return to old ones that have already been extensively argued for and discussed.
It has been extensively discussed, but a lot of people still think “Bayes is the One Epistemology to Rule them All” is the correct conclusion.
If there is no unified theory of intelligence, we are led towards the view that recursive self-improvement is not possible, since an increase in one type of intelligence does not necessarily lead to an improvement in a different type of intelligence.
Shouldn’t you want to believe what is true, not what leads to some arbitrary end-point?
With a diversification in different notions of correct reasoning within different domains, it heavily limits what can be done to reach agreement on different topics. In the end we are often forced to agree to disagree, which while preserving social cohesion in different contexts, can be quite unsatisfying from a philosophical standpoint.
Same problem. If it is actually the case that there is more than one method of reasoning, why pretend otherwise?
Related to the previous corollary, it may lead to beliefs that are sacred, untouchable, or based on intuition, feeling, or difficult to articulate concepts.
So can Bayes. Just set your priors so high that you will never accumulate significant contradictory evidence durign your lifetime.
Often times, this guiding principle is based on intuition, which is a remarkably hard thing to pin down and describe well
Everything is based on intuition, ultimately. (eg your “Qualitative correspondence with common sense.”).
Bayesian methods are often computationally intractable.
That’s minor????
I would add that there are plenty of ways to generate hypotheses by other methods
There is a very simple argument: if you need to supplement Bayes with a method of hypothesis generation then you are no longer using Bayes alone and you are therefore not even using Strong Bayes (NB:: strong) yourself.
E.T. Jaynes never considered to this be a flaw in Bayesian probability, per se. Rather, he considered hypothesis generation, as well as assigning priors, to be outside the scope of “plausible inference” which is what he considered to be the domain of Bayesian probability. He himself argued for using the principle of maximum entropy for creating a prior distribution, and there are also more modern techniques such as Empirical Bayes.
That just means Jaynes did not believe in Bayes is the One Epistemology to Rule them All. So why do you?
Everything is based on intuition, ultimately. (eg your “Qualitative correspondence with common sense.”).
That means, in the context of Cox’s theorem, a very specific set of primitive intuitions about plausibilities, not that everything is reduced to how one feels about something.
Yes and yes and no. Yes, because everything, not just Coxs theorem, is based on some foundational assumption, however much you try to eliminate unjustified propositions from your epistemology. Yes because having an epistemology with a few bedrock assumptions is not the same as deciding every damn thing with gut feelings. No, because the plausibility, to you, of a plausible assumption that you cannot otherwise justify is not that different to a feeling.
No, because the plausibility, to you, of a plausible assumption that you cannot otherwise justify is not that different to a feeling.
Well, that is true for any kind of axiom. In any case, it’s a finite set of simple intuitions that define the content of “common sense” for Cox’s theorem, so that if two people disagree, they can point exactly to the formulas they disagree on.
I’ve rarely seen disagreement on basic axioms. p → p seems to be rather uncontroversial, although it’s based on ‘intuition’. On the other hand, that’s the purpose of deduction: reduce the need of intuition only to the smallest and least controversial set of assertions. This does not imply, as your original formulation seems to, that then intuition can be used for everything.
his does not imply, as your original formulation seems to, that then intuition can be used for everything.
I never said anything of the kind. My point was that intuition is unavoidably involved in everything.
I’ve rarely seen disagreement on basic axioms.
Then check out the controversy over Euclid’s fifth postulate, mathematical intuitionism, the Axiom of Choice, whether existence is a predicate, etc, etc.
. p → p seems to be rather uncontroversial, although it’s based on ‘intuition’.
Some would say that it’s based on truth tables,and defies intuition!
See the logical versus material implication controversy:-
I never said anything of the kind. My point was that intuition is unavoidably involved in everything.
On this I think we agree. I’ll just add that sometimes “intuitions” points to “a short mental calculation” and some other times to “a biased heuristic”. The fact that we don’t have access to which is which is the danger of accepting sentences like “intuition is the basis of everything”. I would rather prefer two different words for the two different kind of intuitions, but there aren’t.
Then check out the controversy over Euclid’s fifth postulate, mathematical intuitionism [...]
Yes, but there are also never been controversy on the first postulate… Some axioms are more basic than others. And indeed challenged axioms produce strong revolutions.
Some would say that it’s based on truth tables,and defies intuition!
This I don’t know how to interpret. Truth table are useful as long as they agree on the axioms. Or one could say that truth tables are based on intuition...
On this I think we agree. I’ll just add that sometimes “intuitions” points to “a short mental calculation” and some other times to “a biased heuristic”.
It can mean either of those, but it can also mean an assumption you can neither prove nor do without.;
Some axioms are more basic than others.
If what you want is convergence on objective truth, it is the existence of axioms that people don’t agree on that is the problem.
And indeed challenged axioms produce strong revolutions.
And pluralism. Intuitonistic and classical maths co-existing, Euclidean and non-Euclidean geometry co-exisitng.
. Truth table are useful as long as they agree on the axioms. Or one could say that truth tables are based on intuition...
Truth tables give you a set of logical functions, some of which resemble traditional logical connectives, such as “and” and “implies” to some extent. But only to some extent. The worry is that they don’t capture all the features of ordinary langauge usage.
It has been extensively discussed, but a lot of people still think “Bayes is the One Epistemology to Rule them All” is the correct conclusion.
Shouldn’t you want to believe what is true, not what leads to some arbitrary end-point?
Same problem. If it is actually the case that there is more than one method of reasoning, why pretend otherwise?
So can Bayes. Just set your priors so high that you will never accumulate significant contradictory evidence durign your lifetime.
Everything is based on intuition, ultimately. (eg your “Qualitative correspondence with common sense.”).
That’s minor????
There is a very simple argument: if you need to supplement Bayes with a method of hypothesis generation then you are no longer using Bayes alone and you are therefore not even using Strong Bayes (NB:: strong) yourself.
That just means Jaynes did not believe in Bayes is the One Epistemology to Rule them All. So why do you?
That means, in the context of Cox’s theorem, a very specific set of primitive intuitions about plausibilities, not that everything is reduced to how one feels about something.
Yes and yes and no. Yes, because everything, not just Coxs theorem, is based on some foundational assumption, however much you try to eliminate unjustified propositions from your epistemology. Yes because having an epistemology with a few bedrock assumptions is not the same as deciding every damn thing with gut feelings. No, because the plausibility, to you, of a plausible assumption that you cannot otherwise justify is not that different to a feeling.
Well, that is true for any kind of axiom. In any case, it’s a finite set of simple intuitions that define the content of “common sense” for Cox’s theorem, so that if two people disagree, they can point exactly to the formulas they disagree on.
That’s rather the point. It saves time to assume something like that from the outset.
Which may lead to agreeing to disagree rather than convergence.
I’ve rarely seen disagreement on basic axioms. p → p seems to be rather uncontroversial, although it’s based on ‘intuition’.
On the other hand, that’s the purpose of deduction: reduce the need of intuition only to the smallest and least controversial set of assertions. This does not imply, as your original formulation seems to, that then intuition can be used for everything.
I never said anything of the kind. My point was that intuition is unavoidably involved in everything.
Then check out the controversy over Euclid’s fifth postulate, mathematical intuitionism, the Axiom of Choice, whether existence is a predicate, etc, etc.
Some would say that it’s based on truth tables,and defies intuition!
See the logical versus material implication controversy:-
http://www.askphilosophers.org/question/4103
On this I think we agree. I’ll just add that sometimes “intuitions” points to “a short mental calculation” and some other times to “a biased heuristic”. The fact that we don’t have access to which is which is the danger of accepting sentences like “intuition is the basis of everything”.
I would rather prefer two different words for the two different kind of intuitions, but there aren’t.
Yes, but there are also never been controversy on the first postulate… Some axioms are more basic than others. And indeed challenged axioms produce strong revolutions.
This I don’t know how to interpret. Truth table are useful as long as they agree on the axioms. Or one could say that truth tables are based on intuition...
It can mean either of those, but it can also mean an assumption you can neither prove nor do without.;
If what you want is convergence on objective truth, it is the existence of axioms that people don’t agree on that is the problem.
And pluralism. Intuitonistic and classical maths co-existing, Euclidean and non-Euclidean geometry co-exisitng.
Truth tables give you a set of logical functions, some of which resemble traditional logical connectives, such as “and” and “implies” to some extent. But only to some extent. The worry is that they don’t capture all the features of ordinary langauge usage.