tag:blogger.com,1999:blog-715339341803133734.post4309093937132844680..comments2023-08-18T04:14:50.151-05:00Comments on Maximum Entropy: The Calibration Problem: Why Science Is Not DeductiveTom Campbell-Rickettshttp://www.blogger.com/profile/07387943617652130729noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-715339341803133734.post-30682706965113841902014-08-19T11:12:00.142-05:002014-08-19T11:12:00.142-05:00Yes, it is always possible that nature will go ...Yes, it is always possible that nature will go 'off the rails,' but this does not invalidate any previous probability assignment. A probability assignment is not a statement only about some external state of the world. It is a statement about our relationship with that state of the world. <br /><br />Two rational agents, possessing exactly the same information, can legitimately arrive at two different probability assignments for the same proposition, if they use different probability models. This does not invalidate either probability assignment. The calculus of probability is impossible without such probability models, and there is no prior principle for choosing one over the other (assuming they are both mathematically valid - and even this criterion is problematic, under the closest scrutiny).<br /><br />We <i>can</i> use past success to predict future events. This does not guarantee those predictions will be correct. (This is just as true, concerning inferences about the past.) We <i>do</i> need to assume some kind of uniformity to do this, but there is no way around this, and there is nothing to say against such a procedure. If we begin to suspect the exact form of our symmetry assumptions (probability models), we can test them by applying Bayes' theorem at a higher level. <br /><br />What Hume and Popper both wanted was for our inferences to be absolutely guaranteed (independent of any vulnerable assumptions). There is no way to grant this wish, probabilistic or otherwise.Tom Campbell-Rickettshttps://www.blogger.com/profile/07387943617652130729noreply@blogger.comtag:blogger.com,1999:blog-715339341803133734.post-23462835088802006532014-08-19T10:27:42.554-05:002014-08-19T10:27:42.554-05:00Hume and Goodman's problems do not require us ...Hume and Goodman's problems do not require us to be 100% certain in our inferences. The problems remain even if we consider our predictions to be highly probable, rather than certain (e.g., that we expect the sun to rise tomorrow with very high probability). It is always possible that Nature is going to 'go off the rails' in the next observation interval. In fact, if Hume and Goodman are correct, unless we presuppose the uniformity of Nature (even in the probabilistic sense), there is no way to assign a probability to the next observation. If this is the case, then we cannot use past scientific success to predict future observations, even probabilistically- which means that we cannot claim to know anything about the world beyond what has already been observed. Note that it is partly Hume's problem of induction which led Popper to reject inductivism in favor of deductivism. But as you rightly point out, given that falsificationism is also inductive, Popper's solution ultimately fails. <br /><br />Now, I am not saying that Hume's and Goodman's problems cannot be solved via probabilistic reasoning a la Bayes; I'm just curious about your thoughts on what this solution might look like. How would Bayesian confirmation theory provide grounds for believing that all emeralds are 'green' rather than 'grue'?YFhttps://www.blogger.com/profile/06353112342089566468noreply@blogger.comtag:blogger.com,1999:blog-715339341803133734.post-13185156302062707932014-08-19T04:49:06.864-05:002014-08-19T04:49:06.864-05:00Thanks for your comment.
The term 'knowledge,...Thanks for your comment.<br /><br />The term 'knowledge,' often defined as 'justified true belief,' is highly problematic. The concept is hopelessly over simplistic, to the point of uselessness, and should be removed from all serious philosophical discussion.<br /><br />It is true that inductive inference can not guarantee the truth of relationships between past, present, or future entities. (For the purposes of inference, there is no important difference between past and future.) But to say that science can't be trusted to make predictions about the future is over simplistic, and a stronger statement than saying that science can't guarantee our inferences. Lack of complete trust is no the same as complete lack of trust. <br /><br />There is no solution to the problem of induction - no way to be 100% certain (independent of a probability model) of anything interesting. We can, however, apply arbitrarily many layers of sophistication in our pursuit of the truth (via <a href="http://maximum-entropy-blog.blogspot.com/p/glossary.html#model-comparison" rel="nofollow">model comparison</a>), and thus examine our hypotheses with arbitrarily stringent tests.<br /><br />It is thus possible to be highly confident of our inferences, and to say "given the information I have now, there is no good reason for acting as if X is not true."<br /><br />Tom Campbell-Rickettshttps://www.blogger.com/profile/07387943617652130729noreply@blogger.comtag:blogger.com,1999:blog-715339341803133734.post-25932287182289793522014-08-18T22:50:09.789-05:002014-08-18T22:50:09.789-05:00Excellent post. Given, as you've argued, that ...Excellent post. Given, as you've argued, that science is inductive and that the proper way to update our beliefs about the world is via Bayesian confirmation theory, I was wondering if you've considered writing a post on whether Bayes can solve Hume's and Goodman's problems of induction. If it cannot, then science cannot be trusted to make predictions about future states, and it becomes a truly a rear-view mirror endeavor. Indeed, if they cannot be solved, then we cannot claim to have any real knowledge about the world at all...YFhttps://www.blogger.com/profile/06353112342089566468noreply@blogger.com