Category Archives: Logic

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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Conditionals, yet again

It’s very predictable, I would imagine, that some of the chapters that have been giving me the most grief as I write the second edition of my logic text are the two chapters where I introduce the material conditional. In the last … Continue reading

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Gerhard Gentzen’s Shorthand Notes

Springer have just published an exceptional volume that should quite certainly be in any university library that has any kind of logic collection. From the blurb of Saved from The Cellar – Gerhard Gentzen’s Shorthand Notes on Logic and Foundations of Mathematics: “Attempts … Continue reading

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Empty domains #1

From wild mathematical universes back to nothing much at all: the question of empty domains in first-order logic. Not that I have anything very insightful to say:  but I want to get my mind clearer before committing myself to a … Continue reading

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Frege on “if”

I’ve been looking at the passage early in the Begriffsschrift where Frege introduces the material conditional — not, of course, using that label, and not of course with our notation. He notes that can be affirmed when A is denied or when … Continue reading

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