It still is the case
that sleeping remains quite
difficult for me. This also makes my life rather difficult, at
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
be the case, in that I do have Sjoegren's
sicca, and Dupuytren's
Contracture, of which the last 2 at least are visible and have been
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
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.
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
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
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
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
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
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
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
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:
To infer conclusions that follow from given
To infer assumptions from which given conclusions follow.
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
Next, here is a simple characterization of abduction by Charles S.
Peirce, who first clearly identified this mode of inference and saw its
"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".)
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:
is a set of statements that accounts for some Observations.
is a statement of particular fact (usually known fact, sometimes
is inferred by abduction from some Observations.
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.
relation between an Observation and a theory is an explanation
if the Observation can be deduced from the Theory.
is a statement about some particular (usually a presumptive fact) that
is deduced from a Theory.
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.
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.
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
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 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."
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.
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
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.
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
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
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
=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
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
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.