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by Rick Lewis
Captain Kirk strode briskly onto the bridge of the USS Enterprise. “Mister Spock! Earlier, when I said that we’d make it through this asteroid field safely because lightening never strikes twice in the same place, and you said I was being illogical, what exactly did you mean by it?” Spock looked up from his antique copy of the Oxford Dictionary of Philosophy and raising one quizzical eyebrow, replied, “Logic, Captain, is the general science of inference. Deductive logic, in which a conclusion follows from a set of premises, is distinguished from inductive logic, which studies the way in which premises may support a conclusion without entailing it.... Aristotle is generally regarded as the first great Earth logician, and Aristotelian logic dominated the subject on your planet until the 19th century.” Scotty winced as another huge asteroid loomed up on the monitor “What he means, Captain, is that it’s just the science of thinking straight. The structure of a sound argument is the same in all sectors of space and applies to Vulcans and humans alike. Ye canny change the laws of logic, Captain.”
Logical fallacies crop up frequently and in all sorts of situations, and we seem to have an instinctive ability to detect them when they occur. For example, in her article Julia Nefsky shows that much humour relies on logic – or on failures of logic. Humour is all about timing, as any fule kno, so when we laugh at a joke which relies on a logical fallacy, it shows that we are recognizing in a split second that something is wrong – even if it might take us longer to work out exactly the nature of the error.
Another source of joy for logical minds are paradoxes. If the universe is consistent, true paradoxes should not exist. But solving a paradox – showing why there isn’t really an inconsistency – can be fiendishly difficult. The most famous of all paradoxes is the Liar Paradox, first expressed by Epimenides around 2,500 years ago. Neil Lefebvre and Melissa Schelein offer their own solution in ‘The Liar Lied’.
Many philosophers have blamed mistakes and misconceptions on the ambiguities and confusions of everyday language. If only, said some thinkers, philosophical arguments could have the clarity and certainty of mathematics. And so they developed symbolic logic with that aim in mind. This is an impressive and interesting intellectual achievement, but nonetheless many people tend to recoil in terror when they see a page of arguments in symbolic logical notation, even when the arguments being expressed are themselves quite simple. I’m among them, which is one reason you’ll almost never come across such notation in this magazine! However, Stephen Szanto tells us not to be scared, and gives a brief and friendly introduction to two of the most important logical symbols.
As Mr Spock (and the Oxford Dictionary of Philosophy) have pointed out, the first and greatest logician was Aristotle, and until a century or so ago pretty much all of logic could be traced back to his ideas. But from then on, logicians began to develop new forms of logic which weren’t based on his ideas. Mike Alder promises enticingly that if you master these new methods of reasoning, you’ll be much cleverer than all your friends; will become a superbeing and will easily defeat any evil galactic overlords you might happen to encounter. (Please note that this claim doesn’t constitute a guarantee by the publishers of Philosophy Now...)
Above all, the aim of studying the structure of arguments is to think more clearly. This is the aim of critical thinking. The idea is to look at the argument for some position, see if you can identify its precise logical form, and then examine that form to see where it might have weaknesses. Robert Davies takes the debate about the legalisation of cannabis as an opportunity to examine two common types of argument in this way.
Just as philosophy in a sense underlies all other branches of human enquiry, so logic is the most fundamental branch of philosophy. Philosophy is based on reasoning, and logic is the study of what makes a sound argument, and also of the kind of mistakes we can make in reasoning. So study logic and you will become a better philosopher and a clearer thinker generally. The aspiration of logicians is to find rules of thinking that apply everywhere, under all circumstances, even on the USS Enterprise. Whether they have done so, or can do so, is itself an interesting philosophical question.