Ed Erwin Again

Ed Erwin Again

 

It’s nice to receive two laudatory messages about Ed Erwin from Michael Tooley and Alan Goldman, both old colleagues of Ed’s at Miami (now posted under my brief notice of his death in May 2022). I observe, however, that neither the Brian Leiter blog nor Daily Nous has posted any notice of his death. I wonder why. Has no one informed them of it or have they decided not to mention it? Is the Miami philosophy department responsible or have they simply chosen to omit it? It seems very strange to me, though depressingly predictable.

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Concepts and Philosophical Puzzlement

 

 

Concepts and Philosophical Puzzlement

 

Michael Dummett has suggested that philosophical puzzlement is caused by our “imperfect mastery” of our concepts (he is by no means the only person to think this way).[1] He gives the example of the concepts past and future: we understand these concepts well enough to make judgments about the past and future of an ordinary kind, but if we ask ourselves why cannot affect the past as we can affect the future we find ourselves puzzled. The reason for this, he says, echoing Wittgenstein, is that we don’t “command a clear view” of the concepts past and future. That is, we have only an “imperfect mastery” of these concepts—a partial mastery, a tenuous grasp, a limited understanding. There is something about them we fail to grasp, and this failure generates perplexity. Such a view contrasts with the idea that we have a limited understanding of the world beyond concepts: we fail to grasp important aspects of reality not our conceptual representation of it; and this is what generates philosophical perplexity. Dummett gives the example of quantum theory: here we have an effective theory for making predictions but we have no satisfactory interpretation of the theory. Some may say this is because we lack knowledge of quantum reality itself; others may say we lack an adequate grasp of the concepts of quantum theory (analytical knowledge not empirical knowledge). Dummett is proposing that philosophical perplexity arises from a deficit in our knowledge of our own concepts not from a deficit in our knowledge of what these concepts are about (sense not reference, in effect).

            This thesis raises some interesting questions. Is the thesis true of all concepts or only some? Do we have perfect mastery of some of our concepts, so that no philosophical puzzlement is occasioned by them? Which are they? Are there degrees of imperfection in our mastery of concepts—are some very imperfectly grasped while others are only mildly so? Are there concepts we possess that we have no understanding of—concepts we can’t use at all? If that is impossible, what about concepts that are almost completely opaque to us? How deep can the imperfection in our mastery go? And why should this be so—why should our concepts lack in transparency? After all, they exist in our minds and we use them in our conscious thought, so why should our grasp of them be so imperfect? Why would nature (or God: Dummett was a Catholic) design us this way? Bear in mind that concepts constitute the meaning of words, so that Dummett’s thesis applies to them too—we have imperfect mastery of the meaning of our own words. We lack knowledge of these meanings; we are ignorant of what we mean by our own words. By contrast there is no paradox in the idea that we are ignorant of the world beyond our conceiving minds—time itself in the case Dummett cites. But it is surely strange to think that our own concepts and meanings are routinely closed off from our knowledge of them. If some philosophical problems are insoluble that would imply that we can never gain access to the content of our own concepts; maybe so, but the idea requires careful consideration. It seems to imply the existence of a vast conceptual unconscious—all the stuff that we fail to know consciously when we employ concepts. Why does this unconscious exist? How inaccessible is it? How is it connected to our conscious thought? Our concepts allow us to make intelligent judgments, both practical and theoretical, but they refuse to allow us to make philosophical judgments (or judgments that command general assent). This is curious to say the least.

            I don’t say the whole idea is preposterous; indeed I think it raises interesting questions about the nature of conscious thought and the concepts it invokes. But it is not an idea to be thrown out without due consideration. No one would think a comparable thesis holds for the case of other subjects: physics, chemistry, biology, psychology, geography, etc. Here the difficulties stem not from our imperfect mastery of the relevant concepts but from our ignorance of the extra-conceptual world.[2]

 

[1] My source for this is a lecture on philosophy of mathematics given by Dummett many years ago (and now available on YouTube).

[2] Once you make the linguistic turn you are bound to find the difficulty of philosophy to arise from the inscrutability of language, i.e. the elusiveness of our concepts.   

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What is Mathematics About?

 

 

What is Mathematics About?

 

Various suggestions have been made about this question: mathematics is about symbols, or mental constructions, or abstract Platonic entities. We can also ask what physics is about and expect a variety of answers: the sensations of the physicist, mind-independent material bodies, an all-pervading consciousness, abstract structure. In the physics case another answer has sometimes been contemplated: physics is about something whose nature we do not know and perhaps cannot know. This usually gets expressed as the thought that matter is an I-know-not-what, a mysterious substratum, a noumenal thingummy. We may know something of its structure and its mode of operation but we don’t know its inner nature. But I don’t know of any analogous view of the subject matter of mathematics: the view that mathematics is about something unknown to us yet partially described by our mathematical theories. Arithmetic, say, aptly represents the structure of mathematical reality, but nothing in it provides a clue about what numbers really are; nor do we have access to anything else that informs us of the nature of number. Thus we have agnostic realism about the mathematical world: numbers are real but we must be agnostic about the intrinsic character of numbers—as we must be agnostic about the true nature of what we call “matter”. Maybe physics and mathematics are ultimately about the same thing, but if so we are ignorant of what that thing is. The advantage of this way of thinking, in both areas, is that it allows us to avoid being forced into unpalatable positions: none of the standard positions is free of difficulty, and at least the agnostic realist position avoids these difficulties. Certainly the long history of mathematics gives the impression of people stabbing in the dark unaware of the vast mathematical world that would later be revealed; the very idea that mathematics has a subject matter would be alien to these early thinkers.[1] The reason is simply that we are not faced with any such subject matter by our senses or by anything else. There is a subject matter to mathematics, objectively real and determinate, but we have next to no knowledge of its ultimate nature; we don’t grasp the underlying mathematical reality (that very concept may be inadequate to its intended referent). The numerals we use are just symbols for we-know-not-what, mere placeholders. That, at any rate, sounds like an option to be added to the usual options. Call it mathematical agnosticism.           

[1] See for example Dirk. J. Struik, A Concise History of Mathematics (1987), which begins 10,000 years ago. Perhaps the earliest mathematicians would say that its subject matter consists of cows and corn, friends and foes.

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Extended Ban

Extended Ban

 

A thought occurs to me: would other university administrators take a similar line? I have to admit that the idea that I would ever be forbidden to attend an academic gathering never entered my head, but that is the reality I now face. So far as I know it is unprecedented. But what about other institutions—would they also ban me? I haven’t been to a philosophy talk in the USA in nine years, so I don’t know. If I proposed to attend a colloquium at some other American university, would I be forbidden from attending? The question divides into three parts: would university administrators ban me, would faculty ban me, and would students ban me? Certainly I have not been invited to give a talk at an American university since 2013, but what about my attending someone else’s talk? What precise grounds could be given for such a ban? None that I can think of, but that doesn’t seem to matter. One would think that the position of the University of Miami would generalize, so that other places would have equal grounds for keeping me out—for example, if I was a deemed dangerous. Or would the mere possibility of protest be sufficient to have me banned? I really don’t know—and that says a lot. Perhaps I should do an experiment and mention to (say) NYU that I plan to attend a colloquium of theirs: what would happen? Would administrators step in to threaten me with expulsion? Would the faculty advise me that I am not welcome? Would the students rise up in protest? The terrible truth is that all these things strike me now as eminently possible. What a world we live in. I expect no improvement in 2023.

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Banned

Banned

 

I recently expressed an interest in attending colloquia at the University of Miami, where I used to teach (I live nearby). I was told by the chairman, Professor Mark Rowlands, that I was banned from campus at the direction of university administrators. No reason was given. There was no protest from members of the department, including the chairman. Apparently the ban is in effect until the day I die. So much for academic freedom, etc. Happy New Year everybody!

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My Mind

 

My Mind

 

How do I get the idea of my own mind? Do I get it simply by having my mind, or possibly by experiencing the mind I have? Do I perhaps have an “impression” of my mind from which I extract the idea? Here is a problem with this theory: based on my mind alone, I cannot distinguish between it and the world. My mind is my world. The world I know is the world presented to me by my mind, so my world and my mind are coeval and coterminous. The limits of my mind coincide with the limits of my world.[1]  When I gaze at my mind all I see is a world. I don’t have an idea of my mind as something in the world. Merely having a mind does not give me a perspective from which I can grasp my mind as an object: I don’t apprehend it as I apprehend the Sun setting on the horizon.

            How then do I get the idea? First let us ask how I get the idea of other minds. This idea is useful in social contexts: it enables me to think effectively about the behavior of other people. We probably have this idea innately, as do other mammals. It enables us to think of minds as things existing in the world. But my mind is not included in this general conception; it stands apart from other minds. How do I bring my mind under the conception that includes other minds? Not by thinking of my mind as other! But one thing I can know about other minds is that I am other to them: they think of me as an other mind. So we can imagine the child coming to realize that he or she is an object of thought for other minds: “Oh, so they think of me as I think of them”. Now she is thinking of her mind as something in the world: it is her world but it is also an object in other people’s worlds. She thinks of her mind as being an object for the minds of others. This is the exact opposite of her own perspective on her mind, in which world and mind are merged. She sees herself reflected in the minds of others, and this gives her the idea of her mind as one thing among other things. So we grasp our own mind via our grasp of the minds of others, by understanding that we are objects for them. Our mind cannot give us an idea of itself as existing in a world containing other minds, but our grasp of other minds can give us this idea once we grasp that those minds take us as objects. This is a very sophisticated idea and it is doubtful that other mammals and small children have it. They may have the concept of other minds, but they don’t really have the concept of their own mind. Only by recognizing that other people think about them can they manage to think about themselves, i.e. grasp that they are entities of the same kind as other people. The thought “I have a mind” is really the thought “This world is an object of thought for people with other worlds”—that is, “I exist in other people’s worlds”. My mind and their minds form a totality for me because I think this way: I think of myself from their point of view, because I think of other minds and realize that I am considered by them. No doubt my first thoughts along these lines centered on my mother: “I am an object in my mother’s world, so I must be something in the world as well as a world unto myself”. Then I realize I am an object among others, and am nothing unique (a sobering thought in my childish egotism).

            These two thoughts always coexist uneasily: the “I” as object in the world and the “I” as constituting the world for me. Can all this really be just one pinpoint thing in a much larger reality? Thus we oscillate between solipsistic egotism (there is only my world) and vertiginous humility (I am just a tiny speck in a huge wide world). The astonishing thought that I am merely one mind among innumerable others brings together two ways of thinking about the self: the idealist conceit that the world is my world, and the realist concession that the world is much greater than I am. In particular, it locates the self in a world occupied by other equally real selves—as an object of their apprehension. In coming to have the idea of my mind I come to realize that I am much smaller than I thought, even though I know no world larger than the one presented by my mind. The concept of my mind is thus the consummate philosophical concept, because it contains an entire metaphysical outlook on reality, one that generates perplexity and intellectual disharmony. It isn’t just a “faint copy” of a perceptual datum, a “simple idea”. It might even be said that putative possessors of this concept don’t really have it themselves, not fully, because it is just too hard to grasp: I never really understand the idea that I am just one mind among others; my own mind asserts itself too strongly to accept that. I am the world; I am not a minute part of it! Certainly some people never seem to get over the idea that everything centers on them—that nothing else is real (not really real).  The idea of one’s own mind as one thing among others is just too lowering, too ontologically disquieting.

            In any case, our concept of our own mind is a concept originally derived from our concept of other minds, particularly from the idea that other minds regard my mind as an object in their world. It doesn’t spring from a simple encounter between me and myself, as if my mind introduces itself to me one day and I recognize it for what it is (“Ah, I’ve heard a lot about you, good to meet you at last!”). It arises from complex reflection on the minds of others, an idea with roots in practical biological concerns. Not every being with a mind has a concept of that mind, even those with a concept of other minds.

[1] Cf. Wittgenstein: “What brings the self into philosophy is the fact that ‘the world is my world’. The philosophical self is not the human being, not the human body, or the human soul, with which psychology deals, but rather the metaphysical subject, the limit of the world—not a part of it”. Tractatus 5.641

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Sons of Gods

 

Sons of Gods

 

According to Greek mythology, Perseus was the son of Zeus and Danae, the former a god, the latter a mortal woman (daughter of Acrisius, king of Argos). One imagines that the conception occurred in the normal way: Zeus paid Danae a visit and impregnated her by penile insertion. Sperm and ovum were involved. She was not a virgin. Zeus may have been a god but he procreated like a man, with Danae playing the woman’s part. All this we can understand: that’s how babies get produced—same way animals do it. Nothing fancy, nothing supernatural, nothing “immaculate”. Zeus passed on some of his characteristics to Perseus, by means (as we now know) of DNA molecules. The case is not really different from that of superior extraterrestrial beings impregnating human females. But the case of Jesus Christ and God is very different: here we are told that Mary was a virgin, the conception “immaculate”, and the means non-corporeal (no penile insertion etc.). It is not to be understood on the standard model: there was no sexual intercourse with God, no passing of sperm or fertilization of egg. Mary did carry an embryo and then a fetus and finally a baby, but there was no initial joining of sperm and ovum; perhaps there was an early-stage dividing cell, but there was no journey of sperm to womb. That’s the story anyway. It raises a number of questions.

            Presumably God had to implant something into Mary’s womb. Did he implant a version of human sperm, but with an extra ingredient, and allow it to join with one of Mary’s eggs, or did he take care of the whole operation himself bypassing Mary’s contribution? Was what he implanted like a human fertilized egg in being composed of DNA? Wouldn’t it have to be in order to develop in the usual way? So God created a DNA complex with the extra bells and whistles needed to allow for the ability to perform miracles (Jesus didn’t pick up these skills by learning). How was the implanting performed—did God directly inject it into the womb or was it sent up the birth canal? We are not told, but either method seems feasible. In any case, that’s roughly how it worked, presumably. But now in what sense is God the father of the resulting child? Granted he is the creator of the child, but is he the father—the actual Dad, the biological parent? The DNA did not come from God’s body, since he doesn’t have a body, so in what sense is he the father? Didn’t Jesus have no real father, though he had a supernatural creator. How exactly did Jesus differ from Adam in this respect, also created by God? God is not Adam’s father because there is no father-son relation between them, but isn’t the same true of Jesus and God according to the official story? What if God had created many children by the same method—would they all have been his sons (and daughters)? After all, a lab scientist who artificially creates chunks of DNA and uses them to produce children by implantation is not thereby the father of these children. Zeus is clearly the father of Perseus because he employs the standard fatherly method of child production, but that is precisely what is not true of God and Jesus. So the doctrine of the virgin birth is really not compatible with the proposition that Jesus is the son of God—that they stand in the father-son relation.

            Secondly, why does God use a woman at all—why not create Jesus from scratch? This is what he did with Adam—he didn’t insert suitable “seed” into a woman in order to create Adam. God is a well-known all-purpose creator, and he created the first man from nothing, so why not do the same for Jesus? It seems like a pointless excursus to bring Mary into the act. And what if she had a miscarriage or smoked and drank her way through the pregnancy? Why take the risk? God could have used Mary’s toenail as a basis for Jesus, as he used Adam’s rib to obtain Eve, so why involve Mary’s womb at all? Joseph had to use Mary’s womb if he wanted children, but God was under no similar constraint. Plus you have the risks of childbirth for both mother and baby. Then there is the question of Jesus’s childhood in which he was essentially useless in his allotted role as Son of God and Savior of Mankind—why not create him fully grown or at least a strapping ten-year-old? One wonders what occupied Jesus’s mind during his callow years, given his divine provenance: did he daydream of growing up to be the son of God, or just a humble carpenter? It all seems rather unnecessary given God’s purposes.

            Third, how did Joseph feel about his wife being impregnated by another man (albeit a rather special one)? Didn’t God involve Mary in a type of adultery vis-à-vis Joseph? True, there was no sexual intercourse involved in the “immaculate” conception, but still someone else’s child was placed in Joseph’s wife’s womb. He was then obliged to raise this child without knowing that he was not the true father, since God had secretly decided that this woman would be his vehicle of propagation. It doesn’t seem very respectful of the institution of marriage. How about asking Joseph’s permission first instead of just foisting it on him? What if God had decided to have a second son by Mary—or a third or fourth? Would that be ok? And isn’t the whole procedure suspiciously like rape? God injects his chosen DNA into Mary’s womb without so much as a by-your-leave and then leaves her to carry his child to term—shouldn’t that be illegal? If someone did that to you, wouldn’t you seek legal remedy? Mary could certainly claim that she never gave her consent to God’s act of impregnation; the lack of actual penetration is not really an adequate exculpation. Powerful men can’t go around impregnating women as they see fit, even when intercourse is not the chosen method. What if Mary didn’t want to give birth to a semi-divine being who would later be crucified? She loved her husband Joe and wanted only his babies. It wasn’t very considerate of God, was it? So the morality of God’s divine plan for mankind leaves a lot to be desired.

            The story of Perseus’s birth makes sense and raises no ethical questions (assuming Danae was willing), but the story of Jesus’s birth is riddled with conceptual difficulties and is ethically questionable (if not outrageous). That is no way for a god to bring a son into the world.

 

Colin McGinn  

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Quantification and Necessity

 

 

Quantification and Necessity

 

What is the connection between quantification and necessity? At first sight none: if you make a singular statement of necessity such as “This table is necessarily made of wood” you express no general proposition; you speak simply of a particular table and a property of it. The statement seems no more quantified than “This table is made of wood”—you aren’t saying anything of a general nature here. Yet there is a whiff of generality in the air; you aren’t just talking about a specific table. For you would be perfectly prepared to affirm something along these lines: “Any table is necessarily composed of what it is actually composed of”. Similarly for modal statements concerning identity, origin, and natural kind: you see that something general is true of which a particular thing is a specific instance. It isn’t just that Hesperus is necessarily identical to Phosphorous; any object is necessarily identical to itself (the same is not true for statements of location, brightness, etc.). So we might reasonably say that all singular statements of necessity are implicitly quantificational—they all presuppose general modal truths. Put in the material mode, particular modal facts involve general modal facts; or in the conceptual mode, all singular modal propositions are conceptually linked to general modal propositions. There is a kind of tacit quantification going on in the background. Modal thinking about particular things is always modal thinking about general categories of things. It couldn’t be that only this table is necessarily made of wood (all the other wooden tables being only contingently so). The concept of necessity is inherently a general concept—involving all things of a certain type.

            But this claim should be distinguished from another claim that is generally adhered to, viz. that modal operators are quantifiers over possible worlds. This too would render necessity inherently quantificational: necessary truth is simply truth in all worlds. For this table to be necessarily made of wood is for all worlds w to be such that this table is made of wood in w. Clearly this thesis is to be distinguished from the thesis enunciated above; that thesis certainly does not entail that modal adverbs are quantifiers over worlds. And it seems evident that such a thesis meets with firm resistance: if I don’t believe in possible worlds I am not thereby inhibited in my modal pronouncements—because I don’t take my use of modal words to have any such entailments. Nothing in mymodal thoughts adverts to the existence of a class of possible worlds over which I must perforce quantify. That’s not what my words mean; it’s just a theory dreamt up by metaphysicians (right or wrong). The theory is not semantically correct. For one thing, where is universal instantiation? Where are the singular terms (demonstratives or proper names) for worlds that might stand in the place of the variable w? How do these worlds feature in the verification of modal thoughts—do I think about them at all when I arrive at modal conclusions? Is “Necessary truths are truths in all possible worlds” analytic? Maybe modal words are semantically primitive sentence operators or predicate modifiers or copula modifiers.[1] But accepting such semantic views leaves it open that there is nevertheless a connection to possible worlds talk: for we might consistently hold that modal truths have consequences for the condition of possible worlds. If this table is necessarily made of wood, then in all worlds it is made of wood—though that is not what the sentence means. That is, if I accept that possible worlds exist in which objects instantiate various properties, I can allow that a necessary truth implies that things are thus-and-so in those worlds. But the kind of fact stated by a modal proposition is not thereby a fact about these worlds; the two facts are separate and distinct. It is just that one kind of fact determines the other kind: the two cannot vary independently (there is a form of supervenience). This accounts for the feeling we have that modal truths match up with truths about possible worlds, without the former collapsing into the latter (or vice versa). There is this kind of generality in the offing, but it is not of the essence (so to speak). You are not strictly quantifying over worlds when you affirm a modal proposition, though you are at liberty to advert to such worlds in your modal ruminations. It may indeed be useful to do so—and such worlds may exist in whatever way they do—but modal talk itself is not committed to them. Thus it is not quantificational in that way. This seems intuitively correct: we are not generalizing over worlds when we make a simple modal statement. And of course modal words don’t look like quantifiers over worlds—which is why you can happily use them while rejecting worlds on metaphysical grounds. The existence and utility of possible worlds is independent of whether modal words are literally quantifiers over worlds semantically speaking.

            So we can say the following three things about quantification and necessity: (a) necessity claims always involve quantification over objects of a certain class (tables, persons, objects in general); (b) the necessity operator is not itself a quantifier over possible worlds, so that modal facts are not general facts involving such worlds; and (c) general facts about possible worlds can coexist with singular modal facts and be dependent on them, without their being any identity between the two. Thus the picture is rather more complex and nuanced than standard views typically recognize. Modality and generality are closely connected, though not in the manner suggested by standard possible worlds semantics.[2]  

 

Colin McGinn

 

[1] See my Logical Properties (2000), chapter 4.

[2] Modal expressions thus differ from spatial and temporal expressions such as “everywhere” and “always”: here it is very plausible to attribute quantificational content thus assigning an ontology of places and times to these expressions. But we don’t have an analogue of point (a) for them: a specific claim about a place or time does not derive from, or involve, a general truth of that kind concerning other places and times (its raining here and now doesn’t imply that it’s raining at other places and times). Modal expressions are more sui generis semantically than has been recognized. To put it differently, modal logic does not reduce to quantificational logic with a domain of possible worlds (i.e. modal facts are not general facts about worlds).  

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