marg wrote:Tarski wrote:I know exactly what Marg is talking about and it is not one of the dumbest things a person could say. I believe what she is talking about is exemplified by the case of the Riemann hypothesis.
The latter states that all the (non-trivial) zeros of the Riemann zeta function lie on the vertical line Re(z)=1/2 in the complex plane.
We do not have a rigorous mathematical proof of this as of yet (well maybe some recent attempts work but it is too early to tell).
Anyway, what we do have is knowledge that all known zeros do lie on that line and the number of cases we know is very large thanks to computers.
So inductive reasoning in the sense used in empirical science might lead us to believe that the RH is true but this is not considered valid in mathematics and would be inappropriate to the subject matter
.
If someone could come up with an inductive proof in the sense of "math. induction" or any other deductive proof (perhaps a proof by contradiction) then we would simply know that the RH is true in a much stronger sense than we know that all electrons are subject to quantum electrodynamics (since the latter would be due to inductive reasoning in the sense philosophers of science worry about).
So when people see how many cases already have been checked and this leads them to conjecture the truth of the RH, they are (kind of) thinking inductively in the sense of induction as understood by Hume etc. But this is not mathematics and we await a (deductive) proof (which may perhaps use the mathematical induction!).
So in short, I knew instantly what Marg meant and it was not stupid by any means.
(Gotta call it like I see it)
Perhaps what you thought she was saying would have been stupid--I don't know. Like I said, you are talking past each other.
Tarski I'm not sure you understand what I was saying. First of all this mathematical induction was what Stak brought up to show that induction requires form. And If I recall correctly his argument was that the reason Dawkins' argument was "bad" Stak's description was because it wasn't valid, the form was wrong, and I believe he argued Dawkins' argument presented (which Stak seemed to think was limited to a particular page with a list) was a deductive argument. Hence according to Stak Dawkins argument was that 'No God exists'. It's been a while since that discussion and I only briefly reread. Then I believe I argued Dawkins' argument was inductive and was not presented in any form of validity. And argued that inductive argument can't be "bad" because of an invalid form as they don't have form. That's when Stak brought in mathematical induction and I looked at his example, actually went through it step by step...but what I understood conceptually was that the mathematics offered a conclusive conclusion..so it was deductive. Sure previous to the equation being worked out on paper whatever one might speculate with regards to an equation would be considered inductive reasoning. Not until the equation and proof is worked out that it it considered deductive reasoning. So in the mathematical inductive example, it was an equation with a variable for any natural number which would hold true to infinity..and there was/is no reason why any variable of a natural number should not be valid...in the equation..then that's a deductive proof.
I don't claim to be knowledgeable in math. The discussion was about concepts and about Dawkins' argument.
I don't think Stak and I were talking past each other. He obviously thought I was wrong, and I thought he was wrong or at least didn't know what he was talking about. I don't think his argument against Dawkins was a good argument. That's what I was hoping you'd address.
Was he correct for the reasons he gave..that Dawkins' argument was "bad" his word?
I am not going to make a big judgement about Marg's intelligence, who wins, or to what extent she just googles things without understanding them but based on this thread alone I would say she does not deserve to be called stupid at all.
In fact, I am absolutely sure that she has much higher intelligence than my wife, my dear mother, my brother and quite a few other people I love and respect. None of them could come close coming up with what she came up with in this thread no matter where she got it.
Where I got it? Mathematical induction I may not have heard of and went to the page Stak linked to. I didn't have to go to wiki to appreciate that was a deductive argument in that it was offering a conclusive proof and also appreciate math does not always map neatly onto arguments for the real world which was Dawkin's argument. Sober I had not read ..so I read that to try to understand Stak's point and I still didn't find that helped Stak. At this point I don't remember what the Sober article was about, but I don't think it showed that Dawkins argument if inductive could be treated as deductive. (Perhaps that's where there is some misunderstanding and we might be talking past each other)
So, what business would I have insulting her intelligence?
In fact, I now feel guilty that I implicitly went along with this Marg is so stupid thing.
Perhaps a rereading of old threads with her and Jak arguing this or that with Gad or CC about Godel or something might move my opinion in one direction or another (I remember being frustrated with her at the time) but I couldn't even come close to thinking that she is just "dumb" or something. That would be totally unfair and false.
What you may not have appreciated in that thread was CC was arguing logic can prove God's existence and he offered Godel's argument for God. CC came into the argument after I was there. Gad didn't like the idea that JAK or I should argue against CC unless we totally understood mathematically Godel's argument. Sometimes one can understand concepts without having to understand all the details. This was a personal thing for Gad, he didn't care about the actual argument, he just didn't us arguing without having studied Godel.
That thread and others is why this board is frustrating. If someone keeps repeating something over and over and I know people hate me using these words but if they are intellectually dishonest that is they want to win an argument because their ego is invested or their livelihood and reputation is at stake or they just have a grudge ...and no one really is following the argument..it just goes nowhere..and the loudest or the one who gathers up friends...ends up being one ones heard..doesn't matter how well they've argued. Whether Dawkin's argument is bad or not I don't think is all that important. But there are other arguments which are important..I won't get into though what I'm referring to.
I appreciate you've taken the time to look at this. I still would like you to evaluate the argument Stak made for Dawkins' argument being "bad" and whether or not my argument against Stak's was correct. That is was I correct when I pointed out Dawkins' argument was inductive ..was I correct that inductive arguments are not invalid based on form. This part of the discussion was at the beginning. Obviously I don't want you to waste too much time on this, but it would be nice if you could evaluate the discussion a little more..rather than assess whether or not "I'm stupid". I do appreciate your comment on that though.
Marg, I believe you were right to say that
mathematical induction is not the same as inductive reasoning and that the former is essentially deductive. Stak wants me to flesh out why one would call it deductive (and I am thinking of what more I can say) but it is already clear that, as you say, it leads to a definite logical conclusion where inductive reasoning as used in empirical science does not.
You were right about this much and Stak was wrong. (IMHO)
I can't evaluate the rest of the issues regarding what Dawkin's was trying to do or how well he did it since it turns out that I have never bothered to read the book. My impression is that he simply lays out the usual stuff about evolution/complexity and the usual unpleasant stuff about the God of the Bible and thereby hopes to make God extremely implausible. That he apparently said little about "serious" theology bothers me less than it does some people.
Did he attempt and fail at a deductive argument or make it sound as if he was going to present something deductive?
I would be surprised if he thinks
that is what he is doing since he always says there is no proof that God does not exist. I also don't think he was attemting to use a probabilistic Bayesean analogue of a deductive argument (which Stak brought up). I doubt he is even explicitly aware of such things.
In short,
I didn't read it.
I also did not read every word of the thread and I don't have time to do so right now especially if I am going to get sucked into a discussion about logic and mathematics.
So what can I say?
I'll say this much, there is an undercurrent personal animosity directed at you that makes it painful to read the thread. Maybe I would understand that aspect better if I read more of your posts but it turns out that I haven't.
I suspect that certain people have been being unnecessarily rude to you and it seems maybe those people are
exactly some of my favorite posters like Stak and Gad. This puts me in an uncomfortable position.
Maybe people would do well to apply a version of some advice from Kuhn (whose name I loath to invoke) when reading not only important thinkers but also when reading each others posts:
... look first for the apparent absurdities in the text and ask yourself how a sensible person could have written them. When you find an answer, ...when these passages make sense, then you may find that more central passages, ones you previously thought you understood, have changed their meaning.
In other words, read charitably.
For example, right now I can't tell if Stak has a
much better or
much worse grasp on formal logic than I do. I suspect, it is a strange combination of both. He is self taught and has been reading different material than me. He has the disadvantage of having little experience with mathematics which is the main place where deductive reasoning is used effectively. I have also been immersed in physical science for 30 years so I have some resulting attitudes toward "inductive reasoning".
On the other hand, he has the advantage of having been studying logic and analytic philosophy as such more recently. I have worried little about things like the compactness theorem or model theory over the years and even have a certain inchoate skepticism about certain parts of the subject. I especially hope that modal logic doesn't come up.
We could learn from each other perhaps.
Right now I am looking at some statements he made that seem confused and asking myself if perhaps they are not confused after all. This is an important part of reading someone with a different background.
when believers want to give their claims more weight, they dress these claims up in scientific terms. When believers want to belittle atheism or secular humanism, they call it a "religion". -Beastie
yesterday's Mormon doctrine is today's Mormon folklore.-Buffalo