Wanted: Philosophy Examples for Sentence Logic

I’d appreciate any suggestions of cool philosophical arguments or puzzles that exemplify (or lend themselves to the exemplification of) key concepts of the sentential calculus.

I find it’s much easier to come up with this sort of thing for the predicate calculus. For example, discussions of Anselm’s ontological argument for the existence of God or Descartes’s argument for substance dualism (or the Heideggarian suggestion that nothing noths) are fun to discuss with students who can handle symbolizations with quantifiers and predicates. But I’m sniffing around for fun things of philosophical applicability to do with students who are just learning to toss around the dots, vels, tildes, and horseshoes.

Thanks in advance!

7 Responses to “Wanted: Philosophy Examples for Sentence Logic”

  1. I’m not very fluent in mathematics, but I’ve been studying a lot of Alfred North Whitehead and his process philosophy. Do you think his project of basing thought on ‘bare entities’ (like in his Concept of Nature) and his project of basing an ontology that equates actual entities with actual occasions might be a step towards a systematic propositional calculus? Maybe this isn’t the right step, but I say this because I’m reminded of Quine’s article on Whitehead’s first work exploring a universally commutative algebra. There’s a continuity of abstract speculation and concrete mathematization in his works, and many of the arguments he makes in Process and Reality point towards a plurality of logics.

  2. Pete Mandik says:

    Hi Taylor,

    I have to admit: your question and suggestions are way over my head. This is due in part, probably, to my not having read any Whitehead.

  3. I realized after I had replied that my comment had nothing to do (explicitly) with your question, insofar as you were asking for an argument and not a philosopher and because you were talking about specific systems of logic. But I think your comment picqued my interest because Whitehead is so adamant about attacking the traditional Aristotelian logic that insists on subject-predicate organizations. He reinterprets Aristotle’s substance-as-ultimate-substratum in terms of events, arguing that events are the true substance of nature. Maybe if I had a better understanding of what you mean by sentential calculus then I could explain more why Whitehead might be enjoyable for your project. I’d love to chat with you about this more sometime.

  4. Pete Mandik says:

    Interesting issues, Taylor. I would think that if someone didn’t like subject-predicate structures, then they’d be hard-pressed to explain the validity of inferences like “All men are mortal. Socrates is man. Therefore, Socrates is a mortal.” However, the sentential calculus, aka propositional calculus, doesn’t deal with subject-predicate structure and instead treats the most basic truth-bearing items as unstructured wholes.

    A nice concise article on the propositional calculus may be found here:


  5. The problem of evil is good in this way. It can be worked out in various ways using either sentential or predicate logic (and thus could be returned to later). The key is to get to G -> not-E and then do modus tollens.

  6. with intermediate steps refering to benevolence, omnipotence, and omniscience, of course

  7. Pete Mandik says:

    Thanks, Eric.

    I totally agree that the PoE lends itself quite nicely to applications of sentential logic. Just last week, in fact, my students proved the validity of this formulation:

    If God exists then an all-powerful, all-loving being exists.
    If an all-powerful, all-loving being exists, then suffering does not exist.
    Suffering does exist.
    Therefore, God does not exist.

    Ideally, I’ll accumulate several examples from the main areas of philosophy accessible at an intro level.