Category Archives: Logic

The metaphysics of logic?

A collection of essays on The Metaphysics of Logic, edited by Penelope Rush, was published as a very expensive haddock — no, no, you idiot spell-checker, hardback — in 2014. Even with my large discount as a CUP author, I balked at … Continue reading

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Core Logic

The revised, surely-more-natural, disjunction elimination rule mentioned in the last post is, of course, Neil Tennant’s long-standing proposal — and the quote about the undesirability of using explosion in justifying an inference like disjunctive syllogism is from him. This revision has, … Continue reading

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A more natural Disjunction Elimination rule?

We work in a natural deduction setting, and choose a Gentzen-style layout rather than a Fitch-style presentation (this choice is quite irrelevant to the point at issue). The standard Gentzen-style disjunction elimination rule encodes the uncontroversially valid mode of reasoning, … Continue reading

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Begriffsschrift and absolutely unrestricted quantification

We owe to Frege in Begriffsschrift our modern practice of taking unrestricted quantification (in one sense)  as basic. I mean, he taught us how to rephrase restricted quantifications by using unrestricted quantifiers plus connectives in the now familiar way, so that … Continue reading

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Which is the quantifier?

A note on another of those bits of really elementary logic you don’t (re)think about from one year to the next – except when you are (re)writing an introductory text! This time, the question is which is the quantifier, ‘’ or ‘’, ‘’ or ‘’? Really exciting, … Continue reading

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Why mandatory reiteration in Fitch-style proofs?

Digressing from issues about the choice of language(s), another post about principles for selecting among natural deduction systems — another choice point, and (though I suppose relatively minor) one not considered by Pelletier and Hazen. Take the most trite of examples. It’s … Continue reading

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The language(s) of first-order logic #3

Back to those choice-points noted in the first of these three posts: one formal language for FOL or many? Tarski or quasi-substitutional semantics? use of symbols as parameters as opposed to names or variables to be syntactically marked? In the second … Continue reading

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The language(s) of first-order logic #2

One theme touched on the last post is whether the language for our preferred natural deduction system syntactically distinguishes symbols used as parameters in (UI) and/or (EE) proofs. Of the nine books I mentioned, two use distinct symbols for parameters, … Continue reading

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The language(s) of first-order logic #1

In presenting a formal theory of first-order logic for an introductory course — or, in my case, an introductory book — there are a lot of choices to be made, even once we’ve fixed on using a natural deduction proof system. (This paper by … Continue reading

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Truth trees for propositional logic

I’ve revised (and of course revised again, and re-revised!) the chapters on truth-trees for propositional logic for the second edition of my intro logic text. What took four chapters and forty pages has now become two chapters and twenty-eight pages, … Continue reading

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