How Much Logic Do I Need?

A reader who reports that his main interest is in contemporary metaphysics inquires:

Should I learn as much logic as humanly possible during my PhD? Or should I learn only what I need along the way? I have a basic grasp of symbolic and predicate logic, but little meta-logic.

First of all, it makes no sense to oppose symbolic to predicate logic.  Modern symbolic logic includes both propositional logic and predicate logic.

Second, learn what you need as you go along.  For example, existence is one of the central topics in metaphysica generalis. To work on this topic in an informed way you have to understand the modern quantificational treatment of existence in mathematical logic. 

Here is the minimum required for doing metaphysics. First, a thorough grounding in traditional formal logic including the Aristotelian syllogistic. Second, modern symbolic logic including the propositional calculus and first-order predicate logic with identity.  Third, some familiarity with axiomatics and the concepts of metalogic including consistency and completeness of axiom systems.  Fourth, axiomatic set theory. Fifth, some (alethic) modal logic both propositional and quantified.

The best way to master these subjects, or at least the first two mentioned, is by teaching them to undergraduates.  

Comments

[Casey]

The book More Precisely may be of some interest to the questioner as well:
https://broadviewpress.com/product/more-precisely-the-math-you-need-to-do-philosophy-second-edition/?ph=520e08a63daa08ffebfa06f6#tab-description

[José]

If I may... I've been studying Bonevac's "Deduction" and it has all the topics that you mention... with the exception of methalogic and set theory. Regarding methalogic it was already adviced to me to study Boolos et al "Computability and Logic".

What about set theory? What books would you advice?

Thanks a lot.

[BV]

Casey,

The book you recommend looks good. I will order a copy for myself even though I know most of the material in it.

Jose,

The book Casey recommends has a chapter on set theory. It will probably provide you with what you need to know and refer you to more technical treatments.

[José]

Oh! Thanks a lot, Casey, for the suggestion.

[Tom]

I’ve purchased both books. Thanks for the suggestion! Has anyone read logic for philosophy by ted sider? Is it any good?

[José]

Well... if I may speak about my own experience. First I studied Lemmon's "Beginning Logic" and Tomassi's "Logic.". After that I tried Bostock's "Intermediary Logic" (it didn't work...) and Sider's book. My experience with Sider's book was the following: we can see that the book is very good and we should learn from it, but it is also quite demanding (it really is not for beginners...) and at the time I was not at the required level. So I decided so study Bonevac's "Deduction" (the book is excelent). After that i'm planning to study Gammut's "Logic, Language and Meaning" and finally go back to Sider's "Logic for Philosophy".

[José]

Oh... I forgot.

Thank you very much Bill for your advice.

[BV]

You're welcome, Jose.

One thing that really angers me about Lemmon's book is his elision of the standard distinction between validity and soundness. "Logic's main concern is with the soundness and unsoundness of arguments . . ." (p. 1)

Ugh!

[Tom]

Jose, that is also my experience with Sider’s book. It’s over my head. So I think I’ll go through Bonevav’s first and see where that gets me.

And yes, thanks again BV. Your advice and opening this for comments it’s very helpful for beginners like me!

[BV]

Tom,

Happy to be of some help.

[DD]

I suggest to take a look at Peter Smith's teach yourself logic guide.
It is extensive and downloadable https://www.logicmatters.net/tyl/

[Tom]

DD, Smith’s guide looks really helpful! Thanks for the suggestion.