Answering Qfwfq

[Doctordick]

This per se is a fair enough claim, leaving aside subtleties about your own definition of "explanation", the correspondence being bijective and why that equation ought to be The Fundamental One.

Let us leave no subtleties about my definition aside as, if there are any problems, the whole proof crumbles anyway; thus there is no need to go further until these issues are settled (whatever you perceive them to be). But first I would complain about your characterization of the correspondence as bijective.

 

According to Wikipedia, the two collections bear a one to one correspondence. That is not what I suggest. The idea that a specific explanation implies specific expectations is the central theme of my presentation but nowhere in the analysis do I suggest that a collection of specific expectations imply a specific explanation. These are quite different things and I don't think isomorphism is a valid characterization. The isomorphism of interest here is with [math]\vec{\Psi}(x_1,x_2, \cdots, x_n)[/math] itself.

 

Furthermore, if you are referring to what I represent as [math]\vec{\Psi}(x_1,x_2, \cdots, x_n)[/math] that notation is a little askew of what is defined as “bijective”. First of all, according to the Wikipedia reference, the number of elements in “X” equals the number of elements in “Y” and my representation makes no such constraint. And I have referred to those elements as sets elsewhere long ago; however, I have was taken to task as to the subtle definitions of “a set”. It seems that what I mean by “x_i” does not constitute a set but is rather “a mere collection of n numbers”. Now, the other side of the coin (the collection [math]\psi_k[/math] seen as components of that vector [math]\vec{\Psi}[/math] in an abstract Euclidean space (that second collection of numbers) might or might not constitute a set depending upon the subtleties of your definition of a set: i.e., it is not at all clear that we are talking about “sets” here.

 

It appears to me that the representation “bijective” is not applicable to any discussion in any capacity whatsoever and only serves to confuse. The only thing of significance in my mind is that the collection of all functions which carry one collection of numbers into a second collection of numbers exhausts the collection of “all functions” essentially by definition: i.e., to complain you need to show me a function which can not be represented by the notation [math]\vec{\Psi}(x_1,x_2, \cdots, x_n)[/math]. The fact that your expectations depend upon what you are referring to (an answer to the question, "probability of what?") implies your expectations are a function of what you are considering.

 

And we can talk about the equation being “Fundamental” after the proof is understood.

 

So, exactly what are these subtleties of my definition which leave you questioning it's universality?

 

Looking to hear from you -- Dick

[Qfwfq]

But first I would complain about your characterization of the correspondence as bijective.

 

According to Wikipedia, the two collections bear a one to one correspondence. That is not what I suggest. The idea that a specific explanation implies specific expectations is the central theme of my presentation but nowhere in the analysis do I suggest that a collection of specific expectations imply a specific explanation. These are quite different things and I don't think isomorphism is a valid characterization.

Well then why did you say "there exists a one to one correspondence between any specific explanation and some mathematical function of the arbitrary numerical references to the circumstances of interest" in what I replied to? Neither had I made the leap from bijection to isomorphism.

 

So it seems like an explanation is not the same thing as a [math]\vec{\Psi}(x_1,x_2, \cdots, x_n)[/math] but it leads to one; no great discovery. This does not indicate some definition of an explanation such as to tell me in which sense you conclude these are tautologies. It doesn't tell me what to apply the notion of tautology to, in order for the statement "They are tautologies." to make sense. What follows from what?

[Doctordick]

Note my opening post on this thread! The current supposed issue under discussion:

 

Let us leave no subtleties about my definition aside as, if there are any problems, the whole proof crumbles anyway; thus there is no need to go further until these issues are settled (whatever you perceive them to be).

Once again I find you essentially avoiding the supposed issue under discussion. As far as I can see you make utterly no reference to any subtleties about my definition of an explanation and I still have no idea as to what you perceive them to be.

 

Instead, you seem dedicated to arguing about conclusions.

 

Well then why did you say "there exists a one to one correspondence between any specific explanation and some mathematical function of the arbitrary numerical references to the circumstances of interest" in what I replied to? Neither had I made the leap from bijection to isomorphism.

All I was doing was complaining about your use of the word “bijection”. If you are happy using the word without making all kinds of implications, I can accept that. But then I do not understand why you are using it other than to add more ambiguity to the language we are using. An act which serves no purpose beyond confusion. You seem to have this propensity for using terms the general public would not comprehend and I don't think it serves any purpose except to imply that you know something they don't know. To me it seems to be a common authoritarian ploy and I really don't think it's appropriate here.

 

So it seems like an explanation is not the same thing as a [math]\vec{\Psi}(x_1,x_2, \cdots, x_n)[/math] but it leads to one; no great discovery. This does not indicate some definition of an explanation such as to tell me in which sense you conclude these are tautologies.

Again you completely avoid the issue supposedly under discussion here; which would be, “subtleties about my definition of an explanation which bother you”. It seems that either you have no complaints about my definition or you have no interest in clarifying them. By the way, in case you have forgotten, my definition of an explanation is "An explanation is a procedure which will provide rational expectations for hypothetical circumstances”. You might try reading, “Laying out the representation to be solved”.

 

It doesn't tell me what to apply the notion of tautology to, in order for the statement "They are tautologies." to make sense. What follows from what?

“They are tautologies” is a conclusion, not an opening issue. If you cannot accept my definition of an explanation as a workable starting point, then conclusions deduced from that definition are absolutely immaterial. And that would certainly make the definition of a tautology immaterial.

 

Why are you even bothering to post? Just to confuse issues?

 

So you suckered me in again. It is quite clear that you have no interest whatsoever in what I am talking about.

 

Have fun -- Dick

[Qfwfq]

I was by no means asking for a definition of tautology, it just plain wasn't the meaning of my words. You simply misunderstood. I guess the cause of your misunderstanding was that I added more ambiguity to the language we are using by introducing a word. :rolleyes:

 

So the [imath]\psi[/imath] functions are a result of the procedure, as I would have guessed. You define the word explanation as being such a procedure and I suppose the boundary is fuzzy, between that and the idea of a "reason why" for something. So if you identify them, I must find in what sense such a procedure is a tautology, which means finding what follows from what. The expectations follow from the hypothetical circumstances? This is so, for a given procedure, but tautology usually means without requiring some further fact so the from "what" must include the chosen procedure as well as the hypothetical circumstances: The expectations follow from the combination hypothetical circumstances + procedure.

 

There's no denying the above, it's even quite apparent in the history of science. If you define the word explanation as the above combination then it follows as a tautology that an explanation is a tautology. That would kinda mean the explanation isn't just the procedure though, so I'm not sure; if that's what you meant.

 

I hope you at least see what I mean by asking what follows from what. Strictly, it should hold vice versa too; both things should follow, each from the other. They ought to be two ways of saying the same thing. I'm not sure if you mean it this way. The only thing I could think of is when there are equivalent models, they lead to the same expectations; they could be regarde as different ways to say the same thing. Symmetries can be regarded likewise too. Is this what you meant?

[Rade]

Could one of you please provide the "definition" of "explanation" that is being discussed in this thread--thanks.

 

If any subtleties exist in the definition, then they can be specifically identified and discussed.

 

==

 

(EDIT Addition)

 

OK, I found it in one of DD posts--here is the definition of explanation where we need to point out specific subtleties:

 

... my definition of “an explanation”: i.e.' date=' a mechanism for generating probabilistic expectations for unknown information consistent with some body of known information....[/quote']

 

We need to look for subtleties in these sections of the definition provided by Doctordick for explanation:

 

1. That all (100%) explanations are a "mechanism"

2. That all (100%) explanations "generate probabilistic expectations"

3. That all (100%) explanations are for "unknown information"

4. That all (100%) "unknown information" is consistent with "some body of known information"

 

As discussed by Doctordick, if we find any subtleties in any of these propositions,

 

...Let us leave no subtleties about my definition aside as' date=' if there are any problems, the whole proof crumbles anyway[/quote']

 

{Second EDIT}

 

Perhaps reading the following will help uncover any subtleties in the definition of explanation provided by Doctordick, that is, if any exist:

 

http://www.strevens.org/research/simplexuality/Expln.pdf

[Qfwfq]

Rade, I had already discussed Dick's definition and, at this point, I was asking him in what sense he states them to be tautology. In fact, one paragraph of my post more or less boils down to asking if he meant Hempel's DN account (if one loosely calls any deductive argument a tautology).

[LaurieAG]

Hi Doctordick,

 

Again you completely avoid the issue supposedly under discussion here; which would be, “subtleties about my definition of an explanation which bother you”. It seems that either you have no complaints about my definition or you have no interest in clarifying them. By the way, in case you have forgotten, my definition of an explanation is "An explanation is a procedure which will provide rational expectations for hypothetical circumstances”.

 

I won't avoid the issue under discussion here and must remind you of a previous discussion with regards to how a certain discrete point, in a previous explanation of yours on another thread, caused the end result of the entire procedure, from that point on, to become 100% predictable and determinative. I don't even think its down to symetries either, especially when you consider that you get similar results by just excluding the bits that don't fit your answer 100%.

 

Qfwfq has similar reservations about your basic methodology. Its more like a form of paralogism than a tautology, a twisted tautology at best.

 

After reading that the greek definition of paralogism was 'to argue fallaciously' I'd have to say there's a good probability that it was a paralogism.

[Doctordick]

If you define the word explanation as the above combination then it follows as a tautology that an explanation is a tautology.

I understand very little of what you say. Are you asserting that my definition of an explanation, "An explanation is a procedure which will provide rational expectations for hypothetical circumstances”, has to be a tautology without further analysis? Or are you asserting via the omitted phrase, “the idea of a reason why for something”, constitutes a critical omission? If that is your implication, I do not understand why you feel that way. Is not, “it fits the known facts”, the very essence of “the reason why”.

 

On the other hand, if you are asserting that my definition lacks a constraint your personal definition requires, it seems to me that is no problem at all. My definition is simply more general than yours: i.e., things which wouldn't qualify as explanations under your definition (whatever that is) would qualify under mine. It is the reverse of that situation which would constitute a problem. Something which qualified as a explanation under your definition which would not under mine.

 

I don't think you are asserting that all explanations are tautologies in your mind. If that is the case, I doubt you would find much support amongst the scientific community. So I presume that can not be what you mean.

 

I would love it if you could give me a single case of something you would accept as an explanation which would not fulfill my definition: i.e., an explanation which yielded no information concerning expectations related to possible circumstances.

 

As Hempel saw it, scientific explanation was of a piece with prediction, requiring the same resources and giving a similar kind of satisfaction.

From my reading of that article (referred to by Rade), Hempel's error was going straight to the predictions whereas your “expectations” with regard to a specific prediction constitute the critical issue of import.

 

Rade, I had already discussed Dick's definition and, at this point, I was asking him in what sense he states them to be tautology. In fact, one paragraph of my post more or less boils down to asking if he meant Hempel's DN account (if one loosely calls any deductive argument a tautology).

Well, I would never have gotten that out of your post.

 

Where have you discussed my definition? I would love to read that discussion. Regarding Hempel, prior to today, I had never heard of the guy. Anything published after the late 1960's would be outside my experience anyway as I was no longer involved in academic affairs. And, no, I would not call any deductive argument a tautology. It becomes a tautology only when the axioms are defined in terms of the conclusions. That is the subtle issue.

 

Dick

[Doctordick]

After reading that the greek definition of paralogism was 'to argue fallaciously' I'd have to say there's a good probability that it was a paralogism.

Paralogism is defined to be an illogical or fallacious deduction.

 

Instead of throwing obscure words at me, why do we not discuss where that deduction might be illogical or false. That is what I have been asking for since the word “go” and only Anssi seems to have taken the issue seriously.

 

Dick

[Qfwfq]

I understand very little of what you say.

Well I don't know which English language you understand. I briefly discussed the implications of your definition as far as I could make out.

 

It is the reverse of that situation which would constitute a problem. Something which qualified as a explanation under your definition which would not under mine.

I only remarked that many people might not call all such procedures an explanation, but I'm not concerned with this. Call it a tomato and tell me in what sense it is a tautology.

 

I agree that many reasons why imply a procedure as of your description. Of course, a reason why such as "because God loves ya" is not nearly as useful as some others, to that purpose, but we are more concerned with those from which a procedure is consequent; so it isn't a problem if you identify the two things as long as you show me how you draw your conclusion and what you mean by it.

 

I don't think you asserting that all explanations are tautologies in your mind.

I can't recognize the predicate of this sentence but, guessing you meant to put "are" after "you" I can say I'm not stating this but asking in which sense you say it.

 

And, no, I would not call any deductive argument a tautology. It becomes a tautology only when the axioms are defined in terms of the conclusions.

Fine. So you seem to mean the true meaning of the word, different ways of saying the same thing, which in logic can be expressed as A implies B and also B implies A. So, given your definition of a tomato, tell me what implies what (or what is equivalent to what).

 

Let's call the procedure P and the hypothetical cirumstances H and the expectations E with some notation if it is necessary to apply the same P to different H's obtaining the corresponding E's from each. Exactly how is P a tautology?

[Rade]

I'm sorry, but I am having a very difficult time following the discussion given the fact that Doctordick puts forth two completely different definitions of what he calls "explanation". We are now 3+ years into discussion of the philosophy of DD, one would hope he has a clear concept of what an explanation is--I mean, it is the basis of all his mathematics.

 

I completely understand that definitions are contextual and change over time--but this only happens logically when new facts are available. The approach of DD is that when he dialogs with person A--he uses one definition, then flip-flop to another definition when he dialogs with person B.

 

I am not trying to be difficult here, but I find it impossible to follow the discussion because I do not think that Doctordick has any clear idea the complexity of the word explanation (as used in philosophy) and how others have written about it.

 

So that everyone can see what I say is true, here are the two definitions recently offered in the past few weeks:

 

Two contradictory definitions of explanation provided by Doctordick:

 

....Are you asserting that my definition of an explanation' date=' "An explanation is a procedure which will provide rational expectations for hypothetical circumstances”, has to be a tautology without further analysis?

 

... my definition of “an explanation”: i.e.' date=' a mechanism for generating probabilistic expectations for unknown information consistent with some body of known information[/color']....

[JMJones0424]

Admittedly, DD's threads are usually over my head. However, I think the last few posts here demonstrate why he is prone to frustration. The definition of words is only important in that you understand the way DD is using them. Arguing over semantics is relatively unimportant, unless you were to suggest a word that better describes a specific concept that DD is trying to evoke. It seems to me, the important definitions are the mathematical ones he uses. In his thread, Laying out the Representation to be Solved, he makes a number of assertions. These are the premises he uses to come to his conclusion. It would seem to me that it is these assertions that would most need to be evaluated, and the logic that he uses to derive a conlusion from them, in order to decide if his conclusions are valid.

 

 

 

For example (cut and paste quotes from the above linked thread):

 

1) There exist no circumstances which cannot be represented by the purely numerical symbolic notation [math] (x_1, x_2, x_3,\cdots, x_n, \cdots, t) [/math]

 

2) All explanations may be identified with a mathematical expression of the form [math] 0\;\leq\; P(x_1, x_2, x_3,\cdots, x_n, \cdots, t)\;\leq \;1 [/math]

 

In other words, an explanation is a function which provides the probability of the circumstances under consideration.

 

His first post in that thread and the clarifications that follow seem to me to be what is referred to in his statement "Let us leave no subtleties about my definition [of an explanation] aside as, if there are any problems, the whole proof crumbles anyway; thus there is no need to go further until these issues are settled."

 

 

 

But then again, I feel like an eight year old eavesdropping on a heated argument amongst adults, so I may be way off base.

[Rade]

It would seem to me that it is these assertions that would most need to be evaluated, and the logic that he uses to derive a conclusion from them, in order to decide if his conclusions are valid. For example (cut and paste quotes from the above linked thread):

 

1) There exist no circumstances which cannot be represented by the purely numerical symbolic notation [math] (x_1, x_2, x_3,\cdots, x_n, \cdots, t) [/math]

OK, thanks. You hit the nail on the head. Words really do matter. So, note that DD claims above that "there exist no circumstances which cannot be represented....". Well, this claim contradicts one of the multiple definitions of explanation he uses. There is indeed a set of circumstances that DD identifies by definition that cannot be represented by [math] (x_1, x_2, x_3,\cdots, x_n, \cdots, t) [/math]. Therefore, his math and his words are contradictory, his conclusions about explanation are not valid.

[Rade]

Rade, I had already discussed Dick's definition and, at this point, I was asking him in what sense he states them to be tautology. In fact, one paragraph of my post more or less boils down to asking if he meant Hempel's DN account (if one loosely calls any deductive argument a tautology).

The negation of a tautology A (~A) is a type of deductive argument called a contradiction. Thus, not all deductive arguments are tautologies--correct ?

[JMJones0424]

So, note that DD claims above that "there exist no circumstances which cannot be represented....". Well, this claim contradicts one of the multiple definitions of explanation he uses.

No it doesn't. That statement is how he mathematically describes a circumstance (or event, or whatever appropriate English word you wish to use). Statement one of DD's that I quoted is not his definition of an explanation, statement two is. (Though he goes on to add further constraints in that thread, and loses me unfortunately). I paraphrased it as "an explanation is a function which provides the probability of the circumstances under consideration."

 

There is indeed a set of circumstances that DD identifies by definition that cannot be represented by [math] (x_1, x_2, x_3,\cdots, x_n, \cdots, t) [/math].

Which is?

 

Indeed, the meaning of words matter. That is why it is important that you make an effort to understand the concept he is trying to convey when he uses a particular word, rather than shoehorning your own specific definition into the mix. If his logic is correct, and you don't agree with his use of the word "explanation" because his definition differs from yours, than replace all instances of "explanation" with a more appropriate word. I can not think of one off of the top of my head.

[Rade]

Which is?

Non hypothetical circumstances that are known a priori. Recall, I have never defined explanation (no shoehorning on my part). I respond to the multiple definitions provided by DD. It is his duty, not mine, to ensure that the multiple definitions he provides for explanation do not contradict (1) each other (2) his mathematical function. He has failed in both attempts.

[Doctordick]

Well I don't know which English language you understand. I briefly discussed the implications of your definition as far as I could make out.

You seem to overlook the fact that English is an extremely ambiguous way of representing things. “Understanding” requires far more than simple knowledge of the language. I have made many attempts to comprehend the thread of logic which I presume must stand behind your comments and, to date, it has simply eluded me. Not to insult you but, to me, most of your posts remind me of those old AI programs which put together questions and comments from the input stream in order to seem coherent. Like I said, I have extreme difficulty unraveling what is going on in your head.

 

I only remarked that many people might not call all such procedures an explanation, but I'm not concerned with this. Call it a tomato and tell me in what sense it is a tautology.

Exactly the kind of response I am talking about. The status as a tautology is only recognized on the other side of the whole argument. There is nothing in my definition of an explanation which requires an explanation to be a tautology. I thought I made that clear from the beginning.

 

I can't recognize the predicate of this sentence but, guessing you meant to put "are" after "you" I can say I'm not stating this but asking in which sense you say it.

Sorry about that. As I have said to Anssi, many times my thoughts get ahead of my typing and I make many errors; however, a little thought can usually uncover what was meant. I have edited the post.

 

Exactly how is P a tautology?

You have to understand both the proof of my fundamental equation and the various deductions of common physics concepts before that issue can even be discussed.

 

Admittedly, DD's threads are usually over my head.

[math]\cdots[/math]

 

It would seem to me that it is these assertions that would most need to be evaluated, and the logic that he uses to derive a conlusion from them, in order to decide if his conclusions are valid.

 

For example (cut and paste quotes from the above linked thread):

 

1) There exist no circumstances which cannot be represented by the purely numerical symbolic notation [math] (x_1, x_2, x_3,\cdots, x_n, \cdots, t) [/math]

 

2) All explanations may be identified with a mathematical expression of the form [math] 0\;\leq\; P(x_1, x_2, x_3,\cdots, x_n, \cdots, t)\;\leq \;1 [/math]

 

In other words, an explanation is a function which provides the probability of the circumstances under consideration.

 

His first post in that thread and the clarifications that follow seem to me to be what is referred to in his statement "Let us leave no subtleties about my definition [of an explanation] aside as, if there are any problems, the whole proof crumbles anyway; thus there is no need to go further until these issues are settled."

 

But then again, I feel like an eight year old eavesdropping on a heated argument amongst adults, so I may be way off base.

Sir, you impress me with the clarity of your post. If there is any part of my presentation which you have difficulty following, I would be happy to clarify my thoughts to you. Your response is far from being childish; it is, in fact, one of the most adult responses I have seen on this forum. You are right on the money when it comes to what must be examined.

 

Statement one of DD's that I quoted is not his definition of an explanation, statement two is. (Though he goes on to add further constraints in that thread, and loses me unfortunately).

I would appreciate it if you would let me know where I lose you. Perhaps others have the same problem you have and a few minor changes in that OP might be in order.

 

Thanks a lot for your contribution -- Dick