On Jan 22, 2013, at 9:55 AM, John F Sowa wrote: (01)
> Fabian, Alan, and Matthew,
>
> This is related to problems of omniscience in theories about knowledge
> and belief (epistemic logic). The simplest theoretical method is also
> the most unrealistic for any practical purpose: assume omniscience.
>
> FN
>> I don't see the need to explicitly talk about all inferences from
>> the axioms as long as we are concerned with ontology languages that
>> are based on truth-preserving deductive inference systems like
>> Common Logic or OWL. If all the axioms in X are true it follows
>> that all inferences from the axioms in X are true.
>
> That is monotonic logic. It's fine for classical mathematics.
>
> But it is impossible for any application to the physical world
> to use classical monotonic logic for anything beyond a very narrow
> special-purpose task.
>
> Physicists use mathematics very heavily as a *tool*, but they are
> very careful to note that their starting assumptions (AKA axioms)
> are fallible. They realize that local consistency and approximate
> accuracy are the most that they can ever hope for.
>
> Practicing physicists, even most theoretical physicists, have
> a very clear and simple slogan:
>
> Physicists don't do axioms.
>
> Some physicists have indeed proposed axioms for quantum mechanics
> and other subjects. But practicing physicists consider them
> irrelevant *toys*.
>
> When you get to medicine, business, engineering, etc., *everything*
> is fallible -- i.e., nonmonotonic and emphatically incomplete.
> (02)
Boy, oh, boy, is my quote being taken out of context ... (03)
I used the term "axiom" above in the way logicians use it. Namely, as the set
of assumptions that are taken to be true for the purpose of some inference. How
you could possibly read that as an endorsement of rationalism is beyond me. So
let me be explicit:
- I don't deny the fallibility of empirical knowledge
- I don't believe that science is a matter of establishing first axioms and
deriving all truths from them.
- I don't believe that the soul is a nonmaterial entity located in the pineal
gland. (04)
I hope that clarifies things. (05)
Fabian (06)
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