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The pragmatic maxim and dynamic logic (technical)

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C.S. Peirce, a master logician, found some difficulty with how the old formula "clear and distinct idea" was defined. He didn't find it very clear. He had a different sense of the purpose of ideas than Leibniz did who wasn't particularly empirical in his thinking. But Peirce had a foot in both logic and science, and so he proposed what is now called the pragmatic maxim:

"Consider what effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object."

Our ideas aren't clear unless we can explicate what I would call the practical difference that the object of the idea would. Note particularly the term conceivably. Lately I've been thinking about this in terms of dynamic logic, a species of modal logic that I've stumbled on recently.

I've been thinking about methods lately, in terms of techniques used in experiments. I try to stay simple, and say that measuring the length of something is a method, then you can measure the various dimensions of an object, and then determine the volume of an object by means of a composite method that combines more basic methods, such as measuring length or volume displacement.

Suppose that a method is operational, which means you have to actually make concrete changes to the subject. This must be modelled in logic as moving by changing the actual world, which means changing from what is now the actual world to one of the possible worlds that are reachable from this world. So the actual world is indexical, there is nothing special about the actual, other than we identify one of the possible worlds as the actual one.

Let's consider this proposition: Striking the match will possibly produce fire. To show the logical form, you put the method inside angular brackets: <strike a match> produce fire. To show that striking a match will necessarily or always produce fire, you would use square brackets: [strike a match] produce fire. But it seems that the former proposition is true because, for example, the match might be wet, and so won't always produce fire. We could correct this by sequencing methods as in [ensure the match is dry; strike the match] produce fire. This is equivalent to [ensure the match is dry][strike the match] produce fire.

The difference between <strike a match> produce fire and [strike a match] produce fire is that the former means that sometimes striking a match will produce fire, and sometimes it won't. This means that it isn't really a good method for producing fire, and most methods that have nothing to do with the outcome will have merely possibility brackets. Some methods might actually interfere with the result making it impossible to produce fire, for instance ~<submerging the match in water> produce water which is the same as [submerging the match in water] ~produce water using normal modal laws.

To me this gets very close to not only articulating Peirce's pragmatic maxim in formal terms, but gets us closer to being able to unravel the logic of scientific method. Dynamic logic has already been axiomatized, but through online sources alone, it seems to be applied mostly to verifying computer programs. I'm going to continue to read more and experiment more to determine whether this logic can or should be applied to scientific logic.

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