Tuesday, June 29, 2010

Loads, shoots, and spoils Thanksgiving

It's peculiar that so many writers in the 18th and 19th centuries (but before that and later on too, of course) spent their time discoursing about "logic" in book after book - Hegel, Mill et alii. Each of them was pushing his own "logic", as if there were more than one to choose from. They kicked around notions such as induction, deduction, abduction (Pierce) - and, of all things, causation - and arrived at various conclusions and claims. But I find it all completely useless. Of course I am aware that my position is post-Hegel, post-Mill et alii, that is, parasitic on what has gone before. No one can accuse me of being ungrateful, although an action for frivolousness might lie.

I feel that there is only one kind of logic for everyday and scientific purposes, and not much worth saying about that. What used to be known as books on logic might be more accurately described as pedantic exercises in how to be convincing. Pedantry aside, that is what used to be called the arts of rhetoric. But these writers seem to be intent on persuasion by new-fangled means, without the traditional training and practice. To me, their writings carry the conviction of Butt-head playing air guitar.

I find that a little Barbara pour ouvrir l'estomac, an amuse-gueule of first-order logic to be followed by Cantor, Gödel, Cohen or Robinson à la meunière, is more easily appropriated by the vegetative system. Mathematical ideas can be conveyed without fancy sauces, and with a minimum of verbiage and ballast. Having acquired familiarity over time with certain mathematical styles, you can peruse recipes in those traditions with profit, even though not yourself a chef.

As an adolescent I had the idea that mathematical logic must have put paid to judicious waffling, but I now know better. I just happened across something that gave me serious indigestion: a description of the so-called Yale shooting problem. Here is how the WiPe article begins:
The Yale shooting problem is a conundrum or scenario in formal situational logic on which early logical solutions to the frame problem fail. The name of this problem derives from its inventors, Steve Hanks and Drew McDermott, working at Yale University when they proposed it. In this scenario, Fred (later identified as a turkey) is initially alive and a gun is initially unloaded. Loading the gun, waiting for a moment, and then shooting the gun at Fred is expected to kill Fred. However, if inertia is formalized in logic by minimizing the changes in this situation, then it cannot be uniquely proved that Fred is dead after loading, waiting, and shooting. In one solution, Fred indeed dies; in another (also logically correct) solution, the gun becomes mysteriously unloaded and Fred survives.

Technically, this scenario is described by two fluents (a fluent is a condition that can change truth value over time): alive and loaded. ...
For Pete's sake ! Where is the conundrum ? It is sufficient to note that the word "shoot" is being used ambiguously here. Apart from that, "a condition that can change truth value over time" used to be called a variable (or predicate, here), and I see no reason to call it anything else. "A fluent" is a preciosity worthy of Molière's médecins.

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