Mathematical Logic

It has always been felt that logic and mathematics have a lot in common. This led to the idea that mathematics reduces to logic. I am going to argue that the converse is true: logic is basically mathematical; logic “reduces” (expands) to mathematics. It’s more complex than it looks in the textbooks. The first and vital point to get clear about is that logic is not concerned with language—words, symbols. It is concerned with thought—logical thought. If we imagine logical thought before language existed, logic is about that. There is no guarantee that the grammatical forms of language will correctly represent the structure of thought; indeed, that is unlikely to be true, given the prime purpose of spoken language, i.e., efficient communication. Logical thought (reasoning) takes place within the individual and has whatever complexity it needs. Logical concepts are not elements of speech. So, you need to open your mind to the possibility that logic de re is quite unlike the formulas you are familiar with from “symbolic logic” class (an oxymoron in my book). I am talking about conceptual logic—logic in the head. Be prepared, then, for some startling suggestions. Logic needs to be re-written from the ground up.[1]

My thesis then is that what we know as propositional and predicate calculus are species of arithmetic. This is easier to see for predicate logic because it is quantificational—it is about quantity, number. It is about “all” and “some”, or the concepts that underlie these words. These are part of a whole system of quantitative concepts corresponding to “a few”, “several”, “many”, “most”, “more”, “nearly all”, “innumerably many”, “infinitely many”, “one”, “two”, “twenty- seven”, and so on. These are all number words, words for counting, adding, etc. They answer the question “How many?”. It is to be noted that this quantificational logic is second-order: it concerns the number of things falling under a concept, as in “The concept dog has many things falling under it”. The thought is captured by that verbal formulation: we are thinking about concepts and assigning numbers to them. So, we are not doing the same thing in thought as we are when we ascribe a property to an object, as expressed by “That dog is brown”. This has long been recognized by philosophical logicians (or logical psychologists). The logical form of a quantificational thought is given by a property and a number: F (n)—e.g.,Dog (many). In predicate logic (quantification theory) we go up a level and think about concepts and their multiplicity; we don’t think about objects and their properties. Logic is meta.

But how does so-called propositional (or sentential) logic fit this description? In this logic we encounter the ideas of a sentence connective, a truth function, an operator on propositions. Natural language is taken very seriously as a guide to logical structure. There is scarcely a linguistic turn; the subject matter is already assumed to be linguistic (not that people are very clear what this means). How do these logical words and concepts assume a mathematical shape? The answer is not far to seek: “and” means “both”, to put it simply. The conjunction “p and q” means “Both p and q are true”; not one of them, or none, but both. This is a quantity word: the mind is working quantitatively when it thinks conjunctively—numerically, arithmetically. If both are true, then not just one is true—truth here requires a number of separate truths. If the conjunction is long, it will require that the corresponding number of propositions be true. The word “and” works like the word “plus”: it adds to the number of conjuncts. So, conjunctions in thought are mathematically conceived; you can’t form them unless you have some basic mathematical competence. Conjunction is often compared to universal quantification and the comparison is apt; but “all” is a number word, and so conjunction is a mathematical concept too, perhaps the simplest one. Disjunction works similarly: “or” means “at least one of the disjoined propositions is true”. It doesn’t have to be all disjuncts, so long as it is some; one will do. All this we grasp when we use the word “or”. We are thinking quantificationally. Hence “or” is often compared to “some”, aptly enough. Propositional logic is thus a species of quantificational logic, as complex and mathematical as it is. Moreover, it refers to propositions, so it is second-order, meta. But what about “not”? That little word has always been a thorn in the side of philosophers of logic (negative facts anyone?); it seems like a thing apart, curious in its connotation. What is this “not-ness”? It doesn’t yield easily to quantificational analysis—where is the “some” and “all”? What does “Not-p” mean? What do I mean when say that snow is not black? I suggest that I mean something like this: “There is no fact corresponding to the proposition that snow is black”, or “None of the facts in the world is the (putative) fact that snow is black”. It is a negative quantifier like “no one”. We could paraphrase our target sentence as “Nothing fits the description ‘black snow’”; or again, “There is no object such that it is both snow and black”. Thus, “not” is a simple word with a complex meaning; it takes a bit of brains to comprehend (animals are probably not up to it). You see why I said logical thought may not be properly reflected in ordinary language? The negative thought is a convoluted thought raising conceptual puzzles. In it the number zero presumably has its beginnings. It goes along with the word “false”: we can equally say “It is false that snow is black”, which is also second-order and meta. To think negatively is to entertain a counterfactual state of affairs and repudiate it as actual. In a way it lies at the very heart of logic, because logic is about necessity and possibility. The concept of possibility is itself tacitly quantificational and hence mathematical: “In some possible world, p”. We can naturally say “In hundreds of possible worlds, p” or “In no possible world, p”. Modal logic is likewise mathematical in character. Logic with negation is also logic with quantification. Similarly for tense logic in which we have quantification over times. All of these are mathematical, though primitively so (actually not so primitive). The logical mind is at bottom a mathematical mind. We would do well to render it more perspicuously in mathematical terms, thereby revealing its affinity with other types of mathematics. It is a kind of pre-school arithmetic.

I end with identity. Logic is sometimes said to include identity, and not without reason because identity is implicit in it. How does identity fit the mathematical analysis? As follows: to say that Hesperus is identical to Phosphorus is to say that Hesperus and Phosphorus are one. There are not two objects here but one object. We thought there were two (or more) and now we learn there is just the one. We counted wrong, as it turns out: if you put Hesperus and Phosphorus together in the same room, you find only one object there; there is one less object in the world than you supposed. In this thought we find the roots of the idea that a perceived plurality might reduce to an objective unity. Identity forces us to think numerically. It is an essentially mathematical concept. Accordingly, even elementary logic (with or without identity) is shot through with mathematical notions, though not particularly advanced ones; we might as well declare it a branch of mathematics. But remember it is not the symbolism that makes it mathematical but the underlying thought content. Mathematical logic is not a branch of logic but its very nature.[2]

[1] Compare my paper “Mathematical Ethics”.

[2] There is an irony in this in that the formulas of symbolic logic were supposed to lay bare the structure of logical thought, but actually it is the structure of logical thought that reveals the real content of those formulas. The thought is mathematical upon closer analysis, and this constitutes the meaning of the symbolic system. The hidden logical form of the formulas is given by the mathematical analysis of the underlying thought. Logic as we have it is a kind of baby math.

A Puzzle about Pornography

Sex and food are clearly powerful forces in the psychic life of human beings. The question may be raised as to which is more powerful (is there a power imbalance?). But there is a curious asymmetry between them: we like to watch pornography but not its culinary equivalent. We like sex porn but food porn not so much. You never hear about people with a food porn addiction. Why is this? People like to watch other people having sex, but not other people eating. People don’t watch food porn videos when they feel hungry—why not? Why do people like watching sex porn when they feel horny? Isn’t it just as pointless as watching people eat when you feel hungry? Isn’t it irrational? The case is like imagination: people regularly have sexual fantasies, but it is not normal to have recurrent eating fantasies. Sexual fantasies are felt as gratifying, but not food fantasies. Teenagers don’t fantasize about chowing down all day. And people like pornography even when sexually active; but they don’t go in for food porn when well-fed. What need is satisfied by sexual images that is not satisfied by gustatory images? Why are there no magazines specializing in pictures of delicious meals? Why is a nude a lot more stimulating than a still life of a plate of food?

A variety of answers suggest themselves. Is it because pornography breaks a taboo but food images don’t? Is it the thrill of violating a taboo? It is true that we see naked food all the time but not naked bodies, and that it is regarded as taboo to want to see the latter. What if we inverted the two? Suppose people were general nudists but food is kept under wraps: you never see people eating food, but you constantly see them naked and fornicating. Would we then revel in food porn? Hardly. Pictures of food don’t have the power of pictures of naked bodies: food going into the mouth is not like the penis going into the vagina (etc.). The two types of “penetration” are not equivalent. Also, it would be breaking a taboo to watch film of people excreting, but hardly anyone would be enthusiastic about that. Taboo-breaking is neither necessary nor sufficient. What about the idea that sex is (partly) visual but eating isn’t? This sounds on the right track: the visual plays a role in actual sex, but not so much in eating. We are stimulated by the look of a naked body but not by the look of a ham sandwich. But is it true that vision plays no significant part in the pleasure of eating? That sounds wrong; it plays some part. And isn’t sex in the dark or blind sex pretty exciting too? Yet we don’t thrill to a purely auditory representation of a sex act. It isn’t that the sense of sight is absent from the food case but essential in the sex case. However, what is true is that sex is typically private and eating is not; and vision is what reveals the private most forcefully, as in voyeurism. Is it that sex porn satisfies our curiosity about this private matter, while food porn would do nothing analogous because eating is public? If we invert the two, the asymmetry seems to fade away: if all sex were public all the time, so that we were inundated with the stuff, we might lose our interest in porn; but if eating were always done privately, away from prying eyes, we might find some frisson in seeing images of it. It’s a question of privacy and curiosity. Yet we don’t have a comparable interest in toilet activity and it is also private; and I doubt there would be much of a market for food porn once the initial novelty wore off (how many times can you watch a man eating a hamburger?). The visual element seems part of the appeal of pornography, and lack of appeal of the food counterpart, but we have not yet identified the crucial difference. It begins to seem quite puzzling.

The puzzle deepens when we recall that food and sex are not just analogous but also connected. People seem to enjoy coupling the two (while coupling) and food-sex pornography is apparently quite popular. Yet no one is interested in pure food porn (except the odd gastronomic weirdo): people don’t want to salivate to the image of a roast chicken or a serving of sushi, no matter how much they may enjoy eating these things. Watching people eat is just not arousing or fascinating or exciting. It is the sex part of food-sex porn that gets people’s juices flowing not the food part. At this point we might be tempted to wax metaphysical: pornography is all about the human condition, death, embodiment, the soul. I don’t think this is completely wrong: thoughts of our animal nature, our talent for creative ideas, our strange juxtaposition of the godly and the goofy, our understanding of interpersonal relations, our grasp of the phenomenon of common knowledge, the mystery of reproduction, civilization and its discontents—all these may come into play. But they omit the primordial character of the depicted sex act—what really sets it apart viscerally. And here I want to mention an obvious fact: the genitals are on full display in all their anatomical glory. And the genitals are of enormous interest to us, because they are the organs of reproduction; the genes have programmed us to be obsessed with the genitals. Their future depends on them. The genitals are objects of endless fascination because of their biological centrality. If we had no interest in them, reproduction would grind to a halt (under normal conditions). I would bet that if you showed a video of the rear end of a female ape in heat to a male ape you would get a reaction. Copulation is genital, trivially. So, pornography is popular because of an ancient biological imperative: genital awareness, genital competence. Sexual selection is part of this: the genitals need to be seen to be present and healthy. Nothing like this holds in the case of food—the female is not going to reproduce with food! Genital know-how is what pornography efficiently enables, and that is useful knowledge to have. Genital curiosity is built into the genes and pornography satisfies this curiosity. A taste for porn is therefore innate and unavoidable. One might even conjecture that pornography works as a learning tool for the human species (think of the wall porn in old Pompei). If we combine this with the other suggestions mooted above, we can see why sex porn has a special interest not shared by food porn. We have no particular interest in plumbing the depths of the mouth and stomach, but the genitals are another ball of wax. We need to keep track of them in sexual encounters, hence the visual element, and their general hiddenness and privacy deprives us of ready access to their anatomy. Pornography enables us to remedy these difficulties. We can simulate in our minds the act depicted, which can then be applied in real life; it is a skill that has to be learned. That is the deep evolutionary meaning of pornography. Puzzle resolved.[1]

[1] I have relegated to a footnote one theory strangely popular these days, namely that the appeal of porn resides in its depiction of women as abused and degraded. This is not plausible as a general theory of the appeal of porn, though some porn no doubt trades on this deplorable proclivity. Obviously, much porn has nothing to do with it. Porn comes in many varieties, though the common factor is the genitals, one way or another. The genes program interest in the genitals and pornography caters to this instinctive interest.

Food and Language

The central place of food in animal life is undeniable.[1] An animal is a food machine. The reason is fundamental: animals need energy to survive and food is the source of energy (it would be different if they could just get charged up like an electric car). It is fair to say that animals are obsessed with food: for themselves and their offspring, mainly. Starvation is not on the menu. They are designed to obtain and consume food. They know their way around food. Many suffer early deaths for lack of it. They communicate about food: in hunting and food-seeking, in learning about it, in sharing or not sharing it. If they could talk like us, they would surely talk about food constantly. We are animals (not plants, rocks, or gods), so we share this obsession: we need food as badly as other animals. We are also speakers. Go back to our early days as a species when we were still on the inarticulate side: chronically short of food, squabbling about it, eagerly consuming it. We were a cooperative social species for whom the food problem was very real (still is for some). Imagine that spoken language was just getting started: what would we talk about? Food, of course—food, glorious (but scarce) food. We would all be Billy Bunters with his “tuck” obsession. Our first tentative language-game would be food-oriented. We would be talkative foodies. This would help us in our hunting and gathering, in our food preparation, in our feasting (or lack thereof). Let’s be honest: we would talk about food a hell of a lot. Talking is energy-consuming, so you are not going to do it if energy is in short supply; but talking about food is talking about energy and how to obtain it, so you would let the talk flow. You would be a natural-born food-talker: a food critic, a food savant, a food fanatic. You would talk about food from dawn till dusk—even over dinner! Here’s what you wouldn’t talk about: sense-data or Platonic universals or material particulars in space and time. Your ontology would be a culinary ontology, which is quite enough to be going on with. Your tools are also mainly food-involving: tools for hunting, cutting, dining with. Fire is mainly used for cooking. Family meals are the center of social life. Your speech acts revolve around the food arena—sharing, requesting, praising, wondering aloud where your next meal is coming from. As time passes, you branch out a bit: you are not only interested in food talk—you are also partial to some mating conversation or family dramas or even discussions of what the Sun is. But you began with food; that’s where your linguistic resources were forged. It therefore seeps into your more general chatter. You use food analogies, food metaphors, food paradigms, food conceptual schemes, food methodologies. For that is the basis from which your language developed—and your thought too. For example, you needed to distinguish food objects from non-food objects, the edible from the inedible; this led you to the concept of a material object in general. You may also start to wonder about the non-digestive organs of the body and differentiate them from the digestive organs. You get beyond the narrow ontology of food proper.

Suppose that sometime later you even start to ponder what we would now call your mind, including your senses. There’s a reality there, you feel, but how to talk about it? You naturally turn to your tried-and-true food language and its conceptual underpinnings: consumption, digestion, etc. You might then start to talk of your mind (though you don’t use that term) as if it is like your stomach and appended organs: perceiving is like consuming, reasoning is like digestion, knowledge is like satiation, memory is like a full larder. Yes, that’s it, you think, no need to invent some newfangled conceptual-linguistic scheme. Thus, you speak of food for thought, indigestible lessons, a healthy intellectual diet, vomitous propositional content. The senses are clearly food-oriented—good at detecting and tracking food, as well as evaluating it—so they have a lot to do with food. The brain is like the stomach as an ingestive organ that processes and transforms what is fed into it. The mind thus becomes modelled on the body, specifically the food organs. In time, some clever cognitive scientist starts referring to various “mental modules” analogous to physical organs of the body–the food module along with the reproduction module and the aggression module. He claims that the food mental module was the first to evolve and that it led to the other two: that is, it is cognitively fundamental. The cognitive mind in general is run on food-representing computations and suchlike things. We are still anchored to those early adventures in food cognition and food speech. And it is true that food naturally radiates outwards, requiring competence in object tracking, inference from evidence, fire management, utensil production, communal dining, fair shares, moral rights, laws governing the proper control of food distribution, and so on. You can’t just be focused on food itself; you need knowledge of the whole matrix in which it is naturally embedded. There is even food science, food medicine, food culture, food ethics, food politics, food art, the foody lifestyle, food disorders and phobias, and food snobbery. It’s a big field, conceptually rich, but all stemming from those early days of anxiously scrambling to put food on the table (an anxiety that has never left us). In the beginning was the meal (deeds were meal-directed).

A well-fed naturalistic ethicist might venture the hypothesis that our ethics is rooted in food ethics: altruistic sharing, natural eating rights, duties to the starving, promises about when lunch will be served, admonitions against stealing food from others. And it is perfectly true that a pride of lions, say, is sorely in need of ethical instruction when jostling for a bite of a freshly killed carcass (greedy buggers). The political theorist might likewise insist that distributive justice primordially requires that food be distributed according to certain abstract principles of fairness, with all other cases ultimately reducing to the food case. Capitalism might be defined as accumulating all the food you can lay your hands on in a free market, including the means of food production; at any rate, this is the basic case. Charities will plead that famine is the worst evil to befall man. Philosophers of physics, not to be left out, will contend that physics is founded on a bedrock of concepts that go back to the hunting and gathering age when we had to chase big lumps of matter through the jungle and then chop them into small pieces (this leading to ancient atomism). What is mass, after all, other than the size of your helping? At any rate, our conceptual scheme and spoken language have a history, and what kicked them off was an obsession with food—this being what led to our species supremacy and the very existence of physicists. We must thank God for giving us a brain that enabled us to solve the food problem—next gravity! A brain that can perform as well as ours in the food department has essentially all it needs to achieve greater things. Even mathematics was invented to do agriculture and count herds. (Is it an accident that a circle is the shape of a pie? I should think not.) Food is at the root of it all (plus some), as a matter of biological fact. That is a truth recognized by our most respected religions: the apple in the Garden of Eden, food rituals, food taboos, religious feast days, the last supper, fasts, and so on. I conjecture that religion began in food-related contexts and then expanded out from there—no doubt anxiety about food fueled early religious practices. Food crops up everywhere in human and animal life; it is part of our natural history (as Wittgenstein would say), a major part. It deserves more recognition in philosophy, linguistics, and psychology.[2]

[1] See my “Evolution by Nutritional Selection”.

[2] A key theoretical tool should be evolutionary derivation not just conceptual analysis and family resemblance: how did some existing adaptation begin and how did it develop over time? This would be a truly biological (naturalistic) philosophy. Of course, it involves expanding biology beyond its narrow professional boundaries. Bio-philosophy will take in food and its conceptual expression. It beats sex and war (with which it is strongly connected).

Objectifying the Fluid Mind

I have argued that our ordinary language and thought about the mind involves an alien imposition or intrusion originating in our concepts of the external world.[1] Here I will expand on this viewpoint, detailing the types of imposition involved and the nature of that on which they are impositions. The second task is much more difficult than the first. In what ways, then, do we apply external-object concepts to mental reality, creating an impression of object-hood in the mind? There are several. First and foremost, we describe the mind as intentional: that is, directed at objects in the external world—trees, rocks, animals, etc. The mind is said to be of or about such objects, and this is held to be essential to its nature. It joins up with the objectual. It has objects built into its fabric. This can lead to the extreme view that the mind is composed of objects, or has no nature apart from its intentional objects (as in Sartre’s idea of consciousness as nothingness). And certainly, the idea of objectless consciousness verges on the self-contradictory. In addition, if we ask ourselves what is left over when the objects are removed, no answer is returned and we stammer in consternation. If there is anything left over, it is deeply mysterious and suspicious. Second, the body: we like to link our sensations with body parts—pain in the foot, itches on the scalp, pleasure in the palate, etc. So, we are thinking of sensations as inextricably tied to the body-object, which shapes their intrinsic character. Third, and connected with the intentionality point, we are apt to conceive the mind’s ability to focus and attend as a kind of pointing: it is directed at something, oriented towards it. This is a physical concept in that our notions of direction and pointing are physical notions; the mind only does these things metaphorically. How else are we supposed to think of such mental acts (and this phrase also is tacitly body-inspired)? Fourth, we are prone to think of memory as a “storehouse”—a kind of library, perhaps, or crammed attic. We have no other way to understand its ability to hold (note the word) items we are not currently conscious of. Then too, we have colorful talk of corners of the mind, depths of the mind, layers of it, mental compartments, modules, theaters, blank slates, slabs of marble, private spaces, zones of emptiness. All these locutions are tinged (saturated) with images of the external physical world. It can seem as if we are desparate to think of something to fill the descriptive void, so we come up with almost anything to remove the conceptual discomfort. Some of it is reasonable enough, even essential, but some seems like pure poetry. No doubt about it, we are apt to objectify the mind—beyond what the mental facts warrant. Some find this repugnant and seek to fashion a mental vocabulary that dispenses with objectual language, placing their money on a supposedly pure subjective language modelled on the blooming buzzing consciousness of an infant or some such. This tends not to amount to much and smuggles in the objectionable vocabulary. It’s all stabs in the dark, basically.

This takes us to the nub of the issue: what is the mind independently of its objectual entanglements? Even when those entanglements are legitimate, as in intentionality, we still have the question of what is mentally involved apart from the objects of the intentional act. What is this of-ness? What is the mind in its pure unadulterated essence? The question is heady and seemingly unanswerable, but I think I may have an answer of sorts. True, it calls for a drastic revision of our conceptual scheme, a complete revolution in human thought, a step into the intellectual abyss—but hey, nothing ventured nothing gained and all that. Actually, it is not quite as startling as it might sound once you get used to it. The answer is this: the mind is a fluid. I don’t mean water or gin or the nectar of the gods; I mean fluid in a more general sense. The OED (bible of the bibliophile) gives us this: “a substance that has no fixed shape and yields easily to external pressure; a gas or (especially) a liquid; able to flow easily; not settled or stable”. We could paraphrase this as “a dynamic, ever-changing process; not a fixed and rigid entity”. To be fluid (and hence a fluid) is to be not a discrete solid thing but a continuous malleable flowing stuff. A Cartesian dualist might well assert that the mind is an immaterial fluid in this capacious sense. We already speak of the “river of consciousness”; well, the mind is fluidic not static, continuous not discrete, a process not a fixed entity. You see how the initial shock wears off? The mind has a fluid mechanics not a solid-state mechanics. It flows and changes; it doesn’t stand still like a dumb rock. It has a fluid metaphysics not a static metaphysics. Granted, we don’t know what this mental fluid is, but we do know that it is fluid—that it obeys the laws of fluids. It is a shifting, formless, flowing, buoyant, bubbly, energetic, fascinating, fluent…not thing, but “something”. It can speed up, slow down, go quiet, rage, and change its shape as the occasion warrants. It moves silently and rapidly. Consciousness, in particular, is a fluid being, flowing this way and that, changing its shape (but it has no shape): now it is perceptually awake, now it is dreamily asleep. It is protean and animated. The mind minds; it isn’t a static object awaiting an outside force to arouse it. It is all action, hustling and bustling. Don’t we experience a wave of emotion, a torrent of thoughts, a rush of memory? Doesn’t our experience sometimes wash over us? Isn’t the will liquidly mercurial? Aren’t our intentional objects like things floating on the surface of our consciousness? Aren’t some things submerged in the roiling psyche? Freud had a hydrodynamics of the mind, and wasn’t he onto something there? Isn’t consciousness phenomenologically liquidy and gassy? Not like other fluid things, to be sure, but ontologically in the same class. Consciousness courses, gushes, and surges. Aren’t we flooded with the stuff?

If so, we have an answer to our earlier question: we objectify what is really fluidic. That is obviously a bad idea on the face of it: fluids aren’t solid objects. Clearly, our folk fluid mechanics of consciousness is primitive, so we supplement it with more familiar concepts drawn from elsewhere. Thus, we get the mish-mash that now exists in our conceptions of mind: an intuitive sense of fluidity combined with a forced imposition of solidity. We are trying to solidify a fluid, to put it crudely. We are imposing an ontological scheme onto a reality that spurns it in its inner nature. We are not going with the flow but contradicting it. We are like people trying to describe colors by shapes. We are trying to reduce the fluidic to the static. And then there is the fact that the mind isn’t even spatial (as we experience it), so we are committing a double category mistake. That’s okay for practical purposes, but we should at least fess up to it. The brain doesn’t operate by principles of fluid mechanics (more electromagnetics), but the mind is all fluidity.[2] No doubt it needs its own mechanics; it won’t do to treat it as just like water. In any case, this picture enables us to give some kind of answer to the question that troubles us, viz. what the mind intrinsically is beyond its habitual description in objectual terms. I heartily agree that this picture is highly speculative, not to say fanciful, but (as Popper says) science proceeds by constructing imaginative theories that are then subject to falsifying test; you can’t just extract theories from the available data. And the more falsifiable the better. In this spirit, I claim that the fluid theory of consciousness (“fluidism”) has not yet been falsified.[3]

[1] See my “Concepts of Mind”.

[2] If we had opened up the human head and found an elaborate hydraulic system, instead of a solid brain made of chunky neurons, we would no doubt have been more disposed towards a hydraulic conception of the mind. As it is, we have only a vague introspective sense of the fluidity of mind; but it is stronger than any sense of the solidity of mind. The river analogy does not strike us as wildly wide of the mark; we don’t say “Oh no, the mind is nothing like a river; it’s more like a pile of dominoes or Stone Henge”.

[3] I actually think Popper’s methodology applies better to philosophical problems than scientific ones, precisely because in philosophy the data are so exiguous. There is a greater role for imagination in philosophy than in science, and philosophy is largely a critical discipline–that’s how it proceeds. Someone comes up with a wildly ambitious theory from nowhere and then other people attack it like a pack of rabid dogs. We call this “philosophy”.