On 10/28/2015 3:57 AM, rrovetto@xxxxxxxxxxx wrote:
> You wrote: (c) (p implies q) cannot be observed, as Hume discussed
> at length... some logicians would explicitly say implication has
> nothing to do with causation, but rather is a relation between
> statements, propositions, or arguments and is related to validity, etc.
> They would say that material implication, for example, is not the
> causation relation. (01)
I admit that I should have added a few more words of clarification: (02)
1. Hume was emphasizing issues of causation, which is an important
use, but only one of many uses for if-then statements. (03)
2. Material implication, as it is used in first-order logic, does
not depend on causation. More generally, FOL is a purely
mathematical theory that relates highly stylized sentences
to formal, set-theoretical models. No observation of anything
(other than diagrams of those models) is required to justify FOL. (04)
3. But I would add that most (perhaps all) applications of if-then
statements to observable phenomena involve some assumption about
a law-like connection between the antecedent and consequent. (05)
4. Those law-like connections cannot be observed in the phenomena.
They follow from some previous assumptions about nature (i.e.,
physical laws) or about human behavior (i.e., deontic laws). (06)
5. In support of point #4, note that explanations of the use
of if-then often involve the word 'because', which suggests
the similarities between law-like interpretations of social
phenomena and physical phenomena. (07)
6. The law-like nature of if-then sentences in ordinary language
are related to modal words like 'must' and 'should', which are
also used in explanations of if-then sentences. In modal logics,
those words are represented by operators that express necessity
or obligation -- both of which depend on laws of some kind. (08)
For an analysis of the relationships between laws and modality,
see http://www.jfsowa.com/pubs/worlds.pdf (09)
John (010)
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