I am currently preparing an article for the Winter 2006 Skeptic journal. The article is about fallacies in thinking and informal logic. This topic has a pedigree ranging back to the writings of the most notable ancient greek philosophers - Aristotle and Socrates in particular. However I don't wish to have to read masses of arcane and esoteric material, so in my article, I propose to bag both Aristotle and Socrates, disparage their writings in the most general terms, and thus avoid having to deal with them. Naturally, I searched for sources which might support my dismissive and shallow account of their work. The best source I found was the Department of Philosophy at Wooloomooloo University's Drinking song. And I quote: (source - Monty Python)
"Aristotle, aristotle was a bugger for the bottle... (and further, Socrates is said to be) a lovely little thinker but a bugger when he's pissed".
My source clearly establishes that both philosophers were crapulous dipsomaniacs; and therefore: (a) their philopsophy was unreliable; and therefore: (b) I am not obliged to know much about their work; and therefore: (c) I will not dignify their writings by referring to them (except for bagging them) in my article.
To avoid criticism down the track, I will also use ironic, self-deprecating humour in the article, and claim that one of my purposes in writing the article was to give clear examples of a range of fallacies in my own writing (e.g. False Attribution and Observational Selection).
This multilayered nested recursion is giving me a headache... or is it?
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2 comments:
Nested recursions used to give me a headache too. Until I read an idiot-simple paper which sorted it all out for me (abstract follows).
"Functions specified by nested recursions are difficult to define and reason about. We present several ameliorative techniques that use deduction in a classical higher-order logic. First, we discuss how an apparent circular dependency between the proof of nested termination conditions and the definition of the specified function can be avoided. Second, we propose a method that allows the specified function to be defined in the absence of a termination relation. Finally, we show how our techniques extend to nested program schemes, where a termination relation cannot be found until schematic parameters have been filled in. In each of these techniques, suitable induction theorems are automatically derived."
Cletus, I came across the expression "nested recursion" when I used BASIC computer language for programming back in the olden days (Osborn 1). It meant cycling through a loop until a condition was met, then dropping down to another loop until another condition was met etc etc. I find it useful shorthand for loopy chains of reasoning which dither about and involve lots of internal, layered exchanges. I suppose I could use "running on the spot while fiddling about" as a more vivid way of expressing much the same thing.
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