horses for courses — bongo fury
What is a good horse for a course (logic for a discourse)? Not, one might naively assume, one whose principles allow inference to exactly all the sentences that are said in the discourse? Or which agree with all the inferential steps or patterns that are claimed in the discourse? Although that does rather sound like G Russell's view.
I'm not clear whether the view tends to arise from the narrower example of proving a logic sound or complete for a perfectly determined 'discourse', as
here:
... where the 'discourse' on the left contains no controversies. Everyone is agreed (no diagrams are denying), in this example, that if everyone loves themselves then everyone loves someone. That would be a principle that needs including in a suitable logic for the discourse. The maths, complicated enough even for such an ideal discourse, is about determining which other principles (LEM, LNC etc) are also required: either for their own sake, or in order to save others from apparent threats like 'explosion' etc.
In informal discourse, by contrast, we are generally faced with controversies, and the usual, classical logic is clearly valued for its ability to help us take sides.
Which side to take, which sentences to save, it never tells. But it shows up some combinations as being either mutually compatible or not so. The compatibility is of course relative to the chosen logic, the chosen set of laws. We choose a logic which we hope will, by showing up compatibilities and incompatibilities (relative to it), have a positive influence on our choices to save and reject.
Thus Popper and Lakatos are rightly fixated on counter-examples, which are signs of incompatibility. At least one of these three will have to be rejected or revised:
- All polyhedra are Eulerian
- x is a polyhedron
- x isn't Eulerian
Lakatos investigates all the choices, to see better what's at stake. But he is completely satisfied with ordinary logic as a test of compatibility. Nowhere does a paradox, superficial or deep, tempt him to bring a more exotic (stronger or weaker) logic on board. Paradoxes are to be resolved by better understanding the vagaries and ambiguities of, and subsequent clarifications and alterations to the reference of, (specific occurrences of) terms such as x, polyhedron and Eulerian.
I suggest it's worth noticing how people so often feel the opposite duty: e.g.
https://thephilosophyforum.com/discussion/comment/550407
https://thephilosophyforum.com/discussion/comment/566367
Which (hey, we must need a more fancy logic) is an attitude that maybe G Russell would identify as pluralist (and my protesting in those places "please not" as correspondingly monist), I'm not sure. I think I protest only because people are seeing logic as a means of revelation, instead of a (standard of) discipline. Reforming premises to meet present standards of compatibility should be tried before reforming the standards to allow all the premises.
To be a law of logic, a principle must hold in complete generality — G Russell
I would rather say that it (the principle, the discipline) must be feasible and/or appropriate for
imposing in complete generality. Which of course it can't be. Witness art and poetry. Horses for courses.
Still, going with G Russell's flow, what's the analogy with ordinary counterexamples? Is it, e.g.,
- All natural discourse makes conjunction introduction intuitive
- SOLO is convincing as natural discourse
- SOLO makes conjunction introduction unintuitive
?
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