Should we be skeptical of inductive logic in the sciences?

[Doctordick]

I notice that the entire "Skepticism and debunking" area (sorry, I had to correct the spelling – it just overwhelmed me) is entirely devoted to issues which are unaccepted by the scientific community: i.e., there is nothing there expressing any skepticism at all regarding accepted science. Now from the perspective that errors might exist in the current perspective (it should be clear to all that scientific breakthroughs related to errors in presumed truths have occurred throughout history) it seems to me that a little skepticism there would be healthy.

I have been posting on "physicsforums" for almost two years now but have managed to achieve little communicative success (I seem to have instead generated a lot of hostile reactions). I have seriously tried to understand why I have engendered hostility in exactly the people I would like to be talking to (that would be the competent educated component). Much has been said about my attitude but I don't really believe that. Instead I think it is criticism of their beliefs which has turned these people off; skepticism with regard to their basic viewpoint. An issue I suspect I have really not really explained very well.

My background is in theoretical physics (the area in which I earned my Ph.D.) and I have had utterly no training in philosophy. The attitude in the physics community (which I was certainly educated to believe) is pretty well the position that philosophical issues are of no scientific interest. Thus it is that I didn't fully really realize that my problems with conventional physics were exactly with the philosophy of science held sacrosanct by the community until recently (I have recently read a little philosophy).

It was only after reading Popper's "Objective Knowledge" that I began to realized that my difficulties with the conventional foundations of physics rested entirely with a single difficulty who's existence was recognized long ago. It has entirely to do with what is thought of as inductive logic. The validity of inductive logic has long been known to be an undefendable proposition. Now, for those who baulk at that proposition, "undefendable" does not mean it's wrong, it just means that the validity can't be proved and could possibly be wrong (quite a reasonable statement).

It is commonly held that there are two very different categories of logic: deduction and induction. In reality, induction is not actually logic; it is in fact, the logical deductions which may be made from the assumption that something which has happened in the past will happen again. Now all logical deduction begins with axioms so why would they want to set this off as a separate category of logic and not just another possible axiom? As I see it, the answer is very simple but difficult to live with and "the powers which are" don't like to bring that fact into the open. The fact is that the assumption "what has happened in the past will happen again" is very difficult to accept as an "axiom" and must be couched in very careful terms in order to be seen as reasonable. In fact, most all errors in our explanations of our experiences which have turned out to be wrong can be traced to exactly that assumption so it behooves us all to be careful with regard to induction.

Now that brings up the issue very close to my heart. Induction is quite clearly a problem which has bothered philosophers for centuries. The real crux of the problem is the fact that without induction we have no mechanism by which to fabricate any "meaningful" definitions (this is the real issue behind the adage, "mathematics has nothing to do with reality"); on the other hand, if we allow induction, we have dispensed with absolute validly of logic. The fact is, this is the very reason that we cannot be assured that any "explanation" of reality is true (they are all just theories). It is the stock answer of the scientific community that this is a conundrum which cannot be resolved and thus no serious effort is ever put into examining the possibilities. The problem is that the very position being promulgated is an inductive conclusion and thus can not be proved valid. As a consequence, I was a serious skeptic of that position.

Being a skeptic, I did examine the problem but not in the manner of attack used by all of the philosophers; rather, being a trained physicist, I examined it in a way much more analogous to the approach used to unravel black body radiation: that is, without concerning myself with the specific details of any applicable deductions, I searched instead for the specific qualities of a stable state solution under the simple constraint that the deductions had to be perfectly consistent with the known data (as in black body radiation, how the actual specific states interact is immaterial, it is the existence of a steady state which is critical). And I found success!

Or at least some very interesting results. The problem is that the results are really quite mundane: there are only a few very minor differences between my steady state solution (steady state in theory development) and current theories of the universe. The difference is not in the results but rather in the means by which I reached them. Just as Maxwell's discovery didn't deny any of the known electro-magnetic experiments (though they predicted phenomena was a tad askew of prior theory), my results don't deny any of the currently known experiments (though it also is a tad askew). Just as Maxwell's equations suggested the existence of phenomena not yet observed (solutions to his equations and not "observed" phenomena), my work also hints at solutions which do not occur in conventional physics.

Essentially, I said, suppose we simply drop induction as a valid logical procedure. What can one say about our experiences then? Everyone, and I mean everyone to the last living soul, refuses to even consider such a thing. They won't even try to come up with possibilities. The adamant refusal to look is absolutely all pervasive. The answer is invariably one of the following: if you drop induction, all you are left with is infinite regression; if all you accept is what you can prove, you're a solipsist and can defend nothing, or, the very best of all, "you're an idiot if you think anything lies down that path". Note that all those positions arise themselves through induction: those are the only solutions anyone has found so there cannot be any others! (In my opinion, right up there with "the Earth is flat", "man can't fly" and "heavy things fall faster".)

I am not putting forward a theory; I am looking at the process of conceiving theories and the the rational constraints which should be placed on those conceptions. In particular, what can one say if one avoids yielding validity to induction. The only reaction I have received so far is "I don't want to look!"; essentially the old monkey issue, "Say no Evil, Hear no Evil and See no Evil". Most all the nuts in the world refuse to entertain your skepticism of their beliefs, why do supposedly intelligent scientists refuse to entertain my skepticism of their beliefs? It certainly isn't because they can prove they are right. I can only conclude that they don't want to think about it.

Another interesting observation: everyone will admit that modern science may very well have errors in it; however no well educated thinker (except myself of course) seems to be interested in exactly why current theory might be wrong. The attitude seems to be "skepticism is for the ideas of others, not for our ideas".

Have fun -- Dick

Knowledge is Power
and the most common abuse of that power is to use it to hide stupidity

 

[dgoodpasture2005]

I'd have to agree... I have fallen victim to these abhorrent illogical conclusions, and now have been outcast from science as well as religion. I'm starting to see a trend... nice article very well written... really touched my heart. It explains exactly who i am and how i think, you're not alone DD.

 

[ZapperZ]

Then both of you must have either missed, or never bother, to look at the bottom of each issue of Physical Review Letters. What do you call those comments that either challenged or criticized papers what were already published? Fan mail? I only need to point just this ONE example to invalidate your accusation about how physics is practiced. This clearly points out that physics ideas and physics publications are being challenged all the time and continuously. Why is this evidence being totally ignored?

If you feel that there's something wrong, then write a rebuttal to the journals. This is how every physicists in the world have to work with, even Nobel prize laureates, and there's no reason why you two are any more special then the rest of us. Go to physics conferences and present your ideas, and challenge what has been done. Instead, you put all of those energies into what... and open internet forum??! And then you used your experience ON HERE, to characterize the whole physics community and how it is practiced? Is this how you collect and consider as valid evidence to draw up your conclusion?!

I can show you PLENTY of evidence where the naive Einstein's photoelectric effect model is "wrong". I can show you plenty of evidence where our conventional idea of particles in matter is wrong. I have done plenty of non-mainstream ideas, be it in physics journals and conferences. Show me a religion that continually practice and tolerates such a thing. Maybe what needs to be changed in the way YOU practice your science and where you wish to engage in such a discussion.

Zz.

 

[russ_watters]

I notice that the entire "Skepticism and debunking" area (sorry, I had to correct the spelling – it just overwhelmed me) is entirely devoted to issues which are unaccepted by the scientific community: i.e., there is nothing there expressing any skepticism at all regarding accepted science.

Since science, by definition, includes the concept of skepticism, it would be redundant to call a forum "Chemistry and Skepticism". Where skepticism is missing - and therefore needed - is with ideas that require "debunking". Ie, ideas not based on the principles of science, such as intelligent design or perpetual motion.

And conversely, since Intelligent Design and perpetual motion and similar ideas are not scientifically grounded, it would not be correct to call them real "skepticism" of scientific ideas. Ie, attempting to "debunk" Relativity by invoking ether theory would not be scientifically valid - though for some subjects, some latitude is given in an effort to help people learn.

 

[hypnagogue]

Note: this thread was originally posted in the Skepticism & Debunking forum but has since been moved here as a philosophy of science topic. It seems Doctordick's primary concern has to do with questioning (being skeptical of) the logical foundations of science, namely inductive logic. Please keep this in mind for any future discussion that may take place in this thread.

edit: I have changed the title of this thread (from "Is skepticism reserved for "nut" theories?") in order to place proper emphasis on the main idea of this thread.

 

[hypnagogue]

As a quick rejoinder to Zapper's and russ's comments, and to once again maintain proper focus for future posters-- please note that Doctordick is not concerned here with skepticism of scientific hypotheses and theories in general (of which there is plenty in the scientific community), but with skepticism regarding the underlying principles of scientific epistemology themselves, particularly those involving inductive logic.

 

[hypnagogue]

Doctordick, assuming we reject orthodox scientific epistemology (at least, those components which rest firmly upon inductive logic), exactly what kind of epistemology do you propose we use in its place to discover the nature of things, and in what ways is this alternative superior and inferior?

 

[Doctordick]

Doctordick, assuming we reject orthodox scientific epistemology (at least, those components which rest firmly upon inductive logic), exactly what kind of epistemology do you propose we use in its place to discover the nature of things, and in what ways is this alternative superior and inferior?

Well, first I am a physicist and not a philosopher so I really don't know what you mean by the phrase "what kind of epistemology do you propose". My position is logically very simple. There is no way to prove that any inductive conclusion is valid and the very existence of errors in our theories can be traced to exactly that conundrum. The scientific attitude is essentially, "that fact is just a tough thing we have to live with and there exists no way of avoiding it; we must accept it and do the best we can with what we have". My position is, you will never solve a problem you refuse to look at it and, from my perspective, everyone seems to refuse to look! I have looked carefully and I believe the examination produced some rather astounding results.

I am not saying we can avoid inductive conclusions, as without them we have no starting place; what I am saying is that there exists a powerful method of avoiding the errors inherent in the process. Let me present to you a subtle path through a thought experiment which might enlighten you to some very important facts.

It is a fact that everything we know is based on what we have concluded to be true by induction (without induction there is no starting place). Langauge itself is an excellent example of this circumstance. Since our understanding of the meanings of the words we use was acquired by induction, the possibility exists that we are wrong: i.e., that there might exist another interpretation of every word we have ever heard which, when taken as a whole, makes the language make as much sense as we think our interpretation does. No matter how unlikely such a possibility is, we need to be aware of its existence. So, to avoid the issue of induction (that is, in order to leave the issue of presumed meaning aside), I proposed the following thought experiment:

Begin with an immortal intelligent alien (immortal because I don't want to place a time limit on the thought experiment) who knows nothing of any human languages. We will provide this alien with a stream of numbers; each number being a specific reference (or label) to a concept, idea or symbol of a language token of some human language. The stream will consist of everything which has ever been written or spoken by a human plus a description of the circumstance surrounding the relevant event. (Think about this as a massive computer record of all this stuff).

By intelligent, I mean that this alien will be able to come up with theories as to what information this stream of data contains. Being intelligent, after a sufficient amount of time, he should (by induction) be able to come up with some idea of what would be a reasonable interpretation of what is meant by some part or parts of the symbolic language being used. Knowing that, he should be able to make some kind of estimates of the correctness of possible statements made in that symbolic language which he could check against what what he has or will receive. Let him put these estimates in terms of the probability he thinks they are valid. This means he is to estimate the probability of the truth of a set of numbers (the numbers representing some statement in that symbolic language). Note that by establishing this theoretical interpretation of the symbolic language, he is creating a mathematical function (the estimate of truth, a probability, is being established as a function of a set of numbers representing some statement in that symbolic language).

If you find any of the preceding confusing, stop here and let me know what part you don't understand or find impossible to comprehend. If, on the other hand, the circumstance described above makes sense to you, continue with the following.
Now, give exactly the same information (in the same form) to a second immortal alien (who has no contact with the first). After sufficient time, one would expect both aliens to agree about the meaning of at least some of those possible statements made in that symbolic language. If you wait long enough, and the quantity of data is massive enough, the possibility of extensive "misinterpretation" should diminish as the aliens, by induction, manage to learn the languages embedded in the data.

That means that the two aliens should agree about the probability (at least to some limited extent) of some statements in that symbolic language (those statements would be expressed by some sets of numbers). As I said, that probability is a number which is then a function of a set of numbers. That means that we are talking about a mathematical function (even if it is only a tabular function). In the cases about which they agree as to the probability of validity, those functions should be very very similar. In fact, if they have made the same interpretations as to the meanings of the symbolic language, they should agree about the validity of expressions. They should both come up with the same mathematical functions (at least with regard to the issues where induction yields a reliable result).

Now, let us add a subtle alteration in the thought problem. Let us give to the second alien, exactly the same set of numbers we gave to the first except for the fact that we will first add a number (any specific number one might choose) to every number in the list. Actually, since these numbers are mere mechanical references (in terms of a computer reference, think of this as a simple address shift of the entire data set), it has utterly no effect on the problem the alien has to solve. When he goes to state his "probability functions", the arguments of his functions are simply shifted by whatever that added number was.

Now let us examine the "probability functions" these two aliens come up with. Since we provided them with the original data, we know exactly what the references refer to including the existence of that numerical shift to the second alien. We know exactly when two "probability functions" refer to the same set of arguments (corrected for the shift). This allows a rather surprising deduction.

If they disagree about the validity of a particular statement, they cannot both be right. At least one must be wrong and perhaps both are wrong. However, if they agree about the validity of the statement, they will have assigned the same probability to the same set of arguments (as seen by us). They may not be correct but at least it is possible their theories are both "reliable" which absolutely can not be the case when they differ. This means that the probability estimate made by alien two's theory minus the probability estimate made by alien one must be close to zero (and, actually zero if they are in fact correct).

Well, this expression divided by the shift number is exactly the form of a derivative with respect to the shift. Since that shift number is absolutely unconstrained, the result holds for any value of the shift number including the limit as the shift goes to zero. Thus it is that, if their theories are to yield the same results for all possible numerical arguments (that would be numerical references expanded to all possibilities) we know that this particular derivative of their probability functions must be zero. That exact shift can also be seen as a simple change of variables where z_i = x_i+ a. Expressing the derivative with respect to a in terms of the arguments z_i leads to a fundamental differential relationship.

This is essentially an extension of Noether's theorem to fundamental theoretical propositions. It is in fact a symmetry argument as it is a direct consequence of the fact that the proposed shift in information coding can not possibly be of any consequence in the analysis of the data even when the data is "language meanings themselves". It may not provide evidence of validity but it certainly provides certain evidence of invalidity as no reliable theory can violate that symmetry. Thus it is a real constraint which may be placed on any theory of any data set prior to applying the theory to the data.

The whole thing can be done in a much more rigorous manner but that requires an attention span beyond what seems to be available. You asked, "in what ways is this alternative superior". It is evidently superior to the standard approach in the simple fact that it gives us another creditable constraint on theories of the same significance as internal consistency itself. In addition, further work along the same lines yields insights simply not available in the standard approach. Insights with deep and profound consequences. All I ask is a little serious interest from a few competent people.

Have fun -- Dick

Knowledge is Power
and the most common abuse of that power is to use it to hide stupidity