By Esa Itkonen
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Additional resources for Analogy as Structure and Process: Approaches in Linguistics, Cognitive Psychology and Philosophy of Science (Human Cognitive Processing, Volume 14)
10). With this restriction, analogical thinking proceeds as follows. First, we observe two apparently unconnected phenomena (or ‘systems’) O1 and O2. Then we realize that if a certain theory ‘T’ is true, then O1 and O2, instead of being unconnected, are exemplifications of a common structure, which means that ‘O1∼O2’ is true. From this we tentatively infer that ‘T’ is true. 21. Next (or perhaps, simultaneously), the second premise and the conclusion are taken to constitute the premises of another inference which yields ‘O1∼O2’ by Modus Ponens.
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.
As noted above, this generalization was achieved by replacing the two discrete numbers 1 and 0 by analogous, but more general designations ‘higher number’ and ‘lower number’. At the same time, the discrete opposition (‘either – or’) was replaced by a continuum (‘more or less’). It should also be noticed that there is a difference between inventing the printing press and inventing either deontic or many-valued logic, a difference which is due to the fact that in the two cases the invented entities are ontologically quite dissimilar.
Analogy as Structure and Process: Approaches in Linguistics, Cognitive Psychology and Philosophy of Science (Human Cognitive Processing, Volume 14) by Esa Itkonen