. There could be science without syntax. What if we had evolved to the present time with the general intelligence we now possess but without ever acquiring spoken language? Language came along recently in human evolution, but our big brains were there all along; so, in principle, it looks possible for us to have developed scientific thought but not spoken about it (solitary Newtons and Darwins, say). And yet it seems funny to say that our present scientific knowledge owes nothing to language, though it may be difficult to identify what it is exactly. Our intuitions are pulling us in two directions: on the one hand, thought as such does not entail spoken language to express it; on the other hand, our scientific world-view seems steeped in language, and inconceivable without it.

The science of linguistics needs language, obviously, because it is about language. But most science is not about language but about the extralinguistic world. We can truthfully say that science requires more than just scientific beliefs: it requires observation, memory, and theory construction—but where does speech come in? Compare history and geography: they too require observation and memory, possibly also theory construction, but do they also require language? Well, look at a typical history or geography book—what do you see? You see sentences, dates, maps, but also names—names of people, names of places, names of movements. If you were to delete these names, you would be left with very little. The knowledge you acquire from these books is typically name-involving (Paris is the capital of France, say). True, you could have some historical or geographical knowledge without the introduction and use of names, but those subjects would be crippled without the apparatus of naming. Such knowledge is name-centric. Thus, if we ask whether history or geography requires language, the answer is yes—part of language, at least. You couldn’t be a languageless being and have our geographical knowledge, because that requires mastery of the practice of naming. Geography would never have got off the ground without naming as a pre-existing psycholinguistic achievement. It could exist in embryonic form but not in its current splendor. Huge amounts of history and geography are about names, in the sense that you have to be aware of what is involved in something being called by a certain name: these subjects are implicitly metalinguistic. One knows, for example, that the city called “Paris” is in the country called “France”. So, they resemble linguistics. Not every concept is like this: some concepts, and the thoughts they feature in, are not tacitly metalinguistic—color concepts, shape concepts, moral concepts, etc. But concepts like Paris and France are, so knowledge involving them is language-dependent. To be Paris is to be called “Paris” (but to be red or square is not to be called “red” or “square”).

The extension to science is obvious. Enormous tracts of scientific discourse consist of name-like expressions–labels, tags, designators, cognomens–and hence introduce a metalinguistic element. You can’t grasp the propositions expressed without understanding the practice of naming. You have to be name competent, and hence a speaker. Without the use of names science would be crippled: just consider zoology and astronomy, to name but two sciences. The ability to name things, often using what are called “technical terms”, is critical to advanced science; that is why neologism is so common in science. The roots of naming no doubt trace back to the vernacular, but this resource is massively exploited in the sciences; and it is very useful there, because we often don’t know the nature of the things we wish to refer to—we need a nondescriptive label. If we could replace all names in scientific discourse with general descriptions, we could in principle dispense with language as an aid to scientific thought; but in practice that is impossible, so we are stuck with them. The result is that science cannot do without language, at least for limited beings such as ourselves. It can exist at a primitive level without language, but once we start to insert names into our scientific statements, we are introducing language into scientific thought. The answer to our question then is that much of science is language-dependent, though not all. Science as we have it requires language mastery for its possession.

This changes our picture of scientific theories. Empiricism pictures science as a congeries of experiences not essentially bound up with language—observations (not observation statements). That is the cognitive kernel of our scientific knowledge. But, according to the position here advanced, it is also a linguistic construction—a congeries of names (name-like expressions). Nor are theories “sets of propositions” that may be grasped by the nonlinguistic, but assemblages of words accessible only to the linguistically initiated. This is “nominalism” not empiricism (or even “propositionalism”).[2] Our scientific knowledge is constrained by our cognitive capacities (trivially), but these involve the apparatus of naming with its distinctive features. Scientists thus need to be speakers in order to do science in any meaningful way. Thinking isn’t enough (though necessary). This is why you have to learn the nomenclature of a science in order to do that science. It is the basis of categories and classification. A monograph entitled “Naming and Science” would be well named. Fortunately, we are prodigious name-users in ordinary life, so the cognitive demands of science are not too daunting. In all probability, we evolved this capacity as a tool of social interaction—we needed names for other people. So, the basis of scientific language is social psycholinguistics (in part). No human science without human society. We called each other by names and we then extended that practice to the rest of the universe (notice how personalized astronomical names are). Our intuition was therefore correct when it prompted us to declare science (partly) parasitic on language—without endorsing the strong and implausible claim that thought is always dependent on language. An adequate theory of scientific knowledge must include an account of scientific naming (a neglected field).[3]

[1] It will be noticed that I bypass completely such views as that scientific knowledge is a “language game” or a series of “texts”. That is an impoverished and misleading picture of what science is. In the first instance, scientific knowledge is a type of psychological state (competence, cognitive structure). So, there is no quick route from science to language.

[2] I don’t mean “nominalism” in its usual acceptation; my neologism is intended to capture the idea that scientific knowledge partly concerns what things are called, i.e., is metalinguistic.

[3] I often think that philosophy of science covers a too narrow range of topics. It has been overly influenced by logical positivism. This paper attempts to introduce a new topic into the subject.

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Administrators

Administrators

University administrators are rapidly becoming the most reviled people in America, and with good reason. When was the last time you heard of one making a good decision? It has always been thus, you say. But it is getting worse: atrocious decisions abound, heavy handedness is the norm, authoritarian attitudes prevail, academic freedom is trampled. Clearly, these people are not up to the job (where were they taught, what kind of qualification do they have?). They don’t seem to understand the basic principles of fairness, proportionality, and common decency. They come across as thugs and fools, completely out of their depth. With this in mind, I would like to offer my professional services, for free: I am available to be consulted by any university administration struggling with its decision-making. I have had a lot of experience in this area, am a competent moral philosopher, and not a total idiot. You could do a lot worse than enlist my aid. In fact, I think I could save you from your worst blunders. So, call me, let’s talk.

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