In one of my logic lessons at Hillsdale I would cover two ways of explaining a word’s meaning. There is the intension which lists the properties, and the extension which lists members of the class. We can indicate the meaning of ‘journalist,’ for example, by describing the attributes: “someone who writes for news media, someone who covers news stories for TV and radio, someone who writes for electronic media,” and so on. Alternatively we might point to Charles Moore, Adam Boulton, Polly Toynbee, etc, listing people covered by the term. I would point out that the more properties we list, the fewer there will usually be in the class. “Animals” includes many examples, but “human animals” has fewer, and “living human animals” fewer still. Each time we add a category to the intension, the extension is usually reduced. Intension is inversely proportional to extension ( i is proportional to 1/e). It follows that if e is infinite, then i will be zero, and vice versa.
The significance of this is that a class which includes everything has no properties. The young Popper understood the difference between the theories then popular in Vienna. Those of Freud and Marx could accommodate every conceivable outcome, whereas that of Einstein would have been falsified had the observations of two stars during an eclipse been different. A theory which can be fitted in with all observations has no information content. If we are told that the warmest winter on record is a sign of man-made global warming, that might be evidence. If we are then told that the same is true of the coldest winter on record (with the name changed for plausibility to “anthropogenic climate change”), it is less convincing. If we are told that the wettest winter on record is similar evidence, and so is the driest, we begin to suspect that any outcome will be taken to support the theory, in which case it has zero information content. We need to know what outcomes would count against the theory for it to be counted as a scientific theory rather than an act of faith.
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