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Natural language statements have quantifiers such as, “most”, “many”, “few”, and “only”. How could ordinary first-order predicate logic with identity (hereafter, FOPL) treat statements containing these vague quantifiers? It seems that FOPL, with only the existential and universal quantifiers at its disposal, is insufficient. I read somewhere that ‘restricted quantification’ notation can ameliorate such problems. Is this true, or are there difficulties with the restricted quantification treatment of vague quantifiers? What are some of the inference rules for restricted quantification notation? For example, in FOPL you have the existential instantiation and universal instantiation inference rules. Are there analogue inference rules for the quantifiers, "many", “most” and “few”? Can you recommend any books or articles that outline, critique or defend restricted quantification? I also read that there are issues with FOPL regarding symbolizing adverbs and events from natural language. Is this true or just a superficial problem? Another complaint about FOPL, (especially Russell’s treatment of statements in the form of “The so and so...”), is that, often there are no obvious correspondences between the grammatical structure of the natural language and its logical notation counterpart. For example, in the English statement, “All men are mortal” to the logical notation, (x)(Mx->Rx), there seems to be no obvious correspondence to the connective ‘->’ from anything in its natural language grammatical structure. In other words, the logical notation seems too contrived. What is the common response to this complaint if any? These seem to be grave problems for the applicability and effectiveness of FOPL to natural language arguments. (I am not referring to the “limits” of FOPL where extensions such as modal, tense, or second-order logic might accommodate the richer parts of natural language, but rather to the apparent inability of any logic(s) dealing with these problems.) Note: Much of these concerns I have come from an article I read by Kent Bach in “A Companion to Philosophical Logic” by Blackwell Publishing. Thanks Kindly for your reply, J Jones

One further point. Toward the end, you write:

These seem to be grave problems for theapplicability and effectiveness of FOPL to natural language arguments.(I am not referring to the “limits” of FOPL where extensions such asmodal, tense, or second-order logic might accommodate the richer partsof natural language, but rather to the apparent inability of anylogic(s) dealing with these problems.)

Waiving the issue about vagueness, there isn't any problem dealing with such quantifiers in a second-order context. Both of the quantifiers I mentioned, "Most" and "Eq", can be defined in second-order logic, so the caveat at the end kind of gives the game away. That said, what perhaps is puzzling about these quantifiers is that, as is the case with second-order quantifiers, there is, as I said, no sound and complete set of rules for them, with respect to the intended semantics. In that sense, there is no "formal" logic for these quantifiers. But, again, that is not to say that one cannot write down some rules for them, and these rules may even be adequate for most or even all of the intuitively valid arguments one might care to give. The really interesting question, to my mind, would be what kinds of resources one actually needs to be able to do that. And that is why it is interesting, to me, how hard it is to write down sensible "elimination" rules for "Eq". For more on that, see my paper "The Logic of Frege's Theorem", which is on my web site. (The example discussed there is more the ancestral, but similar points apply to "Eq".)

Of course, if we don't waive the issue about vagueness, then there are, as I also said, lots of other problems around. But these problems are not special to "few", "many", and the like.

I'm a student with the Open University in the UK, recently due to industrial action my tutors are no longer marking our essays with scores, they now only put comments on them. Personally I prefer this. I find myself feeling motivated to higher levels, and without the scores I cannot gauge what my average is, meaning that each essay is important to me. Initially this was because I didn't want to receive a bad comment, hence a bad score, but now it's because I am so much more absorbed in my subject. But other students don't feel the same, they feel as if it's their right to know their scores, after all, what is a degree if it isn't one massive score. I've decided that those of us who are enjoying the way things currently are, without scores are at University for the pursuit of knowledge. While those who do not like it are at University in pursuit of a degree. Two very different things. My question is, with this in mind, Do you agree that Universities would become better learning establishments, temples of knowledge even, if the current score system were to be abolished and replaced with a discussion and comment system? I also believe that the way Universities work have their roots firmly entangled in capitalist-democratic society and our Universities have been designed to promote the current way of doing things (life) in this society.

Grading at least some of students' work is probably unavoidable, but comments are essential. I've become fond of the British system of separating teaching from assessment. At Cambridge University, where I work, this means that the weekly philosophy essay that undergraduates write for their supervisions (tutorials) receives extensive comments and is the basis for extended discussion between the student and the supervisor, but the essay is not graded. The student's grade is based rather on tests and extended essays (both types of excercise submitted anonymously), and the grading is done by a board of examiners.

Some students who come into this system find it disconcerting: since their examiner is in general not their supervisor, they are nervous that they won't know exactly what the examiner wants to read. But that may be no bad thing, and the system gives students plenty of feedback and separates this from the grade. Since your supervisor is not your examiner, your relationship with her can be a little like that between an athlete and a coach -- you are working together to improve your skill and to help you to train to do well in the exams.

My question concerns existentialism and determinism. I understand that a "movement" like existentialism is very nebulous and diverse. Many of the thinkers given the name "existentialist" hold varying views on various subjects. But one theme, at least as I understand it, that runs through many existentialist works is the idea of freedom, Sartre's "condemned to be free" for example. From what I understand the sum of an individual is composed of their actions, we are what we do. As such we have a responsibility towards our actions. But I was wondering how some of the major existentialist thinkers would address determinism, specifically determinism based on scientific physical laws. It would seem that if this type of determinism were correct, it would undermine the existentialist view of freedom.

By emphasizing human freedom and responsibility, existentialists are not asserting a claim in physics -- such as "it is false that human beings are mechanisms fully determined pursuant to physical laws of nature."

Rather existentialists are making two different points. One is phenomenological. We are condemned to be free or forced to decide. You must decide whether to enlist in the army, whether to pull the trigger, and so on. Physical determinism, even if you could somehow know that it's true, could not take away this predicament of being forced to choose.

The other is a normative point about how we ought to think about our decisions and agency. I ought to take full responsibility for the effects of my decisions. And when there is the slightest doubt about the reach of these effects, I ought to assume that this reach is greater rather than smaller.

Existentialists urge this point retrospectively: I ought not to deflect responsibility by thinking/saying that things just happened ("I could not bring myself to act differently"). And they also, and especially, urge it prospectively: I must lead my life on the practical assumption that it is up to me to change the world, that the whole future of humankind is my responsibility.

This practical instruction, too, is not much disturbed by physical determinism. For suppose again that physical determinism is true and you know this. You might then appeal to it to deny your responsibility ("if I shoot, I will have nothing to do with this man's death, it's all just molecules interacting according to immutable laws"). But you might also accept responsibility ("if I shoot, then I will be the cause of this man's death.") Here the second point touches the first: You are still confronted with the choice between these two attitudes.

Natural language statements have quantifiers such as, “most”, “many”, “few”, and “only”. How could ordinary first-order predicate logic with identity (hereafter, FOPL) treat statements containing these vague quantifiers? It seems that FOPL, with only the existential and universal quantifiers at its disposal, is insufficient. I read somewhere that ‘restricted quantification’ notation can ameliorate such problems. Is this true, or are there difficulties with the restricted quantification treatment of vague quantifiers? What are some of the inference rules for restricted quantification notation? For example, in FOPL you have the existential instantiation and universal instantiation inference rules. Are there analogue inference rules for the quantifiers, "many", “most” and “few”? Can you recommend any books or articles that outline, critique or defend restricted quantification? I also read that there are issues with FOPL regarding symbolizing adverbs and events from natural language. Is this true or just a superficial problem? Another complaint about FOPL, (especially Russell’s treatment of statements in the form of “The so and so...”), is that, often there are no obvious correspondences between the grammatical structure of the natural language and its logical notation counterpart. For example, in the English statement, “All men are mortal” to the logical notation, (x)(Mx->Rx), there seems to be no obvious correspondence to the connective ‘->’ from anything in its natural language grammatical structure. In other words, the logical notation seems too contrived. What is the common response to this complaint if any? These seem to be grave problems for the applicability and effectiveness of FOPL to natural language arguments. (I am not referring to the “limits” of FOPL where extensions such as modal, tense, or second-order logic might accommodate the richer parts of natural language, but rather to the apparent inability of any logic(s) dealing with these problems.) Note: Much of these concerns I have come from an article I read by Kent Bach in “A Companion to Philosophical Logic” by Blackwell Publishing. Thanks Kindly for your reply, J Jones

One further point. Toward the end, you write:

These seem to be grave problems for theapplicability and effectiveness of FOPL to natural language arguments.(I am not referring to the “limits” of FOPL where extensions such asmodal, tense, or second-order logic might accommodate the richer partsof natural language, but rather to the apparent inability of anylogic(s) dealing with these problems.)

Waiving the issue about vagueness, there isn't any problem dealing with such quantifiers in a second-order context. Both of the quantifiers I mentioned, "Most" and "Eq", can be defined in second-order logic, so the caveat at the end kind of gives the game away. That said, what perhaps is puzzling about these quantifiers is that, as is the case with second-order quantifiers, there is, as I said, no sound and complete set of rules for them, with respect to the intended semantics. In that sense, there is no "formal" logic for these quantifiers. But, again, that is not to say that one cannot write down some rules for them, and these rules may even be adequate for most or even all of the intuitively valid arguments one might care to give. The really interesting question, to my mind, would be what kinds of resources one actually needs to be able to do that. And that is why it is interesting, to me, how hard it is to write down sensible "elimination" rules for "Eq". For more on that, see my paper "The Logic of Frege's Theorem", which is on my web site. (The example discussed there is more the ancestral, but similar points apply to "Eq".)

Of course, if we don't waive the issue about vagueness, then there are, as I also said, lots of other problems around. But these problems are not special to "few", "many", and the like.

Why aren't more contemporary ethicists doing work informed by the broader social-biological scope of animal behavior?

I may not be best positioned to address this question, since my own work in ethical theory is mostly not deeply informed by broader social-biological perspectives on animal behavior, but I'll have a try. The question seems to assume (a) that ethicists are not influenced by social-biological perspectives on animal behavior and (b) that they should be. But both assumptions may be open to question. Here, much may depend on what the questioner has in mind by social-biological perspectives and the way in which they might inform ethics. If this is a catch-all for any good work done in the natural and social sciences, then (a) might be doubted. At least, it would be overstated. While some ethicists pursue primarily internal questions about ethics conceived of as articulating principles that both subsume and explain common moral judgments and also provide reflectively acceptable guidance and criticism, others do work that is interdisciplinary in some way or other. For instance, there has been recent work (e.g. Doris, Harman, and Vranas) about how the precepts of virtue theory are affected by the situationist paradigm in social and personality psychology. Many moral philosophers and decision theorists are interested by ways in which conceptions of rationality are affected by the discovery of so-called framing effects. Current work on altruism is often situated in part in relation to discussions in game theory and evolutionary biology. Jurisprudential discussions of responsibility and culpability are often shaped by work done in developmental psychology and neuroscience (a subject in which I have written myself). Now there may be more truth in (a) if "social-biological" is taken to refer to the narrower field of socio-biology. Even here there are some philosophers (e.g. Kitcher, Sober, Ruse, Midgely, Gibbard, and Flanagan) who see potential bearing of socio-biological ideas on some issues within ethics. For instance, Flanagan thinks that socio-biology might place some feasibility/realism constraints on what a moral theory could reasonably demand of agents. But in general caution is needed here. This is issue (b). Socio-biological accounts of the evolution of particular traits and dispositions purport to explain where and why these traits arose. What traits contributed to survival in very different circumstances may provide a poor guide to how we should behave now or what traits we should try to cultivate or reform. Traits that were selectively advantageous relative to a particular environment need not have been selectively optimal for that environment. What was advanatageous/optimal for one environment may not be for another, different environment. And there may be a lot we should care about besides reproductive fitness.

The bottom-line is that ethics, as practiced by most contemporary ethicists, is a normative science (or art), whereas sociobiology is a descriptive or explanatory science. That doesn't mean there can be nothing that one can learn from the other, but it does mean that they are very different enterprises. On this view, which recognizes the autonomy of the two disciplines, it makes no more sense to ask the ethicist why he isn't talking a lot about sociobiology than it does to ask the sociobiologist why she isn't talking about whether we have duties to future generations.

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