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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
Richard Heck
May 7, 2006
(changed May 7, 2006)
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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 natur... Read more
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.
Peter Lipton
May 7, 2006
(changed May 7, 2006)
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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 supervisi... Read more
My 7-year old daughter has asked what philosophy is. Can anybody give an explanation that she would understand? Bonus question: while we were discussing this, she quoted the song, 'Rubbernecking': "Stop, look and listen baby, that's my philosophy". If you can shed light on this you are a legend.
Alexander George
May 6, 2006
(changed May 6, 2006)
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You might also check out some of the ideas and further resources mentioned on the website Philosophy for Kids (you can find a link in the right column of this page).
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How can an exception ever prove a rule?
Thomas Pogge
May 6, 2006
(changed May 6, 2006)
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Here is a third answer focusing on the actual history of the expression: www.worldwidewords.org/qa/qa-exc1.htm
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My 7-year old daughter has asked what philosophy is. Can anybody give an explanation that she would understand? Bonus question: while we were discussing this, she quoted the song, 'Rubbernecking': "Stop, look and listen baby, that's my philosophy". If you can shed light on this you are a legend.
Alexander George
May 6, 2006
(changed May 6, 2006)
Permalink
You might also check out some of the ideas and further resources mentioned on the website Philosophy for Kids (you can find a link in the right column of this page).
Log in to post comments
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.
Thomas Pogge
May 6, 2006
(changed May 6, 2006)
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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... Read more
How can an exception ever prove a rule?
Thomas Pogge
May 6, 2006
(changed May 6, 2006)
Permalink
Here is a third answer focusing on the actual history of the expression: www.worldwidewords.org/qa/qa-exc1.htm
Log in to post comments
How can an exception ever prove a rule?
Thomas Pogge
May 6, 2006
(changed May 6, 2006)
Permalink
Here is a third answer focusing on the actual history of the expression: www.worldwidewords.org/qa/qa-exc1.htm
Log in to post comments
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
Richard Heck
May 7, 2006
(changed May 7, 2006)
Permalink
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 natur... Read more
Why aren't more contemporary ethicists doing work informed by the broader social-biological scope of animal behavior?
David Brink
May 4, 2006
(changed May 4, 2006)
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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 perspectiv... Read more