Does infinity exist in reality?

My thesis supervisor, George Boolos, wrote his own dissertation on the analytic hierarchy, whose description I shall omit. Suffice it to say, for present purposes, that the sets it concerns are infinite, and there are infinitely many of them. At the end of his oral defense, one of his examiners said, "So tell me, Mr Boolos. What does the analytic hierarchy have to do with the real world?" George's response was: It's part of it. Perhaps you had in mind physical reality. Then the question is a scientific one. Space is not, according to current physical theory, infinite in extent. But physics, in its contemporary form, typically describes both space and time as continuous (though, as I understand it, there are or at least have been proposals to quantize space). If that is correct, then space is, in one sense, infinite, in so far as there are infinitely many points even in bounded regions of space.

I have read many philosophic essays pertaining to applied ethics in the abstract, and many political essays dealing with specific ethical questions. There always seems to be a gap between the level at which the former leaves the problem and the latter takes it up. Why is this? How can this gap be bridged? For example, I (like most rational people I think) am bothered about the ethical issues involved in the question of abortion. Yet I have never seen a systematic treatment of the question beginning with philosophical principles? Does such a treatment exist? If not, why not? If so, why does it not enter more into the public debate? Thanks.

There are many excellent philosophical discussions of abortion, andmany of these do tie the question to general moral issues. One classicarticle is Judith Jarvis Thomson's "A Defense of Abortion", Philosophy and Public Affairs 1 (1971), pp. 47--66. Thomson's argument begins, contrary to what public political discussion might lead one to expect, by granting that the fetus has all the rights of a person. She argues that abortionis nonetheless justified because it involves a conflict of rights. Her central example goes like this. Suppose you were kidnapped by music lovers and connected via tubes and wires to a famous violinist whose life now depends upon your remaining connected to him. If you remove the tubes, he dies; if you remain connected for nine months, you both live. Do you have a moral duty not to remove the tubes? Thomson grants that it would be very nice of you not to do so, but, intuitively, you have no such moral duty. The example is meant to be analogous to cases of rape. Here's a...

Philosophically (and perhaps linguistically, what is the difference between the question, "who are you?" and "what are you?". To answer the former, I often describe something about myself like my name or that I'm a student. The latter is often posed to me when people ask about my ethnicity or national origin. And perhaps more broadly, how do we "know" which sorts of identifying information is pertinent in answering either? Thanks, and great site.

You've really answered your own question: The difference between the two questions you mention is demonstrated by the difference between the possible answers to them. Linguistically, wh-questions, as these are known, are derived from underlying structures that are more like declarative sentences. The wh-word then occurs in a more "natural" position. So, for example, the question "Who does John want to win?" is derived from: John wants who to win, and then the wh-word is (at least, ordinarily) moved to the front of the clause for reasons a linguist could explain. Acceptable answers result from replacing the wh-word by an appropriate sort of expression, and the character of the question is connected to the kind of expression that can appropriately replace the wh-word. The difference between the questions corresponds to the different grammatical roles the replacing expression plays (or, again, to the different grammatical roles the wh-word itself plays). For who-questions, the replacing expression...

If philosophy is engaged in a hunt for eternal verities, why does it so often seem as faddish as a clique-obsessed 13 year-old? For instance, in the 1920s logical positivism ruled and their answers seemed on the mark -- until, of course, everybody realized the Vienna Circle was engaged in narrow-minded bilge. Then it was Ordinary Language philosophy -- good on J. L. Austin and Gilbert Ryle -- until of course folks realized that close study of ordinary language revealed little of interest and certainly no grand metaphysical truths. Then it was the Gang of Quine (to be is to be the value of a bound variable) which seemed to have the handle on reality in the 1960s and 1970s -- but does anyone today still recall why anyone thought Quine's work mattered? Where are the eternal truths? Does no one in today's philosophy pursue work designed to last?

My own view is that there is something of value in all of that work, more so in Quine's than in Austin's or Carnap's, but that's just my own view. I believe, in fact, that Quine's work will continue to be taken seriously for a longtime, in part because of its intensely naturalistic focus and in part because of its historical significance within the evolution of philosophical thought in the US. But even if we waive these points, the last question seems to presuppose something about the people mentioned earlier that isn't in evidence, namely: That the positivists, the ordinary language philosophers, and Quine and his accomplices weren't pursuing work that would last. They plainly were. If they failed, well, pretty much everyone has. It's easy to look back at the history of philosophy and think, man, there sure were some great philosophers then. Where are they all now? But the so-called modern period, from Descartes through Kant, spans a couple hundred years, and the canon picks out but six or...

Is the experience of thoughts as predominantly verbal universal, or nearly so? What alternatives are there?

Suppose you trying to figure out how to get from point A to point B. Do you always do so verbally? Or do you sometimes find yourself imagining going from A to B, seeing important landmarks, imagining the turns you'd take, and finding yourself getting there? Or not? There has been a good deal of research on visualization and other sorts of imagistic thought. Whether imagistic thought is, ultimately, verbal, and if so in what sense, is much debated. There may be other sorts of thought that are neither verbal nor imagistic. Think about considering how something one does or says might make someone else feel. In doing so, one might attempt to empathize with that person, and again it is not obvious that such thought is purely verbal. One is, as the saying goes, trying to put oneself in that person's shoes and feel what he or she would or might feel. Or again, are prayer and meditation forms of thought? (Note that it is irrelevant here whether one thinks there is any point to such activities.) Are...

What is an irrational action?

There could be several different sorts of irrational action. Some actions might be irrational in the strong sense that the actor did not have much approaching a reason for the act. The person might "just be reacting". Another possibility would be actions for which the actor has reasons but for which s'he does not have anything approaching a good reason. In this case, one might act contrary to reason, and such an action might reasonably be called "irrational". A really good answer to this question would need more context.

Can a new color be made that is not like, or mixed from, any other?

The answer to this question obviously depends upon what color is. and I haven't a clue. But there is a little we can say anyway. Let us ask: Could there be a color that human beings perceived that was utterly unlike any other? To this question, I think the answer is no. Human color perception, it is now pretty well-established, is tri-chromatic, which means that color-space, as humans perceive it, is three-dimensional, the three dimensions characterized by the primary colors. I suppose it is possible that there are some colors no one has ever perceived that would appear utterly unlike colors to which they were nonetheless chromatically related, but human color vision also appears to satisfy some kind of continuity principle that would rule out that possibility. Some birds, it appears, have vision based upon four dimensions. If so, then the structure of color-space as they perceive it is radically unlike ours. Whether that means that there are colors they perceive that we do not, or whether it...

It seems that many thinkers commit the naturalistic fallacy in thinking about human engineering and enhancement. That is, when thinking about human engineering (e.g., germline engineering) many have claimed that it is "unnatural" to pursue such options or that we "ought" not do such things because it would damage the human race. My question is this: if we take evolutionary theory seriously (with constant change, adaptation, etc.), why ought we not pursue human engineering, especially if larger issues of justice can be adjudicated?

Some people surely do commit the naturalistic fallacy here: Simply to say it's "unnatural" isn't an argument. Couches are unnatural. The worry that genetic enginerring might "damage the human race" is quite different, however, and I for one take it seriously. The worry, very simply, is that we don't know what we're doing and that the costs of mistakes could be horrific. I'm not sure what evolutionary theory has to do with it. Perhaps the idea is that evoution could somehow correct the mistakes over time. But (i) that could take a very long time indeed; (ii) human reproductive success isn't driven by the same kinds of things now that it used to be; and (iii) evolution isn't going to resolve the problems from which the actual people born as the products of misbegotten engineering suffer.

In your response to the question on Twin-Earth, you said that descriptions can be used to fix reference. (E.g.: This colourless, odourless, thirst-quenching object is water.) But if I'm not wrong, Kripke in Naming and Necessity said that definite descriptions can't be used to fix the reference. He said reference fixing proceeds by an initial baptism. Where did I go wrong? My second question is about Kripke's and Putnam's essentialism. Is their essentialism limited to proper names and natural kind terms or does it include non-natural kind terms too? For example, in post-Kripke philosophy, do philosophers believe that terms like "game", "beauty", "chair" have essences? If these terms have essences, what are they?

Kripke argues in Naming and Necessity that it isn't, in general, true that every proper name is associated with some description that is used to fix its reference. He is prepared to allow that some names might, for some speakers, have their references fixed in that way. Perhaps "pi" is an example. Others, mentioned by Michael Dummett are, "Saint Anne", which was stipulatively introduced as a name for Christ's maternal grandmother, and "Deutero-Isaiah", introduced as a name for whoever wrote the second part of the book of Isaiah. (It's well-established that it wasn't the same person who wrote the first part.) And, as Gareth Evans pointed out, if there weren't any such names already, we could introduce one, which he proceeds to do: Let "Julius" denote the inventor of the zipper, whoever that may be. It's then a priori that, if some one person invented the zip, Julius did. Regarding the second question, the answer depends upon what you mean by an essence. One might reasonably suppose that...

Is it possible for one to possibly know what exists after death? As humans, with a mind that exists solely as physical matter (and a soul, if religion is counted), when we die, how is it possible for this purely physical mind to keep on functioning, and allow us to realize that we are dead? As well, if we have souls, how can an entity created purely of energy (or whatever you think a soul is made of) have senses and detect that it exists, or even think?

Some people think they do know what exists after death. As Alex notes, "Nothing" is one option, and some people believe they have strong enough evidence for this view to make it a reasonable belief, and perhaps even to count as knowledge. On the other side, there are people who would claim to know, on the basis of divine revelation, that they will survive the deaths of their bodies. Presumably, not both camps can be right, and both camps might be wrong about their claims to know . But I don't see any general reason, absent consideration of the details, for supposing neither of them could know. Perhaps one wants to say that neither camp can really know, on the ground that truly conclusive evidence isn't available. But truly conclusive evidence is rarely available for anything, and yet we claim to know lots of things. That is to say: The claim that it is not possible to know what exists after death seems to be based upon a general sort of skeptical challenge that, allowed to run free, would...

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