Matthew Zapf’s “Introduction to Philosophical Logic”

I heard this on a comedy programme on Radio 4 and thought I’d share it transcript with you.

This week we continue our look at basic propositions and the validity, or otherwise, of the conclusions we may be tempted to draw from them.

Previously, you may recall, we started with the proposition, “all schnauzers look like Nietzsche” and also the logical implication of adding the secondary statements, “Wolfie is a schnauzer” and “Wolfie looks like Nietzsche”.

Let’s now examine a third case where the secondary proposition is “Wolfie does not look like Nietzsche”. What can we now conclude?

Since looking like Nietzsche is an intrinsic part of what we have called, “Scnausarity”, we can categorically conclude the Wolfie is not a schnauzer, since if he was, he would look like Nietzsche, as laid down in our initial proposition.

However, with a secondary proposition “Wolfie looks like Wittgenstein” can we draw the same conclusion?

It’s tempting, but that would be fatuitous, unless we include a third proposition along the lines of “Wolfie does not look like Nietzsche” or in more philosophical language, “looking like Wolfie is a sufficient condition of not looking like Nietzsche” in which case the conclusion is sound, since by looking like Wittgenstein, we now know that Wolfie cannot also look like Nietzsche and if he doesn’t look like Nietzsche, he can’t be a schnauzer, our initial definition of Scnausarity precludes it.

Having sent this transcript to my local Doctor of Philosophy, he checked the findings and replied:

Basically using Aristotilean syllogisms that is correct.

All As are Bs

X is an A

Therefore X is a B

However, this does not allow for

X is a C

Therefore X is not an A

As the class of A may be wider than just containing B and contain C as well.

This, of course, is what I thought too but it’s good to get a second opinion.

Further to my post here, my Dr. of Phil., R. U. Ready, sent me this via email.

… remember, Aristotelian logic has now been replaced by the Propositional and Predicate calculus. Namely, if an A is a B, and a B is a C, then an A is a C.

I hope that that has cleared up any questions some of you may have concerning Dr. Ready’s use of Aristotilean syllogisms previously.

Published in: on Monday, September 6th, 2010 at 6:55 am  Comments (4)  
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4 CommentsLeave a comment

  1. I remember hearing this episode of “Continuity”, and also an earlier one in which the Schnauzer/Nietzsche discussion was first introduced. Did you happen to make a transcript of that earlier episode as well? If so, I’d be very interested to see it, or at least the part just mentioned.

  2. Sorry, I didn’t catch the previous episode. I only heard this one by accident but I’ll check around and if I find it I’ll put the transcript up.

    I have to say, I thought it was brilliant.

  3. I managed to catch a repeat of the first episode of the BBC’s comedy “Continuity”, and have made a transcription of Zapf’s first schnauzer/Nietzsche discussion:

    Announcer: In a brand new series on Radio 4 this week, Matthew Zapf begins his introduction to philosophical logic.

    Zapf: Let us take two very simple propositions. For example:

    Woman: All schnauzers look like Nietzsche.

    Zapf: … and:

    Woman: Wolfie is a schnauzer.

    Zapf: From these two propositions, we can deduce the conclusion:

    Woman: Wolfie looks like Nietzsche.

    Announcer: Yep, got that.

    Zapf: Because if all members of the set “schnauzers” look like Nietzsche, and Wolfie is a member of that set, it follows that Wolfie must look like Nietzsche. Looking like Nietzsche is intrinsic to his schnauzarity, we might say. However, if we keep our initial proposition:

    Woman: All schnauzers look like Nietzsche.

    Zapf: … but replace our second proposition with the conclusion we have just drawn:

    Woman: Wolfie looks like Nietzsche.

    Zapf: … can we now conclude anything new? (Announcer: Yes, Wolfie is a schnauzer.) No, we cannot. (Announcer: Oh.) Certainly not our second propostion, “Wolfie is a schnauzer”. (Announcer: Look, hang on.) To do so, we would need a supplementary proposition, namely:

    Woman: Everything that looks like Nietzsche is a schnauzer.

    Zapf: … which is clearly not the case. For example, Nietzsche himself looked like Nietzsche, but he wasn’t a schnauzer. (Announcer: OK.) In fact, the only element of schnauzarity Nietzsche had was looking like one, and even that relies on the possibly contentious assumption that because all schnauzers look like Nietzsche, Nietzsche in turn must look like a schnauzer. (Announcer: Right, got it.) A simple grasp of logic is an essential building block to any study of philosophy. For more, do join me, Matthew Zapf, this Thursday evening, here on Radio 4.

    Announcer: Fascinating stuff.

  4. Excellent work Paul. Thanks!

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