June 27, 2013
me+ME: On Hume, symbolization, abduction and induction
1.  On Hume's Fork
2.  The medium Hume was puzzled about
About ME/CFS


It still is the case that sleeping remains quite difficult for me. This also makes my life rather difficult, at the moment.

It keeps going on, and I sleep between 5 and 6 hours each 24, which is not enough, but I also have pain. It probably is connected to the mB12 protocol I follow, but experimenting with it gives no clear clues. And it may also not be the case, in that I do have Sjoegren's Syndrome, keratoconjunctivitis sicca, and Dupuytren's Contracture, of which the last 2 at least are visible and have been medically diagnosed.

The point is that I have too many variables, and those I can manipulate, which are the supplements, make no clear difference. Also, none of these three diseases is well understood, and in a sense I should be glad that now I do have something,
even if not enough sleep is the main one, next to pain.

So... today there are, at least to start with, two notes to Section IV of Hume's Enquiry concerning Human Understanding, that is one of the philosophical classics that I have annotated, in 2005, and I think very well indeed.

One reason is that someone has been seeking materials on Hume's Fork on my site. It is there, and I'll quote it, but indeed it is not very easy to find. Another reason is that I've spend a great amount of time considering just these problems - but I do admit that they are abstract and difficult, and are not considered by many.

Even so, the problems are quite fundamental, and those who disregard them - almost everyone, which in view of their real difficulty may be wise for most - does so by faith.

1.  On Hume's Fork

First on Hume's Fork - and the blue text (not underlined: the underlined blue text within the black text are links) is Hume's:

Notes to Section IV: Sceptical doubts concerning the operations of the understanding

Note 1: All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact. Of the first kind are the sciences of Geometry, Algebra, and Arithmetic; and in short, every affirmation which is either intuitively or demonstratively certain.

This is one of Hume's principles, that incidentally reminds one of a similar distinction by Leibniz between truths of fact and truths of reason. In either case, the distinction seems to me to be incomplete, and to miss something quite important, that may be referred to in Humean terms as Relations of Ideas and Facts, or in modern terms: Semantical Relations.

As the terms chosen indicate, the best and easiest examples of such relations are those that obtain between the terms of a natural language and the natural things they stand for, whatever they may be.

Also, it is clear that these relations must be learned, and have been learned to a considerable extent by anyone who knows a natural language, and indeed have been learned on the basis of associations of the sounds of speech and the facts of experience.

Furthermore, it is clear that these semantical relations relate ideas and facts with the help of the sounds of speech, and that it would be more confusing than helpful to try to reduce these Semantical Relations to either Relations of Ideas or Matters of Fact, precisely because they connect the two, and must be learned, and involve natural language, and are characteristic for human beings, since other animals may as well be claimed to have some Relations of Ideas and to know some Matters of Fact, but evidently lack the ideas required for language that would allow them to tie the two together by speech, and use that to communicate the ideas that have thus been associated to the sounds of speech.

Indeed, it is a curious fact that Hume missed this third kind of fundamental relation, and also that I have not read others who made the same point after him, though it struck me when I first read the Treatise and the Enquiries.

And it is at least fairly obvious that there are in fact three kinds of reports:

- on reality
- on experience
- on symbolizations

These three kinds of reports obviously exist, and there are considerable and systematic differences between them. Reports of real things concern what is there regardless of experience, and this may and often does differ a lot from  reports of experiences of things. And these in turn tend to be rather different from symbolizations in the wide sense of stories, drawings, etc. which involve interpretations of the symbols.

Finally, it should be mentioned here that arguments that involve what is called 'Hume's Fork' are such as to presume that human reason only involves two kinds of fundamental entities 'to wit, Relations of Ideas, and Matters of Fact', and may well be mistaken in missing the Semantical Relations, which are typically human (if indeed not Humean).

So (speaking now, in 2013) for me Hume's Fork is too simpleminded: There also relations between ideas and facts, and these are linguistic or diagrammatic, and by this last term I basically mean: drawn, in any way. But they are mainly linguistic, and they also are typically human: Animals experience facts and have ideas, but they have - it seems, for the most part - no explicit relations between their idead and the facts they experience, that are symbolical.

And the last link is to an item in my Philosophical Dictionary, as follows:

Symbol : Arbitrary sound, mark or gesture - all usually capable of being easily repeated or copied - that represents something by human convention.

Note that symbols are considerably more sophisticated than signs, and that quite a few non-human animals are quite capable of understanding signs, but all non-human animals find it hard or impossible to understand symbols.

Part of the difficulty is that symbols depend on convention, and as a rule have nothing in common with whatever they mean, and another part of the difficulty is that symbols may stand for mere ideas, fantasies, or even impossibilities, and thus require that whoever understands the symbol is aware that it may refer to what someone thinks or feels or what is thought or felt about, or both.

So it seems to me Hume really missed something, that also is exquisitely (nearly) human: the symbolical relations between ideas and facts.

2. The medium Hume was puzzled about

Next, Hume posed the problem of induction, but did not solve it. I treat it in part of my Note 24 to the same chapter or
Section IV:

And here I shall now also provide an answer to Hume's other problem 'There is required a medium, which may enable the mind to draw such an inference, if indeed it be drawn by reasoning and argument. What that medium is, I must confess, passes my comprehension; and it is incumbent on those to produce it, who assert that it really exists, and is the origin of all our conclusions concerning matter of fact.'

In brief, the answer is: Abduction - the mode of inference that consists in the proposing of hypotheses to account for (supposed) facts.

First, what is an inference? In logic, an inference is the assertion of a conclusion, in general because one has already asserted (and thus accepted) certain premisses one considers sufficient to assert the conclusion.

There are three basic kinds of inference, that cover very many specific sorts of inferences:

1. Deductions: To infer conclusions that follow from given
2. Abductions: To infer assumptions from which given conclusions follow.
3. Inductions: To confirm or infirm (support or undermine) assumptions by showing their conclusions do (not) conform to observable facts.

Normally in reasoning all three kinds are involved: We explain supposed facts by abductions; we check the abduced assumptions by deductions of the facts they were to explain; and we test the assumptions arrived by deducing consequences and then revise by inductions the probabilities of the assumptions by probabilistic reasoning when these consequences are verified or falsified.

Next, here is a simple characterization of abduction by Charles S. Peirce, who first clearly identified this mode of inference and saw its importance:

"Abduction. (..) "Hypothesis [or abduction] may be defined as an argument which proceeds upon the assumption that a character which is known necessarily to involve a certain number of others, may be probably predicated of any object which has all the characteristics which this character is known to involve." (5.276) "An abduction is [thus] a method of forming a general prediction." (2.269) But this prediction is always in reference to an observed fact; indeed, an abductive conclusion "is only justified by its explaining an observed fact." (1.89) If we enter a room containing a number of bags of beans and a table upon which there is a handful of white beans, and if, after some searching, we open a bag which contains white beans only, we may infer as a probability, or fair guess, that the handful was taken from this bag. This sort of inference is called making an hypothesis or abduction. (J. Feibleman, "An Introduction to the Philosophy of Charles S. Peirce", p. 121-2. The numbers referred to are to paragraphs in Peirce's "Collected Papers".)

Accepting the conclusion that an explanation is needed when facts contrary to what we should expect emerge, it follows that the explanation must be such a proposition as would lead to the prediction of the observed facts, either as necessary consequences or at least as very probable under the circumstances. A hypothesis then, has to be adopted, which is likely in itself, and renders the facts likely. This step of adopting a hypothesis as being suggested by the facts, is what I call abduction. (Idem, p. 121-2)

Abduction (..) is the first step of scientific reasoning, as induction is the concluding step. Nothing has so much contributed to present chaotic or erroneous ideas of the logic of science as failure to distinguish the essentially different characters of different elements of scientific reasoning; and one of the worst of these confusions, as well as one of the commonest, consists in regarding abduction and induction together (often also mixed with deduction) as a simple argument.

Accordingly, it seems as if what is true of theories conforms to the following diagram, that involves 6 named arrows and three kinds of inference I will briefly comment on:

  • A Theory is a set of statements that accounts for some Observations.

  • An Observation is a statement of particular fact (usually known fact, sometimes presumptive fact).

  • A Theory is inferred by abduction from some Observations.

  • An abduction is an inference towards the best explanation for (presumed) facts. As a rule, abductions are creative hypotheses that may involve guesses and assumed postulated entities of many kinds.

  • The relation between an Observation and a theory is an explanation if the Observation can be deduced from the Theory.

  • A Prediction is a statement about some particular (usually a presumptive fact) that is deduced from a Theory.

  • An induction is a re-calculation of the probability of a theory, given that a Prediction of the theory is found to be true or false in fact. It is a deductive consequence based on probability theory.

  • A test is the deduction that a certain Observation is in fact implied or contradicted by a Prediction from  a Theory, and thus may serve for an inductive argument about the probability of the Theory.

  • An expectation is the deduction that an Observation is implied by a Prediction from a Theory.

It should be noted that all relations represented by arrows in the diagram other than abduction are deductions, but that what is here called induction also involves probability theory, next to standard logic, which is what is used for the other deductions indicated in the diagram.

What is here called induction is otherwise known as Bayesian reasoning, and consists in essence in recalculating the probability of a theory using probability theory and facts from experience.  

Next, what is here called abduction is normally a creative leap to account for some puzzling fact, and is based on imagination, fantasy, analogy or anything else that may be useful to account for something one has no ready-made convincing explanation for.

Abductions, in the form of the theories they produce, are tested and checked in two ways: First, by deducing the facts they are meant to explain from the theory that is supposed to explain them, and this is a necessary condition for the abduction to make sense. Second, by induction in the above sense, to infer what the probability of the theory should be given that one has made an observation that is implied or contradicted by a prediction that follows from the theory.

So - speaking now, in 2013 - this is part of my solution to Hume's problem of induction: It gets mostly (dis)solved by abduction, which is a relation of inference first clearly described by Charles Peirce. I quote from Wikipedia, minus a note:

In 1903 he presented the following logical form for abductive inference:

The surprising fact, C, is observed;
But if A were true, C would be a matter of course,
Hence, there is reason to suspect that A is true.
The logical form does not also cover induction, since induction neither depends on surprise nor proposes a new idea for its conclusion. Induction seeks facts to test a hypothesis; abduction seeks a hypothesis to account for facts. "Deduction proves that something must be; Induction shows that something actually is operative; Abduction merely suggests that something may be."

It is in this sense that I, as well, speak of abduction. Then again, though Hume did not see this, and though this does bring the solution of his problem of induction closer, it does not resolve all problems, which require an assumption of the following form, which I take from my problem of induction, also in my Philosophical Dictionary (and "p(T|P)"  = "the probability of T given P")

The fundamental problem is that one never has just p(T|P) - one always has

(6) p(T|P&X)

where X may be all manner of other facts that occur together with P, that may or may not be relevant, and that may indeed also cover the case considered above, namely that it concerns experienced P's - for in the probabilistic form just given, and with 'E' for 'is experienced', the problem is how to validate the move from p(T|P&E) to p(T|P), just like above the problem was how to validate the move from (y)(Ty & Ey => Py) to (y)(Ty => Py).

But the problem is also considerably more general: X may also include references to the methodology of the experimental set-up; to the stars; to the mole on the subjects face; to the number of days since the prophet Mohammed died; or to anything else that happens to be also true when P is true - and that may be relevant to P or to T or to both, or not.

6. The inductive condition: What one needs, it would seem, to deal with this problem, is a postulate of the following form, that must be added to any empirical theory one seriously proposes, and that I shall call IC (for Inductive Condition). It concerns a theory and its predictions, and is added to it as an assumption. There are several possible equivalent statements of the IP, one of which is:

(IC): For theories T, predictions P and any arbitrary circumstances Q:
      TrelP => PrelQ IFF (PrelQ|T)              

That is: If the theory T is relevant to P then the prediction P of the theory is relevant to Q if and only if P is also relevant to Q if T is true.

Intuitively, a theory and a statement are irrelevant to anything they do not imply anything about, while the irrelevancies in the hypothesis of (IC) are defined as is usual in probability theory: AirrB =def p(A&B)=p(A)*p(B) which in turn is equivalent with p(B|A)=p(B) in any case p(A)>0.

This consequent of (IC) - that claims conditional irrelevance - is defined probabilistically as follows:

(7) P irr Q | T =def Q|P&T=Q|P

Having this, one can proceed as follows, noting that PrelQ IFF (PrelQ|T) IFF PirrQ IFF (PirrQ|T) and supposing that theory T makes prediction P which also is irrelevant to Q, while T satisfies (IC):

(8) T|P&Q=T&P&Q:P&Q       by def
             =T&P&Q:P.Q        by PirrQ
             =Q|T&P.T&P:P.Q   by def
             =Q|P.T&P:P.Q      by P irr Q if T
             =Q.T&P:P.Q         by PirrQ
             =T|P                  by def

And thus one has arrived where one wanted, only using (IC) plus probability theory. And thus one can learn from experience, and confirm one's theories, and those theories one does not need to infer from experience, but can merely propose to explain one's experience, and then use further experience to confirm or infirm one's theoretical guesses.

I am aware that I probably have pleased very few with the above. Yet it concerns quite fundamental problems, that indeed are well explained by my problem of induction. Also, I am aware that few or none sees it as I do, but then - to the best of my knowledge, that is vast in this field - that is a pity for the others.

Finally, I am also aware Bertrand Russell wrote, long ago, that there is a special place in hell for philosophers who believed that they had solved the problem of induction.

Ah well... I may be mistaken, but I do not know where, and I do not know anyone else who made my distinctions, in the way I have.

P.S. The above has been written in the evening of June 26. It depends on my time and energy the next day, whether there will be another file. (There may be, for while I have to do things, I also have to sit. But I make no promises.)


[1] To simplify notation here the p(.) is deleted. If you need it, add it mentally: It means the same.

About ME/CFS (that I prefer to call M.E.: The "/CFS" is added to facilitate search machines) which is a disease I have since 1.1.1979:
1. Anthony Komaroff

Ten discoveries about the biology of CFS(pdf)

3. Hillary Johnson

The Why  (currently not available)

4. Consensus (many M.D.s) Canadian Consensus Government Report on ME (pdf - version 2003)
5. Consensus (many M.D.s) Canadian Consensus Government Report on ME (pdf - version 2011)
6. Eleanor Stein

Clinical Guidelines for Psychiatrists (pdf)

7. William Clifford The Ethics of Belief
8. Malcolm Hooper Magical Medicine (pdf)
Maarten Maartensz
Resources about ME/CFS
(more resources, by many)

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