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I have just started studying logic and wish to find some example arguments by famous philosophers broken down very plainly into their premises and conclusions, along with the logical notation to the argument.

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  • See Gödel's Ontological Argument and Gödel's ontological proof: with logical notation, but not "plain".
    – Mauro ALLEGRANZA
    Commented Apr 5, 2016 at 13:28
  • I'm coincidentally looking for something similar. I've found there's a lot of trickiness to this process "translating a famous philosophical argument to formal logic", c.f., chapter 4 of Catarina Dutilh Novaes' Formalizing Medieval Logical Theories.
    – Alex Nelson
    Commented Apr 5, 2016 at 16:11
  • Oh, and a good preprint on formal methods in the history of philosophy.
    – Alex Nelson
    Commented Apr 5, 2016 at 16:21
  • Bryan Hall, et al., have written The Arguments of Kant's Critique of Pure Reason which attempts to formalize a good portion of the book, but only at the level of propositional logic as opposed to a full-blown first-order logic translation.
    – Alex Nelson
    Commented Apr 13, 2016 at 21:56

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1) The famous logician Kurt Goedel left behind a formalized "proof" for the ontological argument of Anselm of Canterbury.

Anselm gave a "proof" that the term "a being than which none greater can be conceived" must refer to some existing being, i.e., that there must exist a being than which none greater can be conceived.

See the following lecture by the logician Brendel for a formalization of Goedels "proof"

http://wwwmath.uni-muenster.de/logik/Veranstaltungen/cl2010/slides/brendel.pdf

It closes with a critical assessment of what Goedel's formalization proves and what it does not prove.

2) You may also read Gettier's presentation of the "Gettier example" in

http://www.ditext.com/gettier/gettier.html

The Gettier example is considered a counter-example against a widely hold definition of knowlegde as justified true belief. Gettier's formalization is not so extensive like Goedel's argument.

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Some parts of Wittgenstein's "Tractatus Logical-Philosophicus" are written in purely logical notation and Wittgenstein's view at the time (he moved away from it later) was called logical atomism: he wanted to break down all meaningful statements into basic atomic logical sentences. Bertrand Russell was also a proponent of this view. See Russell's famous "the present present king of France" example.

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    W's Tractatus is "about" logic, but I think that it has no examples of "famous Philosophical Argument reduced to Logical Notation".
    – Mauro ALLEGRANZA
    Commented Apr 5, 2016 at 14:33
  • @MauroALLEGRANZA studying Wittgenstein's and Russell's logical atomism would help the op learn how to achieve this for philosophical statements in general.
    – Alexander S King
    Commented Apr 5, 2016 at 15:38
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John Hospers's Introduction to Philosophical Analysis was written as an introductory textbook, with a strong emphasis on providing logical analyses of important arguments. link

There's also a book called Just the Arguments which I think provides nice little argument analyses from the great philosophers. link

I haven't used either text myself, so I can't vouch for the quality, but they seem to fit the description you're looking for.

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