Quantifiers and Mass Terms

 

The usual approach to quantification focuses on quantifier words combined with count nouns, as in “All men are mortal” and “Some sheep are black”. We are told that such sentences require a paraphrase by means of variables ranging over objects (the “domain of quantification”)—“for some object x etc.”. But there are quantified sentences that employ mass terms not count nouns, as in “All coal is black” or “There is some milk in the fridge”. No objectseems to be meant—no x such that… It makes sense to ask how many objects are thus and so in response to a quantification using a count noun, but we can’t ask how many coal are black or what the number of milk is. We can ask how much coal or milk there is in a certain location, but not how many coal or milk is there. Mass term quantifications don’t “range over” a class of countable objects that can be assigned to bound variables. That is not how their semantics works. Yet the logic of such sentences follows the logic of count noun quantifications: from “All coal is black” and “This is coal” we can infer “This is black”. So it looks as if the standard semantics doesn’t capture the logical implications that are involved. This means that predicate logic is inadequate to capture quantifier entailments. Not good!

            It might be thought (hoped) that mass term quantification can be analyzed by means of count noun quantification; we just need to bring in an ontology of chunks, lumps, pieces, volumes, morsels, and smidgens. Thus we have “All chunks of coal are black” and “There is a volume of milk in the fridge”. This already sounds stilted, but it also trades on a correspondence that doesn’t amount to a paraphrase. It is true that we can manufacture a truth about objects by employing such dummy sortals, but that doesn’t mean that the two mean the same thing. Likewise we can contrive a mass term quantification for any count noun quantification, but it would be wrong to claim semantic equivalence. Consider “There are many cod fish in the North Sea” and “There is a large amount of codfish in the North Sea”, where “codfish” functions as a mass term like “salmon” or “halibut”. Where there are fishy objects there is fishy stuff, and where there is fishy stuff there are fishy objects. But does anyone think we can analyze “All men are mortal” as “All man stuff is mortal”? One type of sentence speaks of objects of a certain kind; the other type speaks of stuff of a certain kind. Objects and stuff go together, but talking of one is not talking of the other. Also, the paraphrase in terms of dummy sortals doesn’t always get the truth conditions right: it may be true that all coal is black but not that all pieces of coal are black, because some pieces might be too small to have color; and the milk in the fridge might be scattered about not collected into a discrete volume. And isn’t it consistent to reject an ontology of objects while accepting that the world contains stuffs? There is coal and milk and gold and blood but there are no objects corresponding to these stuffs (“stuff metaphysics”). Stuffs are manifested at locations, according to this view, but there are no real objects that fall under mass terms. You can be an eliminativist about objects but a realist about stuffs. There is certainly no obligation to accept the count noun paraphrase, clunky as it is. It looks like an ad hoc attempt to save a theory not a natural semantic analysis.

            Note that this point also destroys Russell’s theory of descriptions: for we also have “The milk in the fridge is off”, and this can’t be paraphrased by quantifying over milky objects (“There is a unique volume v such that v is milk and v is in the fridge and v is off”). Mass term definite descriptions don’t mean the same as corresponding count noun definite descriptions. Russell’s theory works smoothly enough for descriptions that speak of objects but not for descriptions that speak of stuffs—kings of France but not amounts of butter (“The butter on the table is rancid”). True, we can still use quantifier expressions to paraphrase such descriptions, but these expressions can’t be analyzed by using the standard apparatus of variables and domains of quantification. This is no more plausible than supposing that object quantification can be analyzed using an ontology of stuffs—as with “cod fish” and “codfish”. Objects are made of a certain kind of stuff, but talking about objects is not talking about the stuff they are made of. So it turns out that Russell’s theory, as normally formulated, is too wedded to the standard analysis of quantification; we need to broaden that analysis so as to take in descriptions that employ mass terms.

            So what is the correct analysis of such quantification? I don’t know: it seems to defy the usual type of semantic construction built out of words for objects and properties. What does “some milk” mean? Part of the problem is not knowing what “milk” means: does it refer to the aggregate of all volumes of milk (whatever exactly that means), or is it an abstract singular term denoting the Platonic form MILK, or is it not referential at all? And is some milk a part of the reference of “milk”, or an instance of it, or not a relation to it at all? The semantics of quantifier phrases like this (“most milk”, “a lot of milk”, “nearly all milk”, etc.) is obscure. So we really don’t have a decent semantics for quantifier words as they occur in natural language; and predicate logic (“quantification theory”) is a poor representation of the logic of quantifiers. At best it deals with a restricted class of quantificational inferences. People like to proclaim the great success of modern logical symbolism in capturing the logic of quantifiers, but it turns out that this is only half the story; a lot of quantifier logic is not captured by this symbolism. It works nicely for mathematical quantification because arithmetic isn’t about numerical stuff, but for stuff-related quantification it doesn’t even get off the ground. We already knew that mass terms make trouble for the semantic categories recognized in formal logic (are they predicates or individual constants?); well, it turns out that they also upset the usual theory of quantifiers, both standard and non-standard. Logicians might want to drink some warm milk.[1]

 

[1] I wouldn’t be surprised if linguists have noted the linguistic phenomena here recorded, but my knowledge of linguistics doesn’t extend far enough to be sure. There was a flurry of work about mass terms a couple of decades ago in philosophy, but I don’t recall any mention of the difficulties posed by mass term quantification.

 

 

Why Does Philosophy Exist?

 

It is easy to see why most subjects exist. Geography exists because planet Earth is divided into parts that can be mapped: there are geographical facts that can be ascertained. Physics and chemistry exist because the world contains physical and chemical facts (objects, properties) that can be discovered. Psychology exists because there are minds that can be investigated. Biology exists because there are organisms. Mathematics exists because the world can be counted and measured. Ethics exists because people do right and wrong things. But why does philosophy exist? Is it because the world contains philosophical facts that can be ascertained? That sounds wrong: philosophy consists of problems raised by the non-philosophical world—problems of a philosophical nature. If there were no such problems, philosophy would not exist (the other subjects would still exist even if there were no problems in them). Other subjects may investigate the same phenomena as philosophy, but they do so non-philosophically (the “adverbial theory of philosophy”). So what produces this distinctive type of problem? Following the example of the other disciplines, we might suggest that the world contains philosophical objects, properties, events, and facts–but that sounds like a category mistake. We must rather ask what gives rise to philosophical problems, this being what constitutes the subject matter of philosophy.

            Three suggestions are familiar: reality, concepts, and language. Thus it might be supposed that reality contains philosophically problematic entities such as consciousness and free will. But reality isn’t uncertain about whether it exists or what its nature is: things are not objectively philosophically problematic. Things are philosophically problematic only in relation to us (or other intelligent beings). As God surveys the world nothing stands out to him as philosophically problematic. The uncertainties and theoretical rivalries of philosophy are not mirrored in objective reality: the world is what it is and not some other thing. If the mind is really an immaterial substance, then that is what it is, philosophical disagreement be hanged. Philosophy arises from the state of our knowledge not from the state of reality. It is not that one kind of entity is intrinsically “more philosophical” than another—though one kind of entity can produce more philosophical puzzlement in our minds than another. Meaning is more philosophically challenging than syntax and phonetics, but to an omniscient mind they would be on a par. So the source of philosophical problems (i.e. philosophy) can’t be reality considered sub specie aeternitatis. A second idea is that philosophy arises from the nature of our concepts: our concepts are inadequate or misleading in some way, and this causes philosophical perplexity in us. Perhaps they are superficial or confused or contradictory or just plain crude—in any case, they bring philosophy into existence. If they could be revised or reformed or replaced, we could make philosophy disappear by removing the source of its problems. Philosophy exists because of the defective nature of our conceptual scheme. This view raises many questions: How exactly do our concepts give rise to these problems? Why do we have concepts that lead to such problems? What is it about our concept of consciousness, say, that leads us to the philosophical difficulties we encounter? What would a concept of consciousness be like that did not lead to philosophical problems? It is hard to believe that our concepts could have philosophical controversy baked into them, and into only them; they seem to function perfectly well most of the time, so why do they trip us up when we start philosophizing? It can’t be their constituent structure or their ease of combination. How could human thought necessarily lead to philosophical conundrums—in virtue of what property of it might this happen? Third and familiar, there is the claim that language is the source of all the trouble: reality itself is not philosophically problematic, our concepts are in good order, but our spoken language systematically misleads us (“bewitches” us). But why should our language exercise such enormous power—the power to generate the ancient and venerable problems of philosophy? Can’t we just ignore it, as we ignore parts of it already? It doesn’t have to dominate our thought any more than its sounds do. And what serious philosophical problem has ever been resolved by exposing the supposed logical defects of our natural spoken language? The whole idea is preposterously optimistic. If it were on the right lines, we should have put a stop to philosophy long ago, by judicious attention to linguistic forms. It is simply not credible that philosophy exists because our language is misleading (despite a spate of twentieth century enthusiasm for the idea). So the standard suggestions don’t work.

            But we have not yet run out of possible theories. Might it be that philosophical issues are like political and practical issues in the sense that there is something to be said for several different positions on them? Is Scottish independence a good idea, should the British monarchy be abolished, is Turgenev as good a writer as Tolstoy? There is irresoluble controversy about such questions, as there is about philosophical questions, so perhaps this is why philosophy exists. But this is a bad analogy and the underlying conception of philosophy is mistaken. The issues cited are practical, political, or aesthetic, but philosophical issues are not like that; and there is surely a fact of the matter about the relation of mind to body not just a debatable question about which opinions may reasonably differ. This is why philosophers don’t say, “I can see different points of view on this issue, but I think the wisest course is to adopt theory T”. In this respect philosophical problems are like problems in the sciences—questions about what the facts are, not questions about what stance to adopt all things considered. It doesn’t come down to what to do or think “on balance”. Nor do philosophical problems owe their existence to remoteness in time (like history) or distance in space (like astronomy) or being too small to see (like atomic physics) or being private and unobservable (like psychology); many of them are about present-day perceptible nearby things. Philosophical problems have an obscure etiology not explicable in terms of the usual kinds of inaccessibility. We have viable theories of ignorance in other fields, but in philosophy the ignorance is itself mysterious: we don’t know why philosophical problems are so difficult. In fact, it really shouldn’t be hard to know what knowledge is, say, since we have knowledge and can introspect our epistemic state; and consciousness is arguably the best-known thing there is, yet completely mysterious. Or time, space, matter, causality, value, perception, meaning, and so on through a familiar list. These are all extremely proximate and yet extremely puzzling.

            Here is another idea, suggested by Thomas Nagel’s work.[1] Philosophy arises because of a clash between subjective and objective viewpoints: for example, we can view ourselves from the inside by adopting a first-person point of view, or we can view ourselves from the outside as embodied beings in an objective world of space and time. Now we are approaching the question in the right way, trying to find what is unique to philosophy: perhaps the problems of philosophy arise from a need to integrate clashing points of view generated by a difference between subjective and objective perspectives. But there are problems with this approach, concerning necessity and sufficiency. It doesn’t seem like a necessary condition for the existence of a philosophical problem that it involves a clash of subjective and objective perspectives, since the problems can arise from within a purely objective perspective—for example, relational versus absolute theories of space, or different theories of time, or whether freedom is the ability to do otherwise or just doing what you want, or whether perception is direct or indirect, or whether causality is just constant conjunction or involves some sort of necessity . These problems are independent of subjective and objective points of view. And the difference between subjective and objective viewpoints also arises in other areas and yet philosophy is not the result—as with our different perspectives on the physical world. The perceptual perspective coexists with the abstract mathematical perspective and yet we don’t sense a deep philosophical problem here, because we know that we are conscious beings embedded in a physical universe, so there should be different ways of apprehending the physical world. The mere difference between subjective viewpoints and (more or less) objective viewpoints is not sufficient to generate a distinctively philosophical problem.[2] So these materials don’t provide an adequate explanation of the existence of philosophy, though they are no doubt relevant to some philosophical problems.

            One salient aspect of philosophy seems characteristic of it, namely that we have no surefire method of verification (or falsification) for philosophical claims. We don’t have the method of experiment or sensory observation, nor can we use the method of proof (as in mathematics). All we have are “intuitions” and “arguments”: we don’t have empirical observation, measurement, and calculation. No wonder we face unsolvable problems—we don’t have a method for solving them! We have questions but we don’t have procedures for answering them comparable to those used in other disciplines. There are two replies to this diagnosis. First, we shouldn’t underestimate the methods we do use in philosophy, such as the thought experiment and logical deduction; these methods can lead to genuine philosophical knowledge, typically by producing counterexamples to philosophical theses. And we shouldn’t overestimate the verification methods of other disciplines such as psychology, linguistics, history, and literary theory. A lot remains unverifiable in these fields, yet they don’t count as philosophy. Second, what if astronomy, physics, and chemistry lacked the methods of verification they now possess—would that make them into branches of philosophy? It is only contingent that we can verify claims in these fields, and removing the verification procedures doesn’t convert them into parts of philosophy—they would just be unverifiable science. It has to be something about the nature of the problems as such that makes them into philosophical problems, not the availability or otherwise of verification procedures. But what is that? It is true enough that philosophy lacks apodictic methods, but that seems neither necessary nor sufficient to constitute a subject as philosophical.

            Maybe the problem is epistemic: we suffer from a serious epistemic gap and this is what causes philosophy to exist. Not to put too fine a point on it, we don’t know what we are talking about. Our knowledge of reality is glancing and pragmatically based, geared towards specific practical ends, not designed to reveal the whole truth about the universe, and we labor under this constitutional limitation. For example, there are philosophical problems about color—is it subjective or objective, real or unreal, relational or non-relational? These problems are hard to resolve, though we see colors all the time and have concepts and words for them. It seems that we just don’t know what colors are—what constitutes them. We know what wavelengths of light are (up to a point), so there is no comparable philosophical problem about wavelengths; but we really don’t grasp what colors are, though we are aware of color appearances. Likewise, we know what neurons are but we don’t know what consciousness is—only the way it appears to us. We know there can’t be neurons without brains and chemicals, but we don’t know whether there can be consciousness without brains and chemicals—though we may have firm philosophical opinions on the matter. We know what syntax and phonetics are, but not meaning. We know what ethical behavior is (again up to a point), but we don’t know what ethical value is. We know what digestion is, but we don’t know what knowledge is, though both are attributes of a living organism. We know all about muscle contraction, but we don’t know what freedom is—we have no science of it, no physiology. So the things of philosophical interest are the things that fall outside of our epistemic capacities in some crucial respect (not in all respects). And if you don’t know what something is, you are not going to have very good theories of it, especially if your ignorance is principled and systematic. Why is time so philosophically problematic? Because we really don’t know what time is—that’s why. Thus we are led to entertain the Epistemic Gap theory of the existence of philosophy (precedents of it may be found in Kant and others).

This may seem to answer our puzzle, though it would need a lot of spelling out, but there is a nagging question that remains, viz. why are we thus ignorant? Only if we knew the answer to that question would we know why philosophy exists. Someone might say, “Of course we don’t know what these fundamental features of reality are—that’s precisely why we are philosophically at sea—but that just restates the question, i.e. why do philosophical problems exist?” And indeed it is a real question why the things that are so familiar to us are so removed from our understanding: why should time, say, be so elusive, so maddeningly opaque? We don’t even know whether it can exist in a world without change! Our ignorance about what things are seems gratuitous, strange, and hard to explain. Beings not afflicted with such ignorance might well not recognize philosophy as a separate subject, finding it all plain sailing, so there must be a question as to why we are so afflicted—but we have no good answer to that question. Maybe it has something to do with evolutionary demands (doesn’t everything?) but that is at best a theory sketch or chapter title. And then there is this question: is it really credible that knowledge of what these things are would instantly terminate philosophical uncertainty? Could it not simply accentuate the problems? Now that we see exactly what consciousness is we are struck dumb about how it relates to the brain (just as Descartes was when he concluded that the essence of mind is thought not extension). Our philosophical ignorance is really a very peculiar thing, not at all easy to penetrate: we have no idea of what gives rise to it. Even if the Epistemic Gap theory is true, the gap is quite mysterious, unlike other epistemic gaps, an incomprehensible type of ignorance. So we don’t know why philosophy exists—why the human mind is susceptible to it. Why is there such a thing as philosophy?

[1] See The View From Nowhere (1986). I’m not saying Nagel explicitly adopts such a view of the nature of philosophy, but the view might be inspired by his ideas.

[2] Subjectively the Muller-Lyer lines look unequal in length while objectively we know they are equal, but this is not a philosophical problem.  Subjectively the Sun appears to rise in the morning while objectively we know it doesn’t rise at all, but again this is not a philosophical problem.

 

 

America: A Theory

 

Gotten: Americans say it, the British don’t (nor do Australians and South Africans). One might suppose that Americans started saying it some time after the first British settlers landed in the New World, thus marking themselves as different from their British forebears. But this is wrong: the British were already saying gotten when they got to America (Chaucer, Shakespeare, et al) and the settlers simply continued the tradition, while the British stopped saying it. So subsequent Americans were actually more like the original Brits than later Brits were in this respect. The reason, evidently, is that linguistic forces or fashions operated in England to change the language, which were not operative in the new country. American English was isolated from these forces and so stayed the same. America didn’t add; England subtracted (rightly or wrongly). This kind of phenomenon obviously has wider application: an animal species might spread to a location in which it remains essentially the same while the original population evolves into something different; art forms could persist in a new setting while in the old setting they undergo change; social customs might continue elsewhere while disappearing at home. The original location may be susceptible to influences that don’t apply in the new location, especially if the new location is geographically isolated. Just to have a label let’s call this the Regressive Relocation Effect.[1] Of course, relocation might have the opposite effect: the new place will occasion changes not occurring in the original place, depending on the forces operating there (the Progressive Relocation Effect). But in the right circumstances we could have stasis in the new location combined with revolution in the old location. In an extreme case the new location could find itself hundreds of years behind the old location as the years roll by—still riding horses, wearing top hats, flogging miscreants, etc. Change happens for a reason and the reasons that apply at home may be absent abroad. A geographically new country might thus become a culturally old country as time passes. It might, as we say, become stuck in the past. In such a case citizens of the new country might be more like past citizens of the old country than present citizens of it are. That is what happened with gotten.

            This suggests a theory: America is more like old England than present England is in certain important respects. The America of today is more like the England of 1607 than the England of today is. Not in all respects, obviously, since many events took place in America in the subsequent years that did not take place in England, specifically the waves of immigration from many countries that transformed the culture of the United States—not all of American culture reflects the culture of Great Britain in the seventeenth century. But certain aspects of American life stand out as similar to earlier phases of British life: I am referring to puritanism, racism, tolerance for violence, the penal system (including the death penalty), philistinism, and animal cruelty. These are remnants of conditions that obtained long ago in British society but which have gradually been removed or diminished by a range of influences. Great Britain is itself a complex society full of competing forces, and it is geographically close to other European and Scandinavian nations, as well as having ties to what is called the Commonwealth (ironic name), so it is open to influences that don’t impinge directly on the United States. There are agents of change acting on Britain that haven’t acted on America, or not to the same degree. Accordingly, America has not changed so much in the respects indicated compared to Britain. The persistence of slavery and allied institutions is the obvious example: America supported slavery for longer than Britain, thus exhibiting a similarity to an older Britain that outlived that of Britain itself. Americans were “more British” than the British when it came to slavery (and most of the slave owners were themselves of British descent). The same can be said of the other societal traits I mentioned: puritanism persisted with less opposition in America, as did claims of racial and national superiority, as did penal practices. England became more civilized, less barbaric, as time went by (to put it normatively), while America retained more of the old outmoded ways. Of course, this a matter of degree, and America may be more advanced in other respects, but it seems clear that it contains elements of a culture that has withered away more decisively in the old country. Let me put it bluntly: Americans have the mentality of Englishmen of a century ago (plus or minus a bit). You can see this in prevalent attitudes towards science and learning, in religiosity, in an acceptance of violence as a way of life, in the virulence of white supremacy, and other traits. There is, I’m sorry to say, a fundamental lack of sophistication in the American mind, akin to that which obtained in earlier iterations of the British mind (and which still exists in parts of the latter mind). The reasons for this are no doubt complex, but geographical isolation must surely rank high—nothing proximate is forcing the American mind to change. It is why, to many Europeans, America seems like a savage and barbarous place—technologically modern but spiritually and morally backward. America, it is felt, should really be more civilized than it is (no universal healthcare, for example). My theory is that this fact results from the Regressive Relocation Effect—it is gotten writ large. Americans are actually more British than the British—more like the British of yore. Britain has changed more in the last four hundred years than America has, owing to a variety of internal and external forces. British culture has been more porous than American culture during this period. The American psyche is accordingly more rooted in its historical connections to old England than the contemporary English psyche is. Of course, both are rooted there still, but in America the roots go deeper (notice the strange reverence for the British royal family in the USA). The British in Britain have been more psychologically deracinated than the British in America during the last few centuries.

            If I were to single out the historical event, or series of events, that mainly caused this divergence, I would cite Britain’s gradual loss of empire. This loss wrought huge changes in the mindset of the British, but nothing comparable has ever overtaken the USA. America still has considerable influence in the world (despite some nervousness about China) and so faces little threat to its global power, whereas England has had to accept its vastly diminished status. The result is greater humility in the one and continuing arrogance in the other (nothing compares to American self-righteousness). America today is like England at the height of its colonial power and cultural clout, just so pleased with itself. England has changed tremendously in this respect since the first English settlers arrived on American soil, but America has not suffered such changes, so it has not had to adjust to them. It could therefore continue in the same old way and feel justified in doing so. The American mind is still like the British mind of its colonial heyday, and descends from it, while that type of mind has virtually disappeared from British shores. But I must add that the loss of empire is just one source of historical change and doesn’t explain everything about the divergences between the two countries over the last few centuries. The point I have wanted to urge is that the cultural divisions between the two countries are the result of historical continuity across continents not cultural discontinuity: America didn’t part ways with England; England did. America is England suspended in time. The sources of cultural innovation in America were largely brought by other immigrants (voluntary and involuntary) not by descendants of the original British settlers; the British simply persisted in their old ways (puritanical, punitive, xenophobic). This is why American culture is as fragmented as it is (inter alia). By contrast, the British in Britain were forced to change their ways by a variety of circumstances: geographical location, internal dynamics (class warfare, industrialization, propinquity with other countries, etc.), and loss of empire. America is now more traditionally British than Britain (and not in a good way). The cure for its ills is therefore to stop being so tied to old England. The revolutionary war was never properly completed. This is quite compatible with recognizing that Britain has also had some good effects on American society, but along with these have come various bad legacies, with which we are distressingly familiar. The British may hanker after the past (Brexit etc.) but Americans are the past—what Britain used to be like. Americans are still saying gotten.[2]

 

[1] The effect derives from the Law of Societal Inertia: societies don’t change unless a force is applied to them that makes them change. All societal changes require positive interference; there is no spontaneous change. The interfering factor can be economic, military, moral, scientific, religious, etc. To continue the analogy with physics, America is like a closed system stably preserving its initial state over time.

[2] Compare the metric system: Britain was forced to adopt the metric system in the late 1960s and not without considerable reluctance, but America has never followed suit, feeling no pressure to make the change. It isn’t that Britain always had a metric system and American innovation invented the non-metric system; no, it just clung on to the old system. Similarly with capital punishment: it’s hard to stick with this barbarity when all around you are abandoning it (continental Europe), but in America there is no one around you pushing for a more humane legal system. I could go on: racial segregation, factory farming, lack of universal healthcare, massive income inequality, punitive drug laws, gun proliferation, police brutality, and so on. America is exceptional in these ways, partly because there is no pressure from surrounding countries (Canada and Mexico not having the requisite clout). Nor do we see any rebellion against the past such as we see with countries once ruled for centuries by monarchs. Thus America finds it easy to be complacent about its British heritage (no one in America hates the British, despite that war for independence). America is still dominated by its British inheritance, but that inheritance dates back a long way and has not been subjected to the kind of criticism that has radically altered it in its place of origin.