Metamorphosis and the Self

 

 

It is not implausible to maintain that the caterpillar and the butterfly it becomes are the same organism, but it is another question whether they are the same self. The caterpillar crawls on tiny feet and munches leaves: it has the sensations and motivations that go with these activities. The butterfly has delicate wings and dines on nectar: its sensations and motivations are tailored accordingly. Are these the same conscious subject? If you don’t like attributing mental characteristics to caterpillars and butterflies, then imagine a similar type of creature stipulated to possess such traits. Suppose these creatures have personality as well as consciousness: do they have the same personality at the two stages of their life cycle? Are they the same person? Let us suppose that the psychological lives of the caterpillar and the butterfly are sufficiently different that we would not want to say that they are the same person or self. When the creature leaves its larval stage behind it also leaves its larval self behind, becoming a quite new self with its metamorphosis into a butterfly. This means that the earlier self ceases to exist, to be replaced by a new self in a body also considerably transformed (though biologically continuous). That new self will also eventually die, so that there is a double death in the life of every butterfly: the caterpillar self dies when it is replaced by the butterfly self, and then the butterfly self dies too.

            If we imagine intelligent, reflective, and cultured butterflies, there will be a question about how they understand their own life cycle. Do they grieve over the death of larval selves? Do larval selves fear their impending death? We can imagine that some of them believe that larval selves have an afterlife, maybe even a heaven and hell, while others believe that these selves simply pass out of existence (they may or may not believe that butterfly selves survive bodily death). Some may find the juvenile selves to be morally superior to the adult selves, less vain and flighty; others may find the juveniles to be more psychologically rigid than the adults. But they will all agree that reaching the chrysalis stage is tantamount to the death of the larval self. Nor do they take this death lightly: they don’t suppose that the onset of a new butterfly self somehow expunges the significance of the earlier death.

            How would their predicament affect their view of the death of an adult? When the adult butterfly is contemplating its death how does the prior death of the caterpillar self figure in its emotions? The butterfly knows that its childhood self is already dead, which was not good news for that self; but death has already been endured once, and yet life went on. You can only reach the adult self by going through the caterpillar stage, so you lose one self to gain another. True, the eventual death of the adult self is a bad thing—just like the death of the juvenile self—but it doesn’t have quite the same sting as if there had been no death before. It makes it easier to accept death if you have already been through it once (or your larval predecessor has)–if it is simply part of life. You have been there before and you can go there again.  [1] The butterfly thinks: “I have already died once, I can do it a second time”. Not that its death isn’t a bad thing, but it doesn’t seem as bad—its badness is more bearable.

            Compare your attitude to death if you believe that you are already dead (a self-conscious zombie). If you believe that you are already dead, you will not fear being dead again, or not as much. Likewise, if you think you have no self to be alive, then the prospect of that self ceasing to exist will not bother you too much.  [2] Death has little sting for the already dead or already non-existent. Similarly, if you have already died once and emerged from it none the worse for wear, then the prospect of dying again loses its novelty and fearsomeness. Been there, done that. You are not exactly consoled in the face of death by your earlier demise, but it is recognized as part of your overall life: the first death, though admittedly bad, wasn’t that bad, so why should the second death be? Do we grieve over caterpillars knowing that butterflies will succeed them?  If not, can’t we grieve less over the death of butterflies knowing that other butterflies will succeed them? Why should the death of a butterfly self be worse than the death of a caterpillar self? And that death wasn’t all that terrible, was it?

            Why am I speculating about the death of butterflies? Because of a possible analogy with humans: for don’t we also go through the equivalent of a self-annihilating metamorphosis? I am thinking particularly of adolescence—that time of transformation and upheaval. It is a familiar thought that a single human life might house a succession of distinct selves according to the psychological changes undergone.  [3] We say, “I am not the same person as I was thirty years ago”. Some illnesses, physical or mental, are thought to destroy the self that once was, possibly leading to the formation of a new self. Psychological trauma can make a person feel like someone else entirely. But adolescence affects everyone and the changes are plain to see: the body changes dramatically, but so does the mind. People put away childish things and embark on a new mode of living, priorities reverse, and new motivations take over. A child can transform into another psychological being entirely (from obedient angel to rebellious lout, say). Is it an exaggeration to say that a new self takes root? Given that it does, what happens to the old self? It dies. It is no more. It goes out of existence. It buys the farm. We may regret this passing, even mourn for that lost child, with its sweetness and innocence; but we recognize that it could not persist if an adult self is to take over the premises. Maybe we should grieve more than we do, but the change seems relatively seamless, the body soldiers on, and a brand new self rises up to greet the dawn. We take it in stride—as butterflies do.

            Let us accept that our childhood selves do indeed die (if you can’t accept that, then imagine a species where we stipulate it to be so). My question is how that fact should affect our attitudes towards death. We can also frame the question by supposing that a single human life contains many personal deaths—childhood, young adulthood, middle age, and old age (or even that we die every time we go to sleep). We are not already (finally) dead, but we have already died. But to focus the issue just consider the death of the childhood self—a death we have all been through (I vaguely remember bidding adieu to my childhood self during adolescence and feeling some sadness at his departure). If we let this fact sink in, will it affect our attitude to our later death? I think it will. I have already died once—my first self went the way of all mortal things. That is sad, but life went on; it wasn’t the end of the world (though it was the end of his world). Suppose that at the age of 13 children went into a genetically programmed coma, only to emerge three months later with new bodies and new minds—with different things onthese bodies and minds. Suppose the psychological changes were drastic enough to make us say that these are new persons, tenuously related to the old ones (maybe different parts of the brain are involved pre- and post-coma). We might feel some sadness at the departure of the previous person, but we have to accept it as part of our natural life cycle. We may have rituals surrounding it, softening the blow, reconciling us to the facts of life. Would we then not have a different attitude to later adult death? The coma involved an organically driven loss of consciousness and personality that everyone experiences at age 13: this is the actual death of the juvenile self. But this death, though real enough, is viewed as a rite of passage, nothing to get too worked up about, nothing to despair over.

Then what is so terrible about our final death (though that first death was also final for the self undergoing it)? True, we will no more ever experience the wonderful things of life—but the same is true of the dead juvenile self: she will never again experience the wonderful things of life either. It’s easier to live with future death if you have already died in your life once before. New selves will arrive to replace you, as you replaced your erstwhile childhood self: that’s just the way nature works. No doubt death is tragic for all the selves concerned, but there is tragedy and tragedy. You already died once and it wasn’t the end of the world; some good came of it—the mature you. True, the self that called itself “I” did not make it—a new self came to utter “I” using the same mouth. But that death wasn’t as bad as we are inclined to think when we contemplate death; so maybe we should calm down about our later death too. Maybe we should temper the hysteria.

            There might be a similar death towards the end of life. What if there was a genetically programmed depletion of the self at age 60 that made us say that the previous self was no more? That would no doubt be bad, but not allthat bad. Wouldn’t this make the final biological death a little more bearable? Not because the last self has little intrinsic value but because it will be the third death in a line of previous deaths. Death would not be that one-off catastrophic event that fills us with cold dread, but a predictable alteration in human psychology—the phasing out of selves when they reach their expiration date. They are all real deaths, terminations of a self, and so exact their proper measure of fear and grief; but none is intrinsically worse than any of the others, since all involve the cessation of a self. If you reply that the final death has no natural replacement, as the previous deaths do, then consider that another self can come along to replace my final self—say, the self of my child. These are all brand new selves, stepping into the shoes of other departed selves—just like the caterpillar and the butterfly. No one is returning from death, so every death counts: but they all count equally—and some don’t seem all that appalling. So maybe we can dial it back a bit, this dread of death. It’s bad, yes, undeniably bad: but it’s not super-bad–not weeping-and-wailing bad, not can’t-get-out-of-bed-in-the-morning bad. Maybe indeed the end of that sweet innocent self at age 13 is more to be lamented than the end of that crabby old codger self at age of 80.

            Selves come and go more easily than bodies, with less in the way of injury or illness; they depend on psychology not physiology. The end of a self is not the end of a body—though the end of a body is the end of a self (under current technology). Maybe selves are even more perishable than we generally realize, lasting no more than a decade or so, depending upon contingency. A human life contains not just a single permanent self from womb to tomb but a succession of distinct temporary selves. The living body itself has no intrinsic value—there is no tragedy in terminating a living body that doesn’t house a person—but the value of selves might be less than we customarily suppose, if they come and go so frequently and naturally. Maybe the death of selves isn’t quite as horrifying as we tend to suppose.  We can never be reconciled to death, certainly, but perhaps we can learn to face it more coolly.         

 

  [1] Strictly, of course, you have not been through it, since you are not identical to the larval self that preceded you. But you are both part of the same life cycle and are clearly closely related.

  [2] This is a simple statement of the Buddhist view of death and the self: there is no substantial self to be the subject of death, so no such self is lost at the point of bodily extinction. Derek Parfit holds the same kind of view, as he notes.

  [3] It might be helpful to distinguish two notions of the self that we operate with: first, there is the notion of a subject of consciousness; second, there is the notion of sameness of person where that requires some coincidence of psychological traits. The first is not logically sufficient for the second, since the bare subject of consciousness could change dramatically in its associated psychology (it might just be the brain). I am discussing here the second notion, which brings in character and personality as well as memory, intelligence, desires, ambitions, etc. If I change too much psychologically, I cease to be the same self in the second sense; but the individual subject of consciousness might be the same throughout (that single continuous brain organ or the “transcendental ego”).

 

 

 

 

Quantum Semantics

 

 

The so-called quantum revolution, initiated by Planck and Einstein in the first decade of the twentieth century, was just that: an overturning of entrenched earlier theory. Light (radiation) had been conceived as continuous and wavelike not as having a particulate structure. Much of the experimentally observed behavior of light confirmed this picture (interference and diffraction), and light didn’t look as if it was a swarm of discrete particles. The quantum theory was thus counter to common sense and previous science. But this is not the situation with regard to language: we don’t need to be persuaded that language consists of an array of discrete entities (words) that combine to form ensembles. It isn’t as if language looks to be continuous or that previous linguistics had good theoretical reasons for favoring continuity; it is just part of common sense that language has a particulate structure, as well as a tenet of the science of linguistics.  [1] No one needs to be converted to quantum semantics: meaning is obviously quantized (unlike energy), consisting of discrete semantic units (as well as syntactic and phonetic units). Meanings are not values of continuous variables, and they are either present or not (there are no degrees of meaning). The structure of meaning is evidently a quantum structure. As a consequence, the infinity of language is a discrete infinity not a continuous infinity—an infinity of combinations not of mathematical points. We don’t speak of “point meanings”: meanings are not loci on a continuum. Meaningful words are block-like entities: granular not graded.

I don’t intend to question this assumption—quantum semantics is clearly the correct view—but I do want to raise some questions about it, because it is not a trivial assumption and has important theoretical consequences. First, why exactly do we believe it—what is our evidence for supposing that language has a quantum structure? Why do we think that language is made up of discrete units of meaning—the things we call words? It is important to see that a natural answer to this question is wrong, namely that spoken language is divided into discrete acoustic elements strung together in time. As Chomsky would point out, speech is but the externalization of language not language itself: it is the joint product of an internal cognitive system (language proper) and a sensory-motor system that forms its contingent outer expression (which precedes language in evolutionary history and was not designed to mirror the structure of language itself).  [2] It simply does not follow from the fact that this external vehicle has a discrete digital structure that the underlying cognitive system does. Compare musical notation: just because written sheet music has a discrete digital structure it doesn’t follow that music itself does (it is a continuous medium). Musical notation is designed to be read, and hence must be suitable for the eye—just as speech is designed to be heard, and hence must be suitable for the ear. But music and language are not in themselves visual and auditory, respectively. Language, for Chomsky, is primarily a tool of thought not of communication and as such it need not mirror the structure of spoken language. In fact, it is more plausible to suppose that we impose a quantum structure on speech, based on our prior acceptance of language as discrete, than that we derive the discreteness of language from the observed discreteness of speech. Speech is actually not as discrete acoustically we as tend to imagine, as is revealed by a speech spectrograph; and it has a continuous nature that is irrelevant to its function as a vehicle of meaning. Volume, pitch, and duration have no semantic significance—loud high-pitched fast speech doesn’t have a different meaning from quiet low-pitched slow speech. So it can’t be that our reason for believing that language is discrete is that speech is discrete: that would be a non sequitur given the relation between language proper and vocalization, and anyway it doesn’t deliver the kind of discreteness we attribute to language. We can’t derive quantum semantics from quantum acoustics (or quantum gestural language for that matter).

If language is more a mental thing than its physical externalization, perhaps our evidence for discreteness comes from introspection: we arrive at the idea of quantum semantics by noticing the structure of our innerspeech. Bu this is no more plausible than the first suggestion: inner speech is at least partly silent outer speech (a sensory-motor system) and hence is not guaranteed to reveal the structure of language as a cognitive system (the language faculty); but also it is implausible to suppose that we can read semantic structure off the form of internal acts of speech. Are such conscious acts really as segmented as we take language to be? Is awareness of the (phenomenological) structure of inner speech the reason we so readily acquiesce to the quantum theory of language? What if the introspective system is as misleading as the sensory-motor system when it comes to the intrinsic character of language? The truth is that we do not perceive the quantum structure of language, either outwardly or inwardly—that is, our evidence for that conception is not acquired through perception (though our perception might be conditioned by a prior knowledge of semantic structure).

We might then opt for a strictly theoretical account of such knowledge: we infer it from observable features of language as a theoretical postulate. We know that language has infinite potential and that our vocabulary is finite, so we hypothesize that language must be made of discrete units that combine to produce more complex semantic entities—and hence we know there are such discrete units. We thus have no direct awareness of semantic quantum reality, but we know indirectly that it must be so, or else language could not have the properties we observe it to possess—specifically, infinite potential based on finite means. Combination requires units that combine. However, this kind of reasoning, cogent as it may be, does not do justice to the nature of our knowledge of language: for it is not just a matter of speculative inference that words exist—they are not like atoms or remote galaxies. So we must possess a way of knowing about language that makes non-inferential knowledge of its structure possible; and I think we do possess such a way—we know directly that meaning is quantized. We know this because we have first-person insight into the structure of our language faculty: not by deducing that structure from perception of external speech or awareness of inner speech, and not by theoretical postulation, but rather by a kind of primitive self-knowledge. We know that our thoughts are structured in a similar way—a way that is sui generis and not inferred from other types of knowledge. This basic knowledge permeates our awareness of the expressions of language, both external and internal; it is not the upshot of such awareness. It is based on an immediate intuition of linguistic structure. The epistemology of quantum semantics is therefore obscure and mysterious, and certainly worthy of further study; there is nothing trivial or transparent about it. It really isn’t at all obvious how we come to know that meaning is a discrete and divided thing—yet we do know it (short of entertaining some extreme form of skepticism). As language users, we have implicit knowledge of the structure of meaning—and we know it to be a quantum structure not a continuous structure. Other types of language user might employ a continuous non-quantum language and either know this to be the case or be in the dark about it. I suppose there might be language users for whom the quantum nature of language comes as a surprising scientific discovery, as the discovery of light quanta was for us; but we are not such beings so we are not revolutionized by the revelation that meaning comes packaged in discrete units.  [3] We suffer no paradigm shift or conceptual convulsion when linguists and philosophers announce the quantum theory of meaning (“Who could have guessed—it all looked so smooth and wavelike!”). We are all commonsense quantum theorists of meaning; no one shrilly insists that language consists of continuous variables like loudness and pitch whose values are words. How we know this–and with such certainty–remains obscure, but it is surely so: it is built into our linguistic consciousness.

Now I want to consider a different question: what should we say of the ontology of meaning, given its quantum nature? First, what is the smallest unit of semantic reality? It has been traditional to assume that the constituents of meaning correspond to the logical analysis of meaning: that microstructure and definition go hand in hand.  [4] Thus we arrive at the idea that the most basic units of meaning correspond to sensory primitives or some other definitional foundation. But this kind of correspondence is not compulsory and is not terribly plausible: for why should the microstructure of meaning be tied to what we can reflectively analyze as conscious language users? Why can’t semantic reality possess a structure that goes beyond what is accessible to conscious analysis? Why can’t it have an unconscious particulate nature geared to other concerns than our knowledge of what our words mean? The meaning of a word (morpheme) is surely too coarse to constitute semantic bedrock; it must have some hidden structure that ties it more perspicuously to underlying processes in the brain, computational and other. To suppose otherwise is like supposing that the microstructure of matter goes no deeper than what is revealed to observation by cutting things up with a knife. The meaning of a putative primitive like “red” might have a highly articulated inner constitution that links it to the brain. In other words, the basic semantic quanta might lie outside of commonsense understanding, just like physical quanta. What we call a word and think of as semantically primitive might be in reality a macro-quantum—a bigger chunk of more elementary semantic components. I can’t specify what these components look like; I can’t even promise that they will one day be discovered: I can only urge that they not be ruled out.

            The second question concerns what might be called “the word-body problem”: the problem of how the brain gives rise to and implements language. Specifically, how does the quantum structure of language arise from the brain—how do we get discrete words from brain processes? That may seem like an easy problem, but it is not. It may seem easy because the brain contains discrete units of its own that can (allegedly) form the basis of discrete words: not only physical quanta, atoms, and molecules, but also cells, ganglia, and on-off neural transmission. There is plenty of particulate structure in the brain, more than enough (it will be said) to generate a lexicon of discrete elements. But this is superficial thinking, because none of this brain structure has anything to do with linguistic structure—none of it amounts to the structure that meaning exhibits. It is at the wrong level to explain the existence of semantic discreteness. Other organs of the body have the same kinds of anatomical discreteness as the brain, but no one thinks they provide an adequate basis for the structure of human language—which is a very special kind of structure. So there is a word-body problem analogous to the mind-body problem: both involve mysterious kinds of emergence. Indeed words constitute part of the mind, and they too resist reduction to brain states. In fact brain activity tends to be wavelike, which is not surprising given that it is electrical in nature; but in language we have an entity that is not wavelike (it doesn’t even have “particle-wave duality”). How can quanta of meaning arise from waves of electricity? Why doesn’t an electroencephalograph record discontinuous spikes corresponding to lexical units, as well as those wavy curves? The brain is really no more suitable, on the face of it, for producing language than the heart is when it comes to accounting for semantic discontinuity. This is an “emergent property” of the brain not a recognized aspect of its anatomy and physiology (or chemistry and physics). There is thus a non-trivial explanatory problem here—accounting for the discrete structure of language (construed as an internal mental system). We are familiar with the problem of intentionality for language, but there is also the problem of “segmentality”: the very structure of language fails to map onto underlying brain structure (in so far as we know about brain structure). Accordingly, we have a “semantic quantum problem”, as we have an “intentionality problem” and a “qualia problem”. The architecture of meaning, with its bounded discrete combinable elements, finds no counterpart in the architecture of the brain, at least as we now understand it.  [5] One can imagine someone postulating “pan-quantum-ism” as a way to explain the emergence of quanta of meaning—everything in nature has a hidden quantum structure—but such a view is clearly far from satisfying (what kind of quantum structure and how is it related to the structure of meaning?). Because we tend to take the quantum structure of meaning so much for granted, we don’t see that it produces explanatory puzzles (as it produces epistemological puzzles): but it is really not clear how this aspect of language can be fitted into what we know of the brain. In brief: semantic discreteness is not physical (physiological) discreteness. I won’t say that quantum semantics is as puzzling as quantum mechanics (no reason to postulate violations of determinism  [6]), but it is certainly not a final and finished theory; it awaits unification with the other sciences of body and brain. This most fundamental feature of human language is by no means as straightforward, epistemologically and ontologically, as has been supposed.

  [1] Genetics is somewhere between these two cases: we now know that the genome is essentially a quantum system in the sense that genes are discrete and digital, being either turned on or off; they don’t blend or mix. This is why a child whose parents have different colored eyes doesn’t have an intermediate eye color but has one or other of the two parental colors. Theorists may have been weakly committed to some kind of non-quantum theory, but the change to quantum genetics was hardly a paradigm shift, unlike the quantum theory of energy. (Let me note that I am using the word “quantum” a little loosely here, if we take physics as our guide: a quantum in physics is an amount of energy, but a word is not an amount of meaning. I am using “quantum” to capture the discontinuous nature of word meaning, not the idea of a magnitude divided into discrete steps. And I couldn’t resist the euphony of “quantum semantics”.)

  [2] See Robert C. Berwick and Noam Chomsky, Why Only Us: Language and Evolution (MIT Press, 2016).

  [3] We might date the official academic recognition of quantum semantics to Frege’s “On Sense and Reference” (1892), though no doubt there were premonitions. Frege systematized the intuitive picture of language as consisting of a finite number of discrete meaningful units combinable by rules into larger wholes—there is nothing continuous or blurry in his theory (contrast Hume’s talk of mental images and vividness). It is hard to see how Frege could not have been influenced by earlier corpuscular physics and chemistry (Planck’s and Einstein’s work on the quantum theory of light came a few years later). He does not model his theory of language on Maxwell’s theory of electromagnetism, in which the wave is supreme, because it is obvious to him that words are particle-like not wavelike. People have sometimes spoken of “semantic fields”, but no one hypothesizes that meanings are values of continuous magnitudes acting at particular points in semiotic space. Meanings are more like solid bounded objects than continuous fields of force.

  [4] Thus in Russell’s logical atomism the atom is a sentence with words as atomic constituents—quite a large unit of meaning. He is connecting logical analysis with semantic structure, not allowing for the possibility of semantic atoms at a much finer scale. Shouldn’t atoms at least be invisible?

  [5] Where in the brain do we find the neural basis for nouns and verbs? No doubt there are brain correlates, but what kind of vocabulary should we use to describe these correlates? Why should one neural correlate be noun-like and another verb-like?

  [6] Though it has been claimed that language use is an exercise of free will and as such incompatible with determinism, so there is some analogy there. No uncertainty principle, however. I can imagine a fanciful form of metaphysics that regards physical quanta as inherently semantic, so that quantum semantics underlies quantum mechanics. This would be a version of informational quantum theory, which has its adherents.

                                               

 

 

 

 

 

Knowledge of Entailment

 

 

How do we know that one proposition entails another proposition? If we think of entailment as logical necessitation, how do we know that one proposition logically necessitates another? I suggest that we consider this question by analogy with Hume’s treatment of causation. According to Hume, we do not perceive necessary connection in causally related objects (though it exists in them objectively), so our knowledge cannot be based on any such perception. Instead we perceive constant conjunction and the mind develops the habit of moving from cause to effect as a kind of animal instinct. No matter how much we may scrutinize a cause, such as a billiard ball about to collide with another billiard ball, we never discern any power or necessity in the object: thus necessary connection is invisible (though real). That is, nothing about the nature of the effect can be inferred from the cause considered alone and by itself; we can only gain knowledge of causal relations by observing the conjunction of cause with effect in repeated cases. We believe in causal relations because of these observations, not because we can detect causal power in the individual instance. Causal powers cannot be extracted by the mind from knowledge of the cause considered in itself—though such powers are present in the object considered in itself.

            The analogous view for logical consequence is that we cannot discern in propositions anything that would lead us to deduce their entailments. We cannot examine a proposition and extract from that proposition considered in itself what it entails. The proposition as it appears to us is an entity complete in itself and bounded by its own identity—it makes no reference to other propositions. Its logical powers are not evident from its manner of presentation to the mind. Instead we believe that it entails other propositions because its truth is constantly conjoined with the truth of other propositions: whenever the premise proposition is true the conclusion proposition is true. We perceive no connection between the two propositions—such as logical necessitation—but we form the habit of thinking of one when the other is presented to us by dint of instinct and habit. We take one proposition to entail the other because of the observed conjunction of truth-value, but we detect nothing in the one proposition that could ground the belief that the other proposition must be true. We don’t perceive any logically necessitating properties in the premise that could warrant inferring the conclusion. We don’t apprehend the logical powers of the premise, only a coincidence of truth-value. Our knowledge of entailment is thus general not particular—it comes from observing a totality of instances. We do not and could not perceive in the premise proposition any features that could lead us to infer the conclusion proposition. We perceive no necessary connection between the two propositions.

            This position sounds utterly incredible: surely we can tell just by looking at a proposition what it entails! Propositions have their entailment relations built into them, transparently so.  For instance, once we grasp a conjunctive proposition we see that it entails each of its conjuncts. But the “Humean” skeptic about our knowledge of entailment is precisely questioning this widespread assumption, as Hume questioned a similar assumption about causation: for the entailment skeptic cannot see how we could have access to any such knowledge—as Hume could not see how we could have access to necessitating causal powers in objects. What we have done, according to the skeptic, is to construct a mythology of propositions that bamboozles us into accepting that we can read entailments off propositions. We think that somehow propositions contain their logical consequences, like marbles contained in a drawer. But this metaphysics of containment is a myth, a chimera. Consider sentences, sequences of symbols: no sentence literally contains the sentences that it entails (except itself), since these are distinct sentences.  [1] The sentence “snow is white” does not contain the sentence “snow is white or grass is green”; nor does “Socrates is a man” contain “Someone is a man”. And it is not that such containment is implicit rather than explicit: there is simply no containment of any kind. Nor does a supposed language of thought exhibit any such containment: sentences in any medium cannot contain sentences they manifestly don’t contain. But it must be the same with propositions, whatever exactly they are: they must be made up of constituents that are self-enclosed and bounded, and knowledge of these constituents cannot ground knowledge of entailments. Consider propositions as ordered pairs of objects and properties: nothing in these constituents alone can lead the mind to other propositions—examine them from any angle and you will not be led to grasp logical necessitations. What could a proposition be such that we could detect in it the entailments that it has? Propositions are like billiard balls: we cannot read logical consequence or causal consequence off them by examining their isolated and intrinsic nature. So our beliefs about causation and entailment must derive from some other source, such as constant conjunction. In Hume’s terms, we cannot have any impression of necessary connection, either in causal relations or logical relations; so we cannot gain our knowledge of these relations by perceiving necessary connection. Logical powers and causal powers are both inscrutable in the entities that possess them.

            There seems to be only one way to avert this line of argument: adopt a radical kind of holism about causality and entailment. If we say that causal relations between particulars essentially involve other particulars and their constant conjunction, then we can maintain that causal relations actually embed facts about other particulars, notably effects of similar causes. Likewise, if we say that propositions are constituted by other propositions—all those that they entail and are entailed by—then we can maintain that knowledge of their identity actually embeds knowledge of those other propositions. That is, we hold that a given proposition is identical to the totality consisting of all the propositions logically related to the given proposition. But this is a completely incredible position: it is tantamount to claiming that a given proposition is a set of propositions, possibly infinite, that stands in logical relations with the given proposition. The individuation of propositions collapses under such a theory. A proposition is not the set of propositions it entails and is entailed by; these are distinct propositions. This kind of holism is a desperate attempt to make sense of the metaphysics of propositions suggested by the mythological idea of containment: it takes that idea literally and interprets it as something like set membership. What the mythology really needs is the idea of implicit containment and a corresponding epistemology; but that is precisely what the Humean critique is calling into question. It is the analogue of the idea that a billiard ball may not present its causal powers explicitly but it presents them implicitly, so that we still have access to them in some kind of attenuated form. But this is to enter fairyland (to use another term of Hume’s)—as if propositions contain other propositions in a ghostly form (as causes may be thought to contain their effects in a ghostly form).

            Here is another way to put the point, recalling Wittgenstein according to Kripke. As we “grasp a proposition” we may have certain experiences, such as the formation of a mental image, and it is tempting to suppose that these experiences play a role in producing our knowledge of both the identity of the proposition and its entailments. But no such experience could ever constitute grasping a particular proposition or fixing the entailments of a proposition—for the experience can be interpreted in multiple ways and may not even occur. Nor can our knowledge of entailments arise from access to the dispositions we have to make inferences: for such dispositions fail to track logical entailments, for the reasons Kripke spells out (entailments are normative). So these kinds of facts cannot the basis of our knowledge of entailment; the facts exist, unlike the mythology of containment, but they are of the wrong type to deliver entailment. Invoking them is like supposing that mere contiguity will add up to causation. We need logical necessitation to get entailment, as we need necessary connection to get causality; but we search in vain for experiences or impressions of such necessitation—and dispositions are the wrong kind of thing to ground our knowledge of entailment. The epistemology of entailment is thus as problematic as the epistemology of causation, as Hume diagnoses the latter. It is even difficult to see how we get the idea of entailment, as Hume argued in the case of causation (hence the need for constant conjunction and habit to account for how the idea arises in us).

            Why didn’t Hume extend his critique to logical entailment? I think it is because he had an overly simple theory of ideas, to the effect that all entailment results from the containment of simple ideas in complex ideas—the mosaic theory of ideas. It is a matter of distinguishing the parts of a complex whole. But this model doesn’t work for most logical entailment, such as disjunction introduction or existential generalization. It is as hard to see how ideas contain logical consequences, as it is to see how objects contain causal consequences: for how can other things be present in a given thing? How is the effect present in the cause and deducible from it, and how is an entailment present in a proposition and deducible from it? What is this idea of containment? How can what is absent be present? What are causal and logical powers? How do we manage to see extrinsic consequences of things in those things? Don’t we just see the thing? As Wittgenstein says, it is “as if everything is already present in advance”: but we have no model for such anticipation, and no real idea of what those words mean.

            It might be replied that we can just appeal to the notion of “grasping a concept” as primitive. When we grasp a concept we know in some primitive way what its entailments are—these are evident to us in the grasping. The trouble with this reply is that it is not explanatory and does nothing to address our unease about how such knowledge is possible. It is like agreeing with Hume that nothing perceptible can constitute necessary causal connection and then insisting that we have a primitive apprehension of necessity in objects. Worse, it is like agreeing that nothing could conceivably amount to an impression of necessary connection and then asserting that we just “intuit” the connection by some unknown faculty. The problem is that the Humean has a strong negative argument to the effect that such necessities cannot be discerned in objects or propositions, so the primitive grasp response looks like pure hand-waving. We have no account of how we could extract knowledge of effects from causes or knowledge of entailments from propositions—by what means or mechanism. The very idea is baffling. Hence the threat of skepticism about whether we have knowledge of entailment at all, or the possibility of having to accept a skeptical solution along the lines of habit and constant conjunction. Nothing seemed clearer than that we can know the basic entailments of logic, but upon examination this looks to be deeply problematic for Humean reasons. The root of the problem is explaining how we can know that one thing necessitates another thing. After all, propositions and their entailments are “distinct existences”, as causes and their effects are.

            In response to this it might be suggested that the whole idea of necessitation should be rejected. There is simply no such thing. In the case of causation we replace necessitation between particulars with regularity between types of particulars—the regularity theory of causation. Thus there is nothing inscrutable to begin with; Hume was wrong to believe in necessity in the objects. Knowledge of causal relations is just knowledge of constant conjunctions—there is no “tie” (Hume’s word) between cause and effect, just regular association. The analogue for entailment would be the idea that propositions do not stand in necessitation relations–that would indeed be surpassingly difficult to discern; instead different propositions have regularly associated truth-values—whenever one is true another is. There is no dependence here, no connection, no tie; there is just brute coincidence of truth-value (“just one damn truth after another”). This kind of approach can take different forms, depending on what we generalize over—places, times, substitution instances, possible worlds. The first two are appropriate for indexical entailment, since indexical sentences can vary in truth-value across space and time. The second two are applicable to eternal sentences, which do not vary in truth-value over space and time. Thus we say that entailment consists in the fact that the entailed proposition is true in all the same worlds that the entailing proposition is true, or that pairs of schematic sentences are true under the same substitutions (whenever anything of the form “p and q” is true something of the form “p” is true). Thus we capture entailment by moving from the properties of particular propositions to the properties of collections—as the regularity theorist of causation locates causality in collections of events. We interpret entailment as something like constant conjunction: the truth-values of sentences or propositions are constantly conjoined across space, time, substitution instances, and worlds. We need merely to observe such conjunctions to know that we have an entailment; we don’t need insight into the necessitation relations between individual propositions.

One sees the attraction of such theories once Humean skepticism has taken hold, but it is hard to believe that entailment is merely constant conjunction of truth-value, just as it is hard to believe that individual causation exists in virtue of general conjunction. At any rate, the two issues are similar in form, with the same array of theoretical options and the same difficulty of selecting one option as clearly correct. As Hume called his problem (or one aspect of it) “the problem of induction”, so we can call the analogous problem for entailment “the problem of deduction”: how do we know what is deducible from a given proposition? In virtue of what does one proposition deductively entail another? That problem is even more radical than Hume’s original problem about causation.

 

  [1] Except in the case of conjunction: but the syntactic containment of conjuncts in a conjunction is not the ground of the entailment—that is the concept expressed by “and”. A sentence could contain a pair of sub-sentences without entailing either of them, as in “Snow is white or the sky is blue”.

                                                            Induction Again

 

 

I will consider two instructive thought experiments. First, suppose there are people who have the following psychological deficiencies: (a) they have no concept of the natural powers or dispositions of objects, just concepts of manifest properties; and (b) they have no natural tendency, innate or acquired, to expect certain effects given the regularities in their past experience. All they have is an ability to register particular observable facts and remember what they have registered. For example, they have observed individual instances of the sun rising many times, but they cannot form the thought that the sun has the power or disposition to rise every day; nor do they have a natural psychological tendency to expect that the sun will rise when the hour comes. They do not think in terms of powers and they have no natural instinct to project into the future what they have experienced in the past; but they do observe individual instances of what are in fact broader laws of nature.

I suggest that in this state of psychological impoverishment they will not make inductive inferences from what they have observed. They will view what they have observed as simply a set of particular facts with no implications for what they have not observed. They will believe, for instance, that the sun sometimes rises or has risen such and such a number of times, but they will not believe that it always will rise or even that it is probable that it will. They will not see their limited experience as pointing to anything beyond that experience—to a generalization of law. This is because they lack the concepts or psychological habits that can ground such inferences. They won’t have the thought that the objects they observe have the power to bring about certain effects in virtue of their intrinsic nature, and they won’t find themselves instinctively expecting the repetition of what they have observed in the past. Nature will seem to them to consist of individual facts that point to nothing beyond themselves. They will not believe in general statements based on an incomplete set of particular statements. They will perform no inductive inferences.

If this is right, then the traditional model of our reasoning about the future and the unobserved must be wrong. That model has it that we form our general beliefs by observing particular cases and then extrapolating—from the particular to the general, from some to all. Critics of induction have doubted that such an inference can be regarded as valid, and it would seem that our imaginary people would agree: they have no tendency to generalize beyond the particular. There is nothing in the particular, considered by itself, that could warrant such an inference. Insofar as any generalization is possible, it must be grounded in something like the concept of natural power or a brute tendency to form expectations. Individual instances are impotent to produce knowledge that goes beyond them without non-trivial supplementation. Remove the supplementation and the inference grinds to a halt. So it cannot be that induction rests upon an inference from some to all.

Now consider beings with the following unusual psychology: they have no memory of the past but they do have a faculty of precognition.  [1] They can tell what will happen but they have no knowledge of what hashappened. Suppose they wish to fill this gap in their knowledge by making inferences to the past from the future–for example, they want to know whether the sun rose in the past. They consult their precognitive faculty and ascertain that the sun always rises in the future; then they extrapolate backwards to infer that it rose in the past. Thus they reason from the premise, “The sun will rise” to the conclusion, “The sun rose”. Skeptics will point out that the latter doesn’t follow from the former—the sun might not have risen in the past despite rising in the future. Many things will be true in the future that were not true in the past, so how can we infer the past from the future? These imaginary beings are just like us from an evidential point of view; they merely reverse the temporal direction of our inductive inferences. They proceed from knowledge of particular cases to generalizations about the unobserved, moving from the future to the past. So the problem of induction has nothing essentially to do with reasoning from the past to the future: it applies equally to reasoning from the future to the past. It is temporally symmetric and faculty-relative.

We can even stipulate that our imaginary beings lack the power of perception, so they have a problem knowing what is true at the present time. They can know the future by precognition, but they can’t know the present by observing it with their senses (or the past by remembering it). Wishing to remedy this lack they turn to the future for guidance: they infer that now such and such facts obtain because in the future they will obtain—for instance, objects presently fall to earth and bread presently nourishes. They can’t know these things by perceiving them, but they can at least infer them by working backwards from the future. It seems that they are no worse off (and no better off) from an evidential point of view than we are: they perceive the future and use it to infer the past and present, while we perceive the present and remember the past in order to infer the future. In both cases there is a leap from the known to the unknown of essentially the same type—extrapolation from knowledge of particular facts to beliefs about facts extending beyond that knowledge. Thus there can be a problem of induction with regard to the present: for how can the imaginary beings know about the present on the basis of their knowledge of the future? What counts as inferential depends on the cognitive faculties the knower happens to possess. The imaginary beings may harbor a Hume who torments them with the question of whether they know anything about the present, given that they have direct access only to the future (and similarly for the past).

If we humans had precognition, we would have no problem of induction with regard to the future: we would not need to base our beliefs about the future on our experience of the past, and so would not need to rely on concepts like natural power or fall back on brute inductive instinct. There would be no problem of principle about predicting the future. The problem of induction, as it exists for us, arises from a temporal asymmetry in human knowledge, but that asymmetry could be reversed in conceivable cases.

 

Colin McGinn

 

  [1] I won’t go into the question of whether precognition is logically possible, given the direction of causality. It seems to me hard to rule out on conceptual grounds (especially if we help ourselves to a bit of divine assistance), but it suffices that we can intelligibly raise the possibility and consider its philosophical consequences.