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Logic & Scientific Philosophy

A Slew of Syllogisms

Since a simple syllogism seems a little bit too easy, I have decided to do a multi layered one, because like cakes, the more layers the better. Also, if you’re not a ‘math person’ you may want to skip this post, it may be confusing. Note, xor denotes one thing, or the other but not both.

(Premise 1.1) All mattress  testers like their job. (A is B)
(Premise 1.2) Everybody who likes their job shows up for work on time. (B is C)
(Conclusion 1) Mattress testers show up to work on time. (A is C)

(Premise 2.1) All male members of the Smith family are either mattress testers or ice cream tasters. (if D and E, A xor F)
(Premise 2.2.1) John Smith is male. (D)
(Premise 2.2.2) John Smith is a member of the Smith family (E)
(Conclusion 2.2, Premise 2.2) John Smith is a male member of the Smith family (D and E)
(Premise People who have no tongues can’t taste (G = H)
(Premise John Smith has no tongue (D and E = G)
(Conclusion 2.3.1, Premise 2.3.1) John Smith can not taste (D and E = H)
(Premise 2.3.2) People who can’t taste can’t be ice cream testers (H ≠ F)
(Conclusion 2.3, Premise 2.3) John Smith is not an ice cream tester (D and E ≠F)
(Conclusion 2) John smith is a mattress tester (D and E = A)

Conclusion: John smith shows up to work on time (D and E = C)

Now there are obvious problems with the truths of the premises (simply because they’re fictional), but the arguments themselves are valid, so far as I can tell. If you can find flaws in my logic, please point it out! I’d appreciate it. Now I shall go and brace myself for a Downes attack…



4 thoughts on “A Slew of Syllogisms

  1. The argument is valid. The formalisms are a bit loose. Eg. Premise 1.1 should be represented ‘All A are B’.

    Where you run into difficulties is in mixing quantification and propositional calculus. That’s why it’s a problem that your formalisms are loose. This is especially apparent in premise 2.1. Do you mean:

    For all x, if x is a male and a member of the smith family, then x is a mattress tester if and only if x is not an ice cream taster


    If, for all x, x is a male and a member of the smith family, then, for all x, x is a mattress tester if and only if x is not an ice cream taster

    Clearly you mean the first formulation. But your formalist does not distinguish between the first and the second. So your formalism is insufficient to represent what you mean.

    (Note: P xor Q is the same as P iff ~Q, which represented fully is (If P then ~Q) and (If ~P then Q) )

    This vagueness becomes even more acute when in Premise you introduce the identity operator ‘=’. It is being used incorrectly. When you say A = B you are saying they are identical, that is, every statement that is true of A is also true of B. But clearly you do not mean to say members of the Smith family are exactly the same in all respects as people who show up for work on time.

    Obviously you’re using ‘=’ as a shortcut. But the cost of the shortcut is vagueness. And vaguess is the enemy of logic, just as it is the enemy of computer science.

    I like where you’re going, though. You are anticipating an interplay of quantification and propositional calculus, which is known as predicate calculus. If you like math, you’ll love predicate calculus.

    p.s. be careful with the use of words like ‘can’ – the semantic of “x can be P” is very different from “x is P” and therefore so is the logic.

    Posted by Stephen Downes | October 3, 2012, 7:01 pm
    • Well I think I understood at least half of what you just said, I’ll consider that a good start for now (and if I have the time, maybe I’ll try to fix up this post and tighten up the formalisms). I suppose I should have done better than the vagueness though, I used to write simple computer programs!

      I really appreciate the tips though!

      Posted by nichoman321 | October 3, 2012, 10:54 pm
  2. Nick,

    I really really really really really like the fact that you’ve taken this to the next level. It makes things more interesting, allows you to display multiple forms of syllogisms all at once. Reading this was difficult at first, but one of those things that is really cool to get your head around. Congrats!

    -Jonathan Toews

    Posted by JonathanToews | October 4, 2012, 4:28 am


  1. Pingback: Syllogisms, Evil Clowns and Epistemology – Nicholas « Philosophy 12 - November 8, 2012

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