As a philosophy student with a great interest in math and computing, I can definitely attest to the lack of scientific understanding in my department. Worse, it often seems like some professors actively encourage an anti-scientific ideology. I’m wondering if anybody has any practical ideas on how to converse with students and professors [who are not supportive or knowledgeable of the rationalist and Bayesian world-view] in a positive and engaging way.
JMiller
Karma: 241
Thank you. In that case, does math rely on at least one particular agent or computer having some [true] model that 2+3 = 5?
I found Eliezer’s post “Math is Subjectively Objective” which explains his position very clearly. Thanks for your help.
Tabooing the word “science”seems to be a pretty good idea, along with other scientific jargon. I think many of the idealist and continental philosophy students are not afraid of science exactly, but fear that it somehow makes the human condition worse; more mechanical, and less special.
Thanks
Right, which explains his position: math is real and 2+3 really is 5, but he does not know what that means, or where that is true.
You are right though, it isn’t a fully fleshed out account. All I said is that it explains his position clearly, not that his position itself is perfectly clear.
I don’t have time to read this this week, but when I do I will get back to you. Thanks for the article.
So when an agent or computing device performs an operation on real numbers, say division of 1200 by 7, that result is real, even though the instance of this division requires the agent to do it? The answer IS the only answer, but without an agent, there would not be a question in the first place?
A Probability Question
Thanks. I see why the probability of H1|o and H2|o need to be taken as 25% each. In that case, it seems like Sarah can say that it is 50% likely a boy and 50% likely a girl (at home). Why is the answer to the question then given as 66%?
Thank you, that is very helpful! If I understand it, according to your analysis, Sarah knows less about the total state of the birth order/ gender of the two children. Still, it seems like she knows more about the particular gender of the child at home.
Is that still a problem?
Thank you very much Chaos. I did not realize that my post came off as abrasive, I appreciate you pointing that out. Your example sounds quite reasonable and is more along the lines of what I was looking for.
That makes a lot of sense, thank you.
Pragmatist is correct, I did not realize that the way I stated the problem was different than the original.
I full understand the solution to this problem.
However, lets look at the original problem. John only knows that one of the man’s children is a boy:
1) B, G | 0.33
2) G, B | 0.33
3) G, G | 0.00
4) B, B | 0.33
P(B)|(4) = 1 P(G)| (1,2) = 1
P(B)= .33 P(G) = .66
So lets say that now the woman tells John that the boy is also the eldest:
1) B, G | 0.5
2) G, B | 0.0
3) G, G | 0.0
4) B, B | 0.5
P(B)|(4) = 1 P(G)| (1) = 1
P(B)= .5 P(G) = .5At first I saw a problem because John obviously knows more given the second piece of information, so the fact that his estimate is worse seemed really weird. What I think is going on here is that his learning more really does decrease his ability to predict the gender of the other child: Before, he had 3 options, 2 of which contained a girl-answer. Now, one of those 2 answers are taken away, so he currently has 2 options, 1 of which contains a girl-answer. As he becomes more informed about the total state of the world, his ability to predict this particular piece of information decreases.
You are right to point that out. I think that the spirit of the question assumes equal probability of 50% B,G for each birth independent of previous births and statistics in order to make it a probability and logic question, and not one of biology.
Luke, the link in the third line “Now is your chance to double your impact while helping us raise up to $230,000 to help fund our research program” does not work.
Ah I did not see this post last night. Thanks.
Good for you Philip!
There are many body weight and light weight exercises you can do.
Of course, a good program depends on your goals and limits.
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I am having difficulty understanding the model of ‘physics+logic = reality.’ Up until now I have understood that’s physics was reality, but logic is the way to describe and think about what follows from it. Would someone please post a link to the original article (in this sequence or not) which explains the position? Thank you.
Thank you.
I am somewhat confused about the nature of logical axioms. They are not reducible to physical laws, and physical laws are not reducible to logic. So then, it what sense are they (axioms) real? I don’t think you are saying that they are “out there” in some Platonic sense, but it also seems like you are taking a realist or quasi-empirical approach to math/logic.