By Esa Itkonen
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On the other hand – as might be expected – the analogy between modal logic and deontic logic is not perfect. The tautology of modal logic p → Mp (known as ‘ab esse ad posse’) has no deontic analogue, like p → Pp; and the iteration of operators (exemplified by LLp), which is permitted in most systems of modal logic, produces ill-formed deontic formulae (like *OOp). Furthermore, Type 3 is illustrated by the invention of many-valued logic (cf. Zinov’ev 1963: Ch. 1). Let us represent ‘true’ and ‘false’ by 1 and 0, respectively.
He listed 12 observable properties which electricity and the lightning have in common (including ‘colour of light’, ‘crooked direction’, ‘swift motion’, ‘being conducted by metals’, ‘crack or noise in exploding’). In addition, electricity is attracted by points. Therefore he inferred that the lightning too is attracted by points (which means that electricity and lightning are one and the same phenomenon). 24. It is obvious at once that this type of ‘analogical inference’ is an instance of induction-1 (cf.
E. g. light). In the two other cases, by contrast, grasping the common structure makes it possible to produce an infinite number of new analogous items. This is the difference between discovering analogy in inanimate nature and performing analogical actions (cf. 8). 12 Generalizing about A and B (not from A to B, or vice versa) A mathematical analogue to discovering analogy in inanimate nature is provided by Hofstadter (1995: 195–198): What in ‘12344321’ corresponds to ‘4’ in ‘1234554321’? The answer is obviously ‘3’, and it can be presented in the form of a binary proportion, as in example (5): (5) 1234554321 12344321 = 4 X X=3 What the cases discussed above have in common, is a movement from A to B, mediated by an abstract structure X.