probability question (pertaining to SM+P)
 

We are discussing Hume and Kant in class. Basically Hume says just because an event has happened one billion times out of one billion (ex. the sun rising) it will not necessarily happen again. Kant says it will.

I was wondering how one would express the probability of a unique event occuring if it has happened one billion times out of one billion. assume you have no prior knowledge of the nature of the event (it can't be a coin flip that lands on heads one billion times, then ask the probability of it landing tails the one billion 1st trial).

I would imagine there is no philosophically 100% correct answer to this but is there something that the scientific community uses as standard?

I posted this in probability and didn't get much of an answer.

thanks.

Re: probability question (pertaining to SM+P)
 

Hiya Pokerjoker,

There are quite a few ambiguities with your question, but the easy answer would be:

if there were no one event(sun rising) more likely that the other (sun not rising), then the chance of it rising tommorow is 1 in 2. However the chance of having a sequence of a billion rises followed by another is 1 in ((1 billion + 1)!). My suspicion here is that one event is more likely than the other. [img]/images/graemlins/smile.gif[/img] That is, our assumption that it is equally as likely to rise or not, is not correct.

[img]/images/graemlins/smile.gif[/img]

Re: probability question (pertaining to SM+P)
 

[ QUOTE ]
We are discussing Hume and Kant in class. Basically Hume says just because an event has happened one billion times out of one billion (ex. the sun rising) it will not necessarily happen again. Kant says it will.

[/ QUOTE ]

Hume is right; Kant is practical.

Re: probability question (pertaining to SM+P)
 

Laplace has already calculated the probability that the sun will rise tomorrow. It is exactly (d+1)/(d+2), where d is the number of days the sun has already risen.

Re: probability question (pertaining to SM+P)
 

[ QUOTE ]
Hume is right; Kant is practical.

[/ QUOTE ] I disagree. Both make sense. We can't know which one, if any, is right.

edit: Oh my, did that statement make me look stupid. What I meant to say was: We don't know which one, if any, is right.

Re: probability question (pertaining to SM+P)
 

My understanding of Hume is that he is not questioning that the sun will rise tomorrow, but the validity of our tendency to assume it will. He does not deny cause and effect relationships. What he is essentially saying is that we have no right to be sure the sun will rise tomorrow. We form habits in our mind that constantly connect cause and effect, and for this reason, the relationship is not universal, but only a construct in our mind.

Re: probability question (pertaining to SM+P)
 

Question: why do we assume that the future will resemble the past?

Re: probability question (pertaining to SM+P)
 

Answer: Because it always has.

Re: probability question (pertaining to SM+P)
 

one day the sun will burn out and therefore the sun will not rise. so one day hume will be correct until than kant is correct. i think there both correct kant is betting on the +ev event. hume is the -ev gambler

Re: probability question (pertaining to SM+P)
 

[ QUOTE ]
We are discussing Hume and Kant in class. Basically Hume says just because an event has happened one billion times out of one billion (ex. the sun rising) it will not necessarily happen again. Kant says it will.

[/ QUOTE ]
Kant can't be that stupid.

Just because haven't died in my sleep yet doesn't mean I won't.

Anyway, the answer to the question is that there is no answer. It's a Bayes' Theorem problem, but the values you use for your prior probabilities are subjective.