IFL2 Chapter 20: Quantifiers

Over the next few weeks, I plan to post here draft versions of some individual chapters  from the slowly evolving second edition of my Introduction to Formal Logic. I’m at the stage where feedback would be most welcome!

Seeking reactions to a four hundred page book would be a really big ask, so I’m not going to do that. But I do hope that a few friendly readers might be tempted at least to look intermittently at some relatively short chapters!

All comments, then,  most gratefully received, whether you are a student or a teacher — I’d especially like to know about places where I am less than ideally clear. And if you have some snappier examples or explanatory turns of phrase for me to steal, that would be great! Though, however wise and well-intentioned, I guess it is a bit late in the day for reactions along the lines of  ‘you really should be writing a quite different book’! You can either comment here or by email (address on the draft chapters).

OK: please do remember IFL is intended as a genuinely introductory book (it is based on my pre-retirement first year lecture course). This first instalment is the chapter motivating the quantifier/variable notation and the design of formal languages for quantificational logic. [Link now removed]

4 thoughts on “IFL2 Chapter 20: Quantifiers”

  1. Dear Prof. Smith,

    I am a beginner student of logic in a philosophy program. After a first read, these are a few comments that I can offer as a student:

    1) In the last page, under “20.8 Summary,” it would seem useful to join the last sentence in the first paragraph to the beginning of the summary for clarity purposes, given that both appear to share a similar meaning.

    2) There is a period missing on page 191 after “scopeless.”

    3) On page 192, the paragraph that begins “Consider, for example, the arithmetical truism …” reads “So we see that here too the ‘x’ is just doing the work of a bound pronoun like ‘it’. .” Since the formula is defined as a truism, should we avoid calling the mathematical variable x “bound”?

    4) On page 195, the use of notation for conjunction, disjunction and negation is applied, but these symbols are not introduced elsewhere in the chapter. Perhaps they are stated in previous chapters?

    5) Beginning of section 20.6: the phrase “Where we have got to?” may be replaced by “Where have we got to?”

    I truly enjoyed the chapter.

    Warmest regards.

    1. Many thanks for these! (And yes, re point 4, the propositional connectives have had a good outing in earlier chapters). Genuinely glad to hear that you enjoyed the chapter!

  2. I am a complete lay-person; I have only ever taken one logic course (some forty years ago); but I have read a number of logic textbooks. From my perspective this chapter is quite understandable, and the writing is engaging.

    I have just one small suggestion. The second line on page 200 reads: “pick one of the Fs and call arbitrarily dub it ‘a'”.

    I suspect you want to delete ‘call’.

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