3

The title is a quote from this answer:

Stack exchange is not the place to learn first order logic, buy a book by Quine.

Depending on the interpretation of this quote, it may even contain a grain of truth. I certainly think that stackexchange is a good place to ask questions when you have specific problems while learning first order logic. However, different texts on first order logic use different conventions and different names, so questions of first order logic might have different answers, depending on the books used by the questioner.

The question which provoked the answer from which I took the quote has many answers, but most of these answers contradict the books from which I learned first order logic. However, these books were mathematical books written in German, so I don't want to exclude the possibility that philosophical books written in English really use completely different conventions with respect to that question.

  • 1
    I'd say the statement is correct. Analogously, the Mathematics Stack Exchange is not the place to learn algebra or calculus; HOWEVER, it's a great place to ask algebra/calculus questions. The Stack Exchange is mostly focused on providing detailed answers to specific questions within a subject, not on teaching an entire subject. – David H Aug 15 '13 at 7:51
3

SE is an open platform intended for learning together. I'm not sure about the issues arising from different notations, but the prevalence of logical questions on this stack in particular would at least apparently seem to mitigate against the hypothesis articulated in the quote -- that SE isn't an effective place for getting answers to questions arising from the formal study of logic.

One point here is that SE isn't an academic or formal program of study; at least as currently formulated. However, again, it is an open platform and community replete with students and teachers of -- among other things -- formal logic. So in this respect it's somewhat difficult to countenance the objection wholeheartedly; of course participation in our community is not comparable to a comprehensive course of study, but it certainly might complement and enrich one.

In passing: doing due diligence and research before posting here is of course highly desirable (i.e., not just a courtesy.) I sense that some frustration with particular questions' depth/quality might be lurking underneath the sentiments expressed in the answer. --That said, specific examples of problematic behavior would be helpful if we think there is an issue here to directly address.

3

That question is a difficult case, since I've seen different conventions on the treatment of free variables. Some treat them as if they were implicitly universally quantified, others treat them as ill-formed and incapable of receiving a truth value.

I think, or at least I would hope, that questions about first-order logic are absolutely on-topic. The only thing that I'd be concerned about are questions showing no research effort--- but that is not an issue particular to logic questions.

Also, the fact that different conventions exist should not disqualify the topic since mastery of the topic requires understanding that there are different conventions and learning to switch quickly between different notations and syntactic/semantic treatments.

  • The case for me is even more difficult, since I haven't seen yet a reference which treats free variables as ill-formed. The references I known effectively employ Tarski's Truth Definition from 1956, even if they don't acknowledge this explicitly. But even if some philosophical logic would employ the conception from 1933 instead, free variables are still a natural part of the language, and nothing ill-formed. Only the 1933 definition is capable of assigning truth values to well-formed sentences, because the model is part of the meta-language. – Thomas Klimpel Aug 16 '13 at 6:56
  • @ThomasKlimpel Here is a wiki page that discuss the issue somewhat (1). "Ill-formed" was a poor choice of words. Formulas with free variables are still well formed formulas. What I meant to say is that they are not sentences (by which "closed sentence" is standardly meant) and so do not express propositions. Since propositions are the bearers or truth-values, open sentences are neither true nor false. They may have true substitution instances (e.g., x=y is true if the same referring constant is substituted for x and y)... – Dennis Aug 16 '13 at 8:18
  • ...but statements such as x=y are neither true nor false prior to some such substitution or introduction of a binding operator. It is somewhat common to refer to such statements as "meaningless" (since they express no proposition). You can imagine a (weird)system without a substitution rule or a rule for introducing binding operators. In such a system formulas with free variables would be essentially indeterminate. – Dennis Aug 16 '13 at 8:25
  • I believe that Mendelson's book is one where open sentences are treated almost like they are universally quantified (I am away from my books, though, so I'm relying on memory) in the sense that such sentences are true iff every variable assignment maps the variables to referring expressions that make the sentence true. Equivalently, they are true iff they have all and only true substitution instances. – Dennis Aug 16 '13 at 8:33

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .