Semantical Considerations on Mental Language

I am going to expound a view of the mind (and hence the mind-body problem) that I am disinclined to accept. Still, the view deserves careful articulation and may contain elements of truth; it should be added to the menu of options. And it is agreeably radical. It begins with considerations on the workings of mental language and takes off from a recognizable tradition. The tradition I have in mind contends that various bits of language have a misleading form: they seem one way but are really another way. Logical (semantic) form does not mirror grammatical (syntactic) form; and we tend to be mesmerized by the latter and oblivious to the former. We have to fight our tendency to take surface form too seriously. Thus: quantifier words are not singular terms but second-order functions (Frege); the word “exists” is not an ordinary predicate but concerns a propositional function (Russell); definite descriptions are not referring expressions but should be analyzed by means of quantifiers (Russell); the word “true” does not denote a property but acts as a redundant device to avoid repetition; the word “good” does not denote a simple quality but is used to express emotion (Ayer) or to make a prescription (Hare); the words “I promise” are not used to make a statement but to perform an action (Austin); words for colors don’t stand for intrinsic qualities of objects but for propensities to elicit experiences (many people); arithmetical sentences look factual but are really fictional (mathematical fictionalists); mental words seem to denote inner states but are really ways of summarizing overt behavior (Ryle); words in general seem to us to be names but they are really of many different kinds (Wittgenstein). The broad thrust of these positions is that language is not homogeneous and what seems like the name of an attribute may not be. At the extreme such a view insists that language is never denotational and properties are a myth; all there is to language is use, inference, grammar, linguistic practice. The view I am going to discuss claims that mental language falls into this category: it doesn’t consist of symbols standing for properties or attributes aptly called “mental” (simple, sui generis, distinct and apart) but rather has a different kind of semantics altogether (what this is we will come to). In particular, it borrows from the redundancy theory of truth and the non-cognitivist view of ethics. It treats mental language as strictly dispensable and non-denoting (“non-factual”). It is not about anything real, though it has practical value and is not entirely fictional. The brain comes into it.

It will be best if I just plunge in and come right out with it. Mental language is strictly redundant because the brain contains all that is necessary to record the facts in question: once you have stated all the facts about the brain, you have said all there is to say about the mind. We must immediately add that facts about the brain are not limited to currently known facts, or even conjectured or imagined facts. The basic idea is that there is no further substance over and above the brain whose distinctive properties constitute the mind; there is just the brain and its properties. There are no additional mental facts. Once you know all about the brain you know all about the mind. This knowledge may or may not include concepts we currently apply to the mind. Similarly, there are no facts about truth over and above ordinary facts: there is no more to a proposition being true than what is contained in the proposition—you don’t add anything to a proposition by saying it is true. In principle, the word “true” is eliminable; we use it now because of certain limitations on our knowledge (as in “Whatever the pope says is true”). We don’t as things stand know much about the brain, especially what is going on in it at any given moment, so we resort to mental language to fill the gap; but really, there is nothing happening in a person’s mind other than what is going on in their brain. How could there be? The brain is all there is mind-wise; there is no semi-detached mental substance. Accordingly, our usual talk of mind is strictly redundant, though practically necessary; it is really an indirect way of alluding to the brain. Instead of saying someone has a certain brain state right now, we say they have a belief or desire; but there is nothing going on except the brain state, which is hidden from us. Our mental words don’t denote or describe this brain state, though they may be said to allude to it, so they don’t introduce any real property that people possess—as the word “true” denotes no real property of things. We may be under the illusion that these words denote real properties, but careful analysis reveals that they do not. There is no additional fact for them to express.

So, how should we interpret speech acts containing mental words?  We might venture an expressivist semantics for mental language analogous to an expressivist view of truth language: mental talk expresses our attitudes towards people and animals without attributing any properties to them, as our truth talk merely expresses our attitudes of commendation or fellow feeling. Less drastically, we might follow Ryle in thinking of mental discourse as the issuing of “inference tickets” conceived as permissions to draw various inferences about the individual so described. In the terms of more recent philosophy, we might speak of “inferential semantics” as opposed to “truth-conditional semantics”: these words aren’t about anything (objects, properties) but they enable us to make predictions and offer explanations. I will propose something more novel and geared to the particular case we are considering: what I will call “correlational semantics” as opposed to “denotational semantics”. Correlated with a given mental state (so called) we have a brain state, which is also correlated with a use of a mental word: if the word applies, then there is a corresponding brain state correlated with it. The word does not denote the brain state but its existence is required for the truth of an application of the word. A correlational semantics assigns this brain state to the word, not as its denotation but as an associated entity (we might include it in the word’s connotation).[1] Thus, there is a firm reality invoked in the semantics, unlike in pure expressivist theories, but it isn’t supposed to be part of what the word means. For example, the word “pain” applies to an individual just if that individual has a certain kind of correlated brain state (as it might be, C-fiber firing). The semantics does not assign the property of pain to the word “pain”, for there is no such property (like the putative truth property). We use the word because we don’t know enough about the individual’s brain to make a more informed statement, and we have practical aims to fulfill, but there is no real property that we thereby denote. There is no fact over and above the brain state, but we talk as if there is for purposes of convenience and practicality (like with truth). Mental words express pseudo-properties (if you like that way of talking).

You might argue that pain and truth differ in a crucial respect, namely that we have an impression of a mental property in the pain case but we have no impression of a truth property. We just have the predicate “true” (and the concept) but we have more than the predicate “pain” (and the concept)—we have the feeling of the property. No doubt there is something right in this, but how much does it prove? Does it prove that there is a distinct property of pain, analogous to a physical property? Not obviously, and the type of theorist I am envisaging will not give in so easily—what if the feeling in question is illusory? I doubt that Russell would give up his theory of existence just because someone asserted (however correctly) that he had an impression of existence as a first-order quality, or that Ayer would throw in the towel when someone objected that he had an impression of goodness as a primitive objective quality. In any case, I am not trying to defend the approach I am describing against all objections; I am just trying to spell out what a coherent view of this type would look like. No doubt such a view, radical as it is, would face the usual philosophical argy-bargy. The intuitive idea powering the correlational-redundancy theory is simply that mental language may not be correctly modeled on other types of language, especially physical language; it may have a type of semantics all its own, contrary to appearances. Surely the brain plays a pivotal role in fixing the mind, and this ought to show up in the semantics. Compare: surely the properties of possible worlds (assuming they exist) play a role in fixing modal facts, and this should show up in modal semantics—hence possible worlds semantics. The realities should shape the semantics, and the brain is as real as it gets. In the end, the mind reduces to the brain (possibly under novel concepts) and we want to reflect this in our theory of mental language. Thus, we get a kind of semi-fictionalist redundancy theory of the mind joined to a correlational semantics of our current mental discourse. The same kind of theoretical structure can be applied to ethics: moral words don’t denote real properties (according to non-cognitivism) yet they have an expressive use and can be treated to a correlational semantics of linked non-moral properties (the descriptive properties on which they supervene). True, this kind of structure is unfamiliar in the semantical tradition (while borrowing from it), and is moderately complex, but it does have some reasonable motivations and precedents. Isn’t it highly likely that the grammatical structures of our language, themselves limited and regimented and uniform, might conceal a good deal of semantic variety that takes some effort to excavate? Mental language, in particular, is constructed from linguistic materials originally employed for other purposes (chiefly physical description), and there is no presumption that the ontology and epistemology of the mind will be subsumable under this format. The hiddenness of the brain, along with its immense complexity, must surely shape the way we talk about the mind, as much by its conspicuous absence as its presence. It would be different if the brain’s workings were open to view and easily discerned—what would our mental discourse look like then? Mental language has evolved as a makeshift compromise, largely practical in function, not as ideal science (it leaves us enormously ignorant of other minds, and of our own). Semantics reflects epistemology. Probably our mental language, and its semantics, will change with increasing knowledge of the brain. Eventually, a respectably denotational semantics will come to apply—or so it will be said.

A feature common to all the cases we have considered is that language has a tendency to suggest simplicity where complexity obtains. The simple subject-predicate sentence suggests the simple object-property model, with the property assimilated to familiar perceptual properties of things. Everything gets compared to perceived color and shape. But it turns out that things are always more complicated—even color and shape. The world is complex and multifarious, deep and hidden. Existence is an abstract construction from propositional functions (and it seemed so simple!). Definite descriptions are really quantified propositions with a uniqueness clause tucked in, not simple referring expressions. The truth predicate is a strange disappearing device for avoiding repetition, not the name of a property. Color is some kind of hard-to-pin-down propensity or disposition to cause experience, not a categorical property of objects. Goodness is not a simple unanalyzable quality, but a complicated practice of emotional reaction (allegedly). The little word “must” denotes a huge collection of complex entities called possible worlds. Words like “belief” and “desire” turn out to express complicated arrangements of brain parts and behavior, not simple qualities of consciousness. Inductively, we should not be surprised when the simple object-property structure turns out to be inadequate to the facts. Practicality favors brevity and simplicity, but philosophical understanding may need more capacious schemes. The brain needs to be brought in somehow, but not in the simple way proposed by classic property-identity theories. It took a while to find a semantics for modal language; no doubt the same is true for mental language. It is striking how little progress has been made in this direction. We might need a completely new way of doing semantics in order to represent mental language adequately.[2]

 

[1] See my “On Denoting and Connoting” on the proper use of the word “connote”.

[2] It could turn out that what we call mental language is semantically heterogenous within its own domain. Maybe sensation words and propositional attitude words function differently, not to mention words for emotions or character traits. The unconscious might differ semantically from the conscious, being closer to the brain conceptually. Folk psychology is more likely to be ripe for elimination than scientific psychology (or vice versa). Psychological semantics is in its infancy. Whether this would help with the mind-body problem remains to be seen.

Predicating and Necessity

(Bear in mind Kripke’s Naming and Necessity when reading the following.) When a speaker uses a predicate (“man”, “cat”, “rose”, “square”, “red”, “runs”, “clever” etc.) he or she refers to a property or attribute: but how is this done? One answer is by means of ostension: the speaker points to an instance of the property, being momentarily acquainted with it (as Russell would say). Another answer is that the speaker has in mind a description of the property or attribute: “large-brained speaking biped”, “furry feline with sharp claws”, “nice smelling pretty flower”, “four-sided figure with equal angles”, “the color of British mail boxes”, and so on.[1] The first theory could be called the direct reference theory; the second theory could be called the description theory. The meaning of the predicate is given by the property it directly refers to, or by the descriptive concepts the speaker uses to identify that property.[2] There is descriptive mediation, or there is not. The proposition expressed either contains the reference directly and intrinsically, or it contains only the concepts used by the speaker to latch onto that reference. The description theory of predicate meaning looks plausible and powerful—it is hard to see how it could fail to be the case (we can use predicates and not be in a position to point to instances of the properties they denote). Yet the theory seems demonstrably false; and the arguments against it are quite obvious. First, speakers can make mistakes about the properties they refer to—for example, British mail boxes might not be red (this is an illusion they give off). Second, speakers may not have sufficient information to identify the property uniquely—many types of flowers can be described as pretty and nice smelling. Third, it is not generally analytic to couple a predicate with a description of its denotation—it may just be a contingent empirical fact. Fourth, a predicate “rigidly expresses” its associated property but a speaker’s descriptive beliefs about it are generally not thus rigid—in some possible worlds, cats don’t have sharp claws, though another species may. Fifth, at some point we will reach descriptions that have no definition in terms of other descriptions, so that the predicates used in the descriptions will not be explicable in terms of the description theory. Sixth, syntactically speaking simple predicates are not complex in the way envisaged by the description theory—they are not pieces of shorthand, not disguised descriptions. Seventh, nothing like this actually passes through the mind of the average speaker: he or she just doesn’t bring to bear this sort of descriptive knowledge. Eighth, the whole model of descriptively mediated reference smacks of overgeneralization: definite descriptions work by singling something out by means of uniquely identifying description, but not every device of language works like a definite description—take proper names or demonstratives or pronouns or sentence connectives. Thus, the description theory of predicating runs into decisive refutation, despite its apparent attractions.

I have just run through Kripke’s arguments (and some others) against description theories of names for the case of predicates (common nouns, adjectives, verbs). I said nothing about ordinary proper names. So, those arguments have nothing specifically to do with names; they apply also to predicates. It isn’t that namesconstitute a special problem for a description theory of reference; predicates do too. The substance of Naming and Necessity could have been presented under the title Predicating and Necessity. Kripke himself extends the doctrines he puts forward to the case of “common names”, so he implicitly acknowledges (indeed asserts) that his critique applies also to this category of expression. But he could have proceeded by first mounting his critique for the case of predicates and then extending it to proper names. He could have begun with natural kind terms and moved on to the case of names of individuals. And, if the description theory doesn’t work for descriptive predicates, it is hardly going to work for non-descriptive names. Neither category of expression is to be understood as abbreviations of descriptive definitions. On the positive front, there is nothing to prevent Kripke from offering his theory of initial baptism and chain of communication in the first instance to predicates, then extending it to proper names. Long ago the English language baptized squareness “square”, then the word was passed along from person to person in a reference-preserving chain—with no descriptive reference-fixing knowledge necessary. First, a causal theory of predicates; then, a causal theory of names. There is nothing distinctively name-oriented about this conception. The focus on names is entirely adventitious in these debates. In fact, names are a relatively marginal feature of natural languages; predicates are where the real work gets done. For some reason, proper names became the focus of discussion, going back to Mill and Russell (not so much Frege), and Kripke is simply following in this tradition; but it gives a skewed impression of what the real issues are. If Kripke had not extended his discussion to the case of common nouns, he would clearly have distorted the import of his arguments—as if they concerned only the very limited part of language comprised of proper names (of people and places). In fact, they apply to a wide region of language—not only common nouns but also predicates in general. The title should have been Naming, Predicating, and Necessity(or better Names, Predicates, and Necessity, since Kripke’s book is not so much about naming as an action as about names as a semantic category).[3]

Finally, names and necessity: does the former have anything particularly to do with the latter? It does not. This is by now old hat: names have no more to do with necessity (epistemic or metaphysical or analytic) than other classes of expression—definite descriptions, indexical words, predicates, connectives, quantifiers. In particular, definite descriptions can be as rigid as names (“the successor of 3”). De re necessity has nothing to do with names as such, being quite independent of language. We can express the necessity of water being H2O either by using “Water is H2O”, where the terms are used as names (singular terms), or by using “Anything that is water is H2O”, where the terms are used predicatively. We can either use “Heat is molecular motion” or “If something is hot, it has high molecular motion”. Both formulations express the fact that a certain de renecessity obtains. When Kripke begins his lectures by saying that he hopes people see some connection between the two topics of the title, he is being misleading (and has misled many readers). I suppose there is “some connection” (everything is connected to everything else somehow), but there is no special proprietary connection between names and necessity—whether the necessity is analytic or synthetic, de dicto or de re. It is not even true that names form necessarily true identity statements but descriptions never do, since descriptions can be rigid (as well as occur with wide scope). When I say “Nothing can be red and green at the same time” there is no name in sight, only general color predicates, yet my statement is as necessary as can be; so yes, there is “some connection” between predicates and necessity! As there is “some connection” between connectives and necessity (look at the theorems of propositional logic). If we read Naming and Necessity as claiming that names are uniquely not open to a description theory and uniquely connected to necessity, then we read a lot of error into that classic text; but I don’t think anything important hangs on those claims, mistaken as they are. It can all be rephrased to avoid such mistakes. Surely Kripke would agree.[4]

[1] A variant of this approach, Russellian in spirit, would opt for descriptions that refer only to sense-data, as in “the animal species that causes such-and-such sense-data” or “the property that seems thus-and-so”. There is something empiricist about the traditional enthusiasm for description theories.

[2] The famous deeds version of the description theory of names of people finds a parallel in the “conspicuous instance” description theory of predicates, as in “the shape of the earth” for “spherical” or “the kind of animal that my pet Tabby belongs to” for “cat”. This is the kind of knowledge that ordinary speakers may be expected to possess.

[3] We could also choose to treat names as predicates: the name “John Smith” is parsed as “a John Smith” or “he John Smiths”. Then we would have assimilated names to predicates, treating predicates as basic in logical form.

[4] It is puzzling to me why Kripke falls into these incautious formulations, or fails to warn against natural but incorrect interpretations of his words and procedure. It is difficult to believe he didn’t see the points I am making, which are hardly earth-shattering. Nor was he much of a respecter of intellectual tradition. Let me also add that his classic discussion of the identity theory of mind and brain does not depend on the assumption that “pain” is a name as opposed to a predicate.

Contradiction and Synonymy

This is to be an essay in the philosophy of logic. Regrettably, logic today is taught as mainly formula manipulation with little attention paid to philosophical questions. I will be engaged on foundational questions, not unlike the foundations of physics (crucial but ignored by the mainstream). No doubt this is all about aspiring to be a “science” etc. In any case, my question concerns the meaning of what is called the law of noncontradiction, specifically what this law is really about. Let’s start with an obvious and familiar point: the connection between contradiction and synonymy. A sentence only counts as contradictory if it contains synonyms, as in “This is both red and not red”. The sentence “This is both a bank and not a bank” can be true if we mean different things by each occurrence of “bank”. It is not always easy to tell when contradiction is avoided because of a lack of synonymy: “This is both identical to that and not identical to that” (qualitative and numerical identity); “It is both raining here and not raining here” (uttered when moving about); “This creature is both large and not large” (relative to different classes of animal, e.g., mice or mammals in general). The same words can be used to say different things. So, we must stipulate that contradictory-seeming statements are only contradictory if words are used synonymously in them. But then any difficulties that attach to synonymy carry over to contradiction; and isn’t that a frail reed when trying to formulate the basic laws of logic? What if you are a skeptic about synonymy (like Quine) but a true believer in logic? Is logic only as solid as the concept of “saying the same thing”? If there is no such thing as synonymy, is there no such thing as the law of noncontradiction? Is it possible to detach the two questions, avoiding reliance on the concept of synonymy? It might be thought that it is: why not say something like “This is both red and not that”, where the demonstrative refers anaphorically to the previous utterance of red? Then we can express the law of noncontradiction by saying that nothing of that sort can be true—intuitively, that the same thing cannot be both red and not what I just said. I thus avoid using the word “red” twice and having to answer the question of synonymy; I use it only once and then refer back to that use. Okay, that sounds feasible, but it is contrived and artificial, a mere trick. And I am still using the notion of identity as between things said: first I say something and then I refer to my saying it. The point here is not that such notions are taboo or indefinable; it’s that we shouldn’t have to employ them in order to state the logical law in question. Also, this is surely not what I am thinking when I accept the validity of the law of noncontradiction—I am not thinking about synonymy or what is said. That is not what the law is about, or a presupposition of accepting the law. Really, it might be thought, the law is not about language at all; so why should we get tangled up in questions about meaning? The law isn’t intrinsically meta-linguistic; it’s not about what kinds of statements can be true. The law may have consequences for what statements can be true but it isn’t a law of statements.

So, what is it about? Properties, you might reply: it says that an object cannot both instantiate a property and not instantiate it (at the same time). An object cannot have the property of being red and not have this property. That sounds a lot cleaner; it doesn’t make logic subject to the vagaries of language (saying, meaning, synonymy). As a bonus, we see that the law can apply to things not expressed in language—properties that have no name and may not even be known. The basic notion is simply that an object can’t both have a property and lack it. Doesn’t that sound intuitively correct? But there are two lines of resistance: first, we still have a problem of individuation; second, is the notion of a property broad enough to capture all that we want to capture? Criteria of identity for properties are hard to come by—do we really want to make logic dependent on the success of that search? Objects can clearly have different properties at the same time; it is only identical properties that cannot both be instantiated and not instantiated at the same time. There is, for example, no difficulty in the proposition that an animal can both be a creature with a heart and not a creature with a kidney, these being distinct properties that happen to have the same extension. And don’t we want to extend the law of noncontradiction to “good” and “exists” without supposing them to denote properties in good standing? We don’t seem to be employing an ontology of countable properties in acceding to the law of noncontradiction, and we do seem to be thinking more generally than this notion normally admits.[1] But now we are running out of ideas—we cannot capture what it is that we are thinking when we accept the law in question. The open-ended generality of the law outruns our vocabulary for stating it.

Let’s try a different tack: the idea of the paradigm and its extensions. What really happens in your mind when you are persuaded that the law of noncontradiction holds good? Perhaps something like the following: you gaze at a red object and think “Nothing could be both like that and not like that”. You focus on an example and try to think of the negation of that example existing along with the example. You try to combine perceptual opposites, failing dismally. Then you say to yourself, almost as an afterthought, “And similarly for everything else”, not worrying too much about the exact analysis of that statement. Notice that you don’t even attempt to articulate what kinds things cannot both obtain and not obtain—you don’t think about predicates or senses or properties; you just think demonstratively of what you are gazing at (“like that). You leave the thought in an unarticulated form, relying on ostension. This seems an accurate enough description of the phenomenology of elementary logical thinking, but it leaves much to be desired theoretically. We want to be able to formulate the law more explicitly and rigorously, casting the alleged paradigm aside and spelling out what the respect of similarity is supposed to be between the paradigm case and all conceivable cases. That kind of thinking isn’t very…logical. It isn’t impressive, masterful, exam-ready. But it’s the best we can come up with without falling into muddy waters and limp hand waving. This suggests a scary thought (notice how much I am relying on the vernacular): you don’t really know what you are saying! The law of noncontradiction is true, and you know that it is true, but you can’t say what precisely it is. It is the basis of our reasoning but we can’t formulate it, except obliquely and inadequately—we can only approximate it. We think things like “Nature cannot contradict itself” or “Reality must be consistent”, but we can’t get any further in saying what in nature or reality is incapable of contradiction. We know that something and its opposite cannot both be, but that “something” is left unspecified. Our conviction of the truth of this thought does not depend on our making philosophical sense of synonymy and properties; it is more basic and general than that. It seems anterior to language and ontology—pure logic, as it were. The form of any possible reality. The necessary structure of the world. The way things have to be. Let’s admit it: this is pretty mysterious stuff, mystical even. It transcends what we can properly understand (the “limits of language”). We only partially grasp the meaning of the law of noncontradiction. Not that it betokens the divine, or ushers in the supernatural; but it does indicate the limits of human understanding. We only glimpse the logical truth that we fail to formulate explicitly; we don’t mentally embrace the full import of our words (this too is a puzzling phenomenon). Thus, we feel that the law of noncontradiction expresses a sort of magical exclusion: reality excludes other reality. If one thing is so, then its opposite cannotbe so—reality is necessareily selective. It won’t allow everyone into the club. Once things are thus and so, nothing can contradict how they are. Reality has the power (almost godlike) of suppressing alternatives; it has made up its mind and nothing can change that. If this object is red, then it absolutely cannot (will not) be not red: that is simply out of the question. It is not surprising that some people balk at this putative power, denying that contradictions are absolutely impossible: for what kind of power is it—what kind of brute metaphysical exclusion? It seems like dictatorial annihilation (it crushes the opposition). The opposite could have been so, but for some reason once it isn’t so it cannot get a foot in the door. It cannot exist once reality has come to a decision about its contents. Contradictory statements can coexist—one person can disagree with another—but somehow reality prohibits such largesse. Reality never disagrees with itself. This can seem arbitrary, groundless, narrow-minded, not even clearly stateable, and yet we are told it must be so. But our conceptual and epistemological position makes the situation intelligible: we don’t fully grasp the import of the logical law in question. It is, in short, a mystery, or a partial mystery. It hints at the ineffable.

The language of logic is not in the best shape either. A trip to the dictionary is somewhat disconcerting. For “contradiction” the OED gives us “a combination of statements, ideas, or features that are opposed to one another”; for “contradictory” we have “mutually opposed or inconsistent; containing inconsistent elements”. The word “contradict” comes from the Latin contradicere, meaning “speak against” and dates from the sixteenth century. It is certainly possible to contradict someone else (speak against them) and the law of noncontradiction does not forbid such acts of speech; it says that contradictions cannot be true, or cannot occur in reality. It would be better (and brisker) to use the phrase “the law of consistency” to affirm that statements and states of affairs must be consistent; we don’t want a law prohibiting disagreement between people! And surely the law existed and was recognized long before the word “contradiction” came into use. But what I find most telling here is the disjunction in the definition, especially the “feature” disjunct. Evidently, the word cannot make up its mind as between a de dicto and a de re use: statements and ideas, on the one hand, and “features” on the other. The right thing to say is that statements and ideas should not be contradictory (inconsistent) because reality cannot be contradictory (inconsistent): the de re underlies the de dicto. There cannot be a contradictory combination of features, though clearly words (and ideas) can be contradictory. The world cannot contain contradictions but language can. Use-mention confusion runs through the dictionary definition. But further, the use of “feature” suggests the difficulty I have been alluding to, namely that it is hard to find a word of sufficient generality to cover the case. Is existence or goodness a feature of things, like the contours of a person’s face? Hardly. Yet these also are subject to the law of consistency (nothing can exist and not exist at the same time, or be good and not good at the same time). Must we accept a metaphysics of “features” in order to endorse the law of consistency? Do we have any clear idea of what this word means in the present context? Better to admit that the thought outruns our means of expressing it; and the thought can be true and known to be true without being fully articulated or analyzed. The thought (our thought) is elusive and programmatic, unlike (say) “The cat sat on the mat”. It is schematic not filled in. The OED is straining to catch its generality while conceding its lack of perspicuity. We should accordingly be semantic mysterians about the (so-called) law of noncontradiction.[2]

[1] Certainly, we don’t need to be Platonic realists about universals in order to assert the law of noncontradiction (or excluded middle for that matter), and there is a danger of that if we quantify over properties. Not that we must reject such a theory, but neither should it be a necessary presupposition of basic logic. Aristotle doesn’t need Plato.

[2] I note that the words “object” and “property” are used with incredible promiscuity in philosophy, with little explication; we don’t want our logical laws to participate in such promiscuity, whatever may be said of our metaphysics. Self-evident laws of logic should not depend on dubious metaphysics, or even sound metaphysics. They are pre-metaphysical (also pre-linguistic). We might almost describe them as visceral (instinctive, primordial). They belong in the belly part of our conceptual scheme. The logician speaks from his gut.

Dichotomous Knowledge

There is a long tradition of recognizing two distinct categories of knowledge: knowledge of logic, meaning, and mathematics, on the one hand, and knowledge of geography, history, and chemistry, on the other (these lists are not exhaustive). We might name these “A-type knowledge” and “B-type Knowledge”, so as to be neutral about the nature of the distinction. It is not obvious what the difference actually consists in. Looking for something more descriptive, philosophers have hit on a pair of Latin terms that seem vaguely evocative and have stuck, namely “a priori” and “a posteriori” (usually italicized to mark their somewhat esoteric meaning). If we try to dig into them, we do not return with conceptual gold: they translate as “prior” and “posterior”, as in “before” and “after”. The OED gives us “existing or coming before in time, order, or importance” and “coming after in time or order; later”, respectively. Before or after what, we ask. Not breakfast or lunch, presumably; no, before or after something called experience. That notion is not pellucid or theory-independent; it is usually specialized to sense experience, i.e., the five human senses. Here things start to get controversial; also, the reference to temporal order is questionable—does A-type knowledge always precede B-type knowledge in time? The original distinction is not so much clarified as immersed in definitional murkiness. Does this form of definition really capture what we intuitively recognize in the examples cited? Isn’t it more of a place-holder than a theory? Not surprisingly, other concepts have been invoked in order to hit off the distinction: experiential vs. non-experiential, analytic vs. synthetic, intuitive vs. observational, innate vs. acquired, abstract vs. concrete, causal vs. non-causal, rational vs. sensory. These all have their merits and demerits, which have been amply discussed; I think they are all lacking in one crucial respect—they don’t tell us about the internal structure of the two types of knowledge. They focus on the means of acquiring the types not their constitutive anatomy. They don’t say anything much, if anything, about the inner cognitive architecture of knowledge of A-type truths or B-type truths. They tell us about etiology but not about form—causation not constitution. We are trying to articulate epistemic natural kinds and to do that we have to look at the internal structure of the two types of knowledge. How do they operate, and what kind of structure permits that operation? To answer these questions is going to take some fresh thinking.[1]

B-type knowledge proceeds as follows: first, observations of particular states of affairs take place; then, inferences to generalizations are made. General knowledge is inductively inferred from perceptual knowledge of instances of the putative generalization. Singular instances precede general truths. The particular is anterior to the general: the former justifies the latter, while being itself justified by experience. That is the basic structure of what we call a posteriori knowledge. Notice that the singular premises are separate and distinct—one observation does not entail another. We may think of these as the atoms of this kind of knowledge, its ultimate constituents or building-blocks. B-type knowledge is thus atomistic and inductive (or abductive). I know that the Sun will rise tomorrow because I have seen it rise many times in the past, each of these a separate act of knowing. If we were to draw a diagram of this kind of knowledge, it would have an array of points on one side, corresponding to the totality of singular observations, and a bunch of arrows pointing right to the general truth thereby justified. The cognitive structure has this kind of shape and it operates by the depicted procedure; we might call it the singular-to-general structure, or the “sing-gen” structure. Experience is the medium in which this occurs, its enabling format. But A-type knowledge is not like that; in fact, it inverts this order of reasoning. Logic is the paradigm: we don’t know that modus ponens or the law of non-contradiction is logically true by inductive inference from individual instances; instead, we know the general principle directly and then deduce its instances. The order of justification is reversed. If we were to draw a diagram, it would have a general principle on the left with arrows pointing to individual instances on the right: it would have a general-to-singular structure, or a “gen-sing” structure. What we call reason or intellect is the medium in which this occurs. First, we know the generalization by what we call “intuition”, then we move deductively to its logical consequences. It is the same with mathematical and semantic knowledge: we don’t infer that every number has a successor from individual instances by induction, or that bachelors are unmarried by observing that similar propositions have always been true in the past (e.g., the proposition that spinsters are unmarried). We grasp a general principle and know it to be true, and then we deduce its particular instances. This implies that such knowledge has a holistic character in that the consequences are united by a general principle and are not known separately from each other. You can’t know that 4 has a successor but not know that 6 does, or that sisters are female without knowing that brothers are male (given that you have the concept). You know a general property of numbers and of meanings (that semantic containment generates analytic truths). The general is epistemically prior to the singular, whereas with B-type knowledge the singular is prior to the general. In addition, B-type knowledge takes the form of a bundle while A-type knowledge takes the form of a unified whole. The form of what we designate as a priori knowledge is aptly captured by a system of general axioms and theorems; but the form of a posteriori knowledge consists of a collection of singular instances linked inductively to a general proposition. The fundamental unit of empirical knowledge is the singular proposition, but the fundamental unit of a priori knowledge is the universal proposition. A-type knowledge is principle-based and holistic, while B-type knowledge is particular-based and atomistic. So-called a prioriknowledge is systematic and organized (“logical”); so-called a posteriori knowledge is fragmentary and haphazard, dependent upon the knower’s location and sensory acuity (“accidental”). We could say that the latter type of knowledge pertains to a totality of particular facts, while the former concerns a body of general principles. The two types of knowledge move in different “spaces”, proceeding by different methods. The cognitive apparatus is different in the two cases, differently structured.

The two types of knowledge are therefore opposites of each other. The faculties involved have contrasting forms. The process of knowledge formation accordingly varies in the two cases. It isn’t just that they have different types of causation—one is caused by experience and one isn’t—they have a different inner structure. The rest is extrinsic. Moreover, all varieties of the two types are unified in their structure: all a priori knowledge fits the “gen-sing” form and all a posteriori knowledge fits the “sing-gen” form. Thus, we can include metaphysics (and philosophy in general) and ethics in the category to which logic, mathematics, and semantics belong; and we can include knowledge of mind in the category to which geography and chemistry belong. For example, knowing the nature of identity belongs to the A-type category and so does knowing that cruelty is wrong; and my knowledge that I am in pain or that people have an unconscious belongs in the B-type category. There really are two large and distinct types of knowledge—two basic epistemic natural kinds. This is a philosophical discovery of the first importance. Trying to discredit is a fool’s errand. And it is an interestingdiscovery: we have two very different modes of knowing co-existing (and interacting) in our head—it’s surprising we have a single word (and concept) for both of them. Knowledge is deeply dichotomous. Some knowledge is constructed from separate pieces picked up by the senses—it is compositional, aggregative; but some knowledge is based on general principles that are recognized by the intellect and imply many (infinitely many) individual truths. They are polar opposites, yet both qualify as types of knowledge. Memory of particular facts is the hallmark of one, but not of the other (we don’t remember that 4 is even or that every number has a successor). Memory is atomistic and selective; reason is holistic and inclusive. If anything, we have underestimated the differences between the two types of knowledge, as if they only differ in their origins and not in their intrinsic character—innate versus acquired, derived from experience or the result of intuition, based on the senses or the intellect. But actually, they differ in their fundamental modus operandi and internal logic (induction or deduction, derivational structure). It’s not a matter of what comes first but of the deep nature of what comes.[2]

[1] I published my first paper on this subject nearly fifty years ago: “A Priori and A Posteriori Knowledge” (1976). I am still thinking about it.

[2] This paper is quite programmatic; a more thorough treatment would require looking in detail at specific areas of knowledge and teasing out the role of the singular and general within them. The kinship between the senses and the singular, on the one hand, and that between the ratiocinative and the universal, on the other, is however quite intuitive and traditional (see Plato). Just consider the contrast between the propositions of pure geometry and ascriptions of shape to particular objects. Generality is at the heart of the a priori, while the a posteriori has trouble escaping the bonds of the particular (witness the problem of induction).