Null Quartet

          Null Quartet

 

          I have a perverse fascination for invalid reasoning. I like to identify it, analyze it, play with it, for I find it amusing. Absurdity attracts me, the same way mice attract cats, fires attract firemen, and bacteria attract leucocytes.  Now I’m on the trail of yet another form of invalid thought, and I have PETA and Prof. Singer to thank for it.

          I could go on and on about PETA’s hypocrisy, smugness and fanaticism, but what got me going was how they justify their stand. On the one hand their theorists say that ‘a boy is a cat is a mouse is a chimp is a whale’; and that because of that inner unity, humans have the moral obligation not to eat other animals. I see a tension in that logic, for cats and chimps - if not mice and whales - do not have scruples against meat-eating. Are humans morally superior to other animals or not? And may humans eat other animals or not? I thought over both questions, and found to my surprise that you can link them any way you wish! The result is what I am now tentatively calling a “Square of Irrelevancy”, or a “Null Quartet”, which proves the “orthogonality of the issues”.

          For consider these four arguments:

SE. Humans are superior to other animals, so we may eat them.
SN. Humans are superior to other animals, so we may not eat them.
NE. Humans are not superior to other animals, so we may eat them.
NN. Humans are not superior to other animals, so we may not eat them.

          I submit that all four arguments have equal rhetorical force; but they are as a whole incompatible; and this, I submit, demonstrates that the two issues involved are mutually irrelevant.

          “Humans are superior to other animals, so we may eat them.” This is the argument from privilege; the higher has power over the lower. This ancient logic goes straight back to the state of nature.

          “Humans are superior to other animals, so we may not eat them.” This is the moralistic argument; we superior humans must live to a higher standard than beasts.

          “Humans are not superior to other animals, so we may eat them.” This is the naturalistic argument; animals may eat animals, so we, their equals, may too.

          “Humans are not superior to other animals, so we may not eat them.” This is the argument from empathy; to consume our equals is cannibalism.

          Obviously these four arguments can’t all be true. Actually, no two of them can both be true! This doesn’t stop people from combining these arguments. For instance PETA uses both SN and NN; we are equal to animals, and therefore we may not eat them, even though they eat each other, because we are superior. No doubt a pro-meat-eating group could cite SE and NE: we are superior to animals, and therefore we may eat them, for they eat each other, and we are their equals.

          So PETA indulges in a logical switcheroo; they derive their predetermined conclusion from shifting grounds. This is like calculating the derivative of a function. First we say h doesn’t equals zero, so we can cancel it in Newton’s Ratio; then, having cancelled, we set h equal to zero in our simplified Newton’s Ratio, and thus find the derivative! (Berkeley objected to this, so Weierstrauss invented the epsilon-delta definition of the limit, to torment all future calculus students with.) It also reminds me of the shifting rationales preceding the Iraq War.

          So I was wondering; what other Squares of Irrelevancy can you find? Their form is, in general, this quartet:
          AB: A, therefore B
          nAB: not A, therefore B
          AnB: A, therefore not B
          nAnB: not A, therefore not B

          - all with plausible rhetorical support. Partisans for B will cite both AB and nAB ; partisans for not-B will favor both AnB and nAnB; but the real effect of a Null Quartet, once comprehended in full, is to reveal the mutual irrelevancy of A and B; their ‘orthogonality’.