apathist
If you are trying to say that the least assumptive theory isn't necessarily (or simply isn't!? ) the most probable (are you saying that? ) then I honestly would like to know why you think that as you are not the first person to express such a thought to me and yet I haven't ever been told the reason why some people sometimes think that and I would like to know why some people sometimes think that.
Originally posted by apathistno, you misunderstand; oc-razor is not a function of the number of assumptions (yet another common misunderstanding of oc-razor) but rather is a function of the total assumptiveness of the whole set of assumptions and note that not all assumptions are equally assumptive.
As if any scientific assumption doesn't imply an even longer list of assumptions as well.
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Thus oc-razor sometimes favors the theory with a greater number of assumptions because, despite that theory having the greater number of assumptions, that set of assumptions can still be less assumptive that an alternative theory that has less assumptions.
It would be far too simplistic to say oc-razor favors the theory with the least number of assumptions.
example:
consider the two arbitrary opposing theories below:
Theory 1, plants use solar energy to chemically absorb carbon dioxide and water to form sugars and gaseous oxygen.
Theory 2, plants do not use solar energy.
If you erroneously think oc-razor says the theory with the least number of assumptions is the most likely then you might think that oc-razor recommends theory 2, above. After all, theory 1 does make a greater number of assumptions;
plants use solar energy AND do so to chemically absorb carbon dioxide and water AND then sugars and gaseous oxygen are made from this. In contrast, the only thing theory 2 assumes is that plants do not use solar energy.
But, actually, oc-razor recommends theory 1 because, in this case, we happen to have good evidence for each of its assumptions including the “ plants use solar energy” part that directly contradicts theory two and, therefore, the sum of the 'magnitudes' of all the 'assumptions' in theory 1 (although the word 'assumptions' here may be the wrong word to use here since we are actually talking about the scientific facts) is less than the sum of the 'magnitudes' of all the assumption in theory 2. Thus theory 2, despite having less number of assumptions, is more assumptive and thus disfavored by oc-razor.
I think 'assumption' is the wrong word to use for things that we have strong evidence for. Occam's razor is more to be used when we have no evidence either way. When there is evidence that is not conclusive then the calculations become more complicated and I am not sure we would call such calculations Occam's razor.
Originally posted by twhiteheadso what you are saying is oc-razor is only for when all we have is prior probabilities.
I think 'assumption' is the wrong word to use for things that we have strong evidence for. Occam's razor is more to be used when we have no evidence either way. When there is evidence that is not conclusive then the calculations become more complicated and I am not sure we would call such calculations Occam's razor.
Originally posted by humyI think it applies when we have two plausible explanations and insufficient evidence either way and one explanation involves less assumptions than the other.
so what you are saying is oc-razor is only for when all we have is prior probabilities.
I don't think your example where something isn't being explained as such but rather we are asking the question 'do plants use solar power' relates to Occam's razor at all. Occam's razor applies to possible explanations for a known phenomenon. What is the 'known phenomenon' in your example? What is being explained?
Originally posted by twhiteheadI believe you are referring to the older more conventional concept of oc-razor. I have been adapting the concept of oc-razor to apply to a far greater range of situations than that more conventional idea of oc-razor but I admit I now just started to think I have gone way too far with doing that. Assuming I have gone too far, then the correct reply to apathist's comment of
I think it applies when we have two plausible explanations and insufficient evidence either way and one explanation involves less assumptions than the other.
I don't think your example where something isn't being explained as such but rather we are asking the question 'do plants use solar power' relates to Occam's razor at all. Occam's razor applies to ...[text shortened]... for a known phenomenon. What is the 'known phenomenon' in your example? What is being explained?
"...As if any scientific assumption doesn't imply an even longer list of assumptions as well...."
should have been something more like simply;
"...is what you call a "scientific assumption" here supported by evidence? If so, oc-razor doesn't apply. If not, give an example..."
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I will have to revise this whole issue.
Originally posted by apathistforget about my last reply to that comment of yours;
As if any scientific assumption doesn't imply an even longer list of assumptions as well....
Is what you call a "scientific assumption" here supported by evidence? If so, oc-razor may not apply (depending on how you define oc-razor ). If not, give an example of such a scientific assumption that consists of even longer list of assumptions so I can see what you mean.
Originally posted by humy
because the least assumptive theory is the most probable.
I question that assertion.
If we have two exhaustive mutually exclusive theories, theory X and Theory Y, and theory X makes an assumption A that theory Y doesn't make but theory Y doesn't make any assumption that theory X makes, then theory Y is the least assumptive. Therefore, theory Y is the most probable because, regardless of what the probabilities are of each assumption the two theories both make, for theory X to be true, that extra assumption A has to be true and there must be a non-zero probability that assumption A is false. If you just do the maths, you see that means theory Y is more probable.
And the rabbit cannot catch up to the turtle.
There were a host of unstated assumptions in your description, and so a host of other probabilities. Does a couple of incorrect assumptions outweigh a dozen correct assumptions? Of course not. But according to your argument, a two-assumption theory must be more likely to be correct than a twelve-assumption theory. ALL that matters is whether the assumptions are correct, not how many there are!
Note oc-razor doesn't guarantee the ...
I understand that point.
Originally posted by apathistIf you knew which said 'assumptions' are correct and which are incorrect, they wouldn't be 'assumptions' to you and thus you couldn't apply oc-razor to them.
... Does a couple of incorrect assumptions outweigh a dozen correct assumptions? ...[/b]
I will show a mathematical proof (at the moment it isn't fully mathematical but mainly deductive and not yet worthy of publication), that makes no assumptions i.e. it is purely deductive, of oc-razor validity when I publish my research results next year and then I will start a new thread about it here. But although I can prove oc-razor is valid, I have to confess that in just the last 3 days and to my great surprise, I have deduced that oc-razor is redundant and superfluous and is only needed if you have inferior understanding of probability else you can simply and easily dispense with it just by sticking to calculating the probabilities directly.
Originally posted by apathistNo! Unless you completely arbitrary and pointlessly define probability itself as 'guessing' it Doesn't! With mathematical proof and contrary to all conventional wisdom, I will show (prove) in my book how the derivation of all probability is ultimately purely deductive! And, by doing so, this would also solve the problem of induction. The reason why I call my system of logic "tie logic" is because it acts like what I call a 'tie' between deduction and induction and this 'tie' makes induction just a side-branch and specialized application of deduction. That claim that induction is just a specialized application of deduction would be considered pure nonsense, even gibberish, according to conventional wisdom. But I can and will prove that claim correct.
But that requires guessing.
Originally posted by apathistYou don't seem to understand statistics at all. There is no guessing, only probabilities. If something is more probable than another, it doesn't mean it is true. But neither is it guessing to say it is more probable.
But that requires guessing. Pull 'em outta the arse type statistics, ....
Like the wonderful Drake equation.
There is nothing 'guessing' nor 'Pull 'em outta the arse type statistics' in the Drake equation. Only those who claim to have filled it in must use 'Pull 'em outta the arse type statistics'.