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The plan of this essay is as follows. I first address the fundamental concepts
relating to knowledge: truth, reality and certainty; I then discuss logic,
inference, deduction, induction, proof and disproof. After denying the
validity of induction I present the Scientific Method as understood and
clarified by Popper. In doing so, I highlight the role played by "epistemological
hysteresis" or faith in this process. I then reflect on how all this relates
to Plato's epistemology and then relate the theoretical framework that
has been developed to ethics and education.
One of the distinguishing marks of human beings is inquisitiveness, the
appetite to learn: to acquire knowledge and expertise. This is especially
characteristic of children, who know that they have much to learn and generally
enjoy doing so. It is less characteristic of adults, who tend to believe
either that they "know it all" already or that they will never get to grips
with some topic and so give up the struggle to learn and acquiesce in their
ignorance. In the worst case, the attitude will be adopted that because
something is perceived to be beyond their understanding it isn't important
or "relevant to their lives".
Scientists are fearless children who have never "grown up",
and insist on asking that most annoying question:
are adults who have realized that reality is dangerous.
They have become fearful and insecure.
They try to obtain security by telling themselves that they have all the
They reinforce this by imposing their simplistic answers on others.
are adults who have realized that reality is complex.
They have become confused and insecure.
They try to obtain security by telling themselves that it doesn't matter.
They insist that truth must be cut down to the level of their own mentality.
They reinforce this by denying the truth of any theory and opposing any
The importance of knowledge
Plato taught that almost every positive characteristic of a human being
could be identified as a form of knowledge or expertise. Hence for a Platonist,
epistemology: the study of what knowledge is, how it can be identified
and distinguished from what might masquerade as knowledge and how it might
be acquired is of acute importance.
Two types of Knowledge
Knowledge comes in two species. The first is theoretical knowledge and
the second is practical. Theoretical knowledge gives an understanding of
what is happening in the environment of the knower. It enables him or her
to decide, as a subject, what is beneficial or harmful and helps the subject
to set objectives that - if met - will result in them flourishing. Theoretical
knowledge also results in pure intellectual pleasure. It is not necessary
for it to have any bearing on life for it to be worthwhile in itself. The
obtaining of such knowledge is itself a game, and can be enjoyed for its
own sake, just as can any other game. Practical knowledge - or expertise
- gives an understanding of how to accomplish objectives that have been
set. It informs the activity of the knower as an agent, enabling him or
her to act effectively and with minimum cost, risk and effort. Practical
knowledge generally requires a basis of theoretical knowledge or the environment,
but additionally, it requires self-knowledge: an understanding of the knower's
potentiality, talents and limitations.
Conventionally, knowledge has been linked with the notions of "reality",
"certainty" and "truth": to know something is to know that it is certainly
true and real. Before proceeding further, it is necessary to consider these
What is truth?
Any sufficiently complicated living system will have internal states that
map onto and so represent aspects of the present and past environment
of the life-form. These states can be identified as impressions and memories,
they are ideas. Whether these states exist as solitonic waves or within
a neural net is of little importance. In each case, some representation
of external reality exists in the internal states of the system. Truth
can be understood as "correspondence with reality" [Aristotle,
A. Tarski, K.R. Popper]. The correlation of an idea with the state
of the environment that is supposed to correspond to it is its verisimilitude
or degree of truth. Of course quantifying such a metric is a difficult
What is reality?
This is a difficult question. As an "Objective
Realist", I want to say that reality is the object of our knowledge. It
is the environment in which we exist and which would itself continue to
exist even should all human beings - and indeed all knowing or conscious
beings - cease to exist. According to the late professor Richard Feynman,
reality has the habit of kicking back when we kick it. It doesn't let us
have our own way, but rather insists on having its way with us. This reality
is constituted from what we call "things" which exist in "space-time".
Space-time is, in fact, just "when and where things can be". I accept
that this answer is no more satisfactory than the answer I elsewhere try
to give to the question "what is consciousness?" I rather suspect that
the reason it is difficult to answer either question is pretty much the
Of course, there are others: "Subjectivist
Relativists", who discount the idea of objective reality and insist
that reality is a construct of the conscious individual: a theory imposed
upon their experience, of their own volition, in order to bring pattern
to what would otherwise be chaotic sense data. Such people do not distinguish
between "reality" and "truth" and proceed to conclude - rightly in their
own terms - that no one account of "reality" is to be preferred over any
other. As "reality" is no more than a personal construct, each person is
entitled to their "own truth" and no-one else has any basis on which to
dispute its validity.
In my view, this whole outlook is based on a confusion between the ideas
of "truth" and "reality". In the end it is indistinguishable from "pure
idealism" which makes reality into a world created by the imagination of
the observer. Moreover, it begs the questions:
Where does the sense data that are to be organized originate?
How does it happen to be possible to organize them if, of themselves, they
Why it is that the accounts of reality that most people give are quite
In particular, how it is that physicists are able to agree on a common
set of equations?
How is it that people are able to experience phenomena as external to themselves
that they are altogether incapable of causing or even conceiving of themselves?
In particular, how can people with no musical talent listen to and enjoy
In particular, how can scientists can read and understand research papers
that propose new ideas that they personally had not thought of?
What is certainty?
Certainty is a self-referential concept. One would be certain of something
if one knew that one knew it. Either it is a redundant concept: any knowledge
necessarily involving certainty, or it is unattainable: involving an infinite
regression of knowing. Cardinal Newman introduced the idea of "certitude"
to try and nuance this problem. He suggested that one could gain sufficient
"certitude for action" by the accumulation of evidences, none of which
was sufficient to justify certainty ["Grammar of
Assent" (1870)]. This brings us immediately to one of the central
problems of epistemology: that of induction.
Proof and Disproof
Conventionally, two means or procedures are posited by which knowledge
may be obtained, these are named induction and deduction.
Deduction depends on the acceptance of some system of logical inference,
by which the truth or falsehood of one proposition "the conclusion" can
be determined from the truth or falsehood of (an) other proposition(s)
"the premise(s)" on which it is
supposed to depend. Many such systems have been invented by ingenious
philosophers and mathematicians, but the one that seems to be "true" of
the world in which we live is the simple deductive system first codified
In this system, called "Classical Inference", disproof is almost as important
as proof, and can often be easier to obtain. Typically, a proposition can
be disproved just by showing that it involves a contradiction. In which
case it is said to be is self-inconsistent or incoherent and the proposition
is said to have been "reduced to an absurdity" (reductio ab absurdem).
The importance of disproof lies in the fact that it gives rise to a means
of proof. This is because, according to Aristotle's "Law of the Excluded
Middle", if some proposition can be shown to be false, then the exact
inverse of this proposition must be true. Hence if it is absurd to say
"such and such" then "not such and such" must be true.
Note that I would say that while I accept and always attempt to employ
Classical Inference because I believe that it is valid and applicable to
the real world. I would not say that it was "true". This is because "truth"
is the (degree of) correspondence between an idea in someone's mind and
some aspect of objective reality. Now, the laws of Classical Inference
are not "things" that exist "out there". There is no Form of "The Law of
the Excluded Middle", for example! Hence although my conviction that Classical
Inference is trustworthy and applicable is intuitive, I would not describe
it as "self-evident knowledge", as I do not think that it is any
kind of knowledge, but rather a "manner of proceeding" that I have adopted
and will continue to employ until I am forced to reject it in favour of
some other methodology.
The liar paradox
The liar paradox is central to the problem of
truth, for it sets out to show that the very concept of truth is self-contradictory.
In brief it asks one to consider a man who says: "This statement is a lie".
Now, it would seem that:
This paradox can be resolved in a number of ways. The most obvious is to
allow of a third option besides "true" and "false", namely "meaningless".
This is supposed to be the logical condition which characterizes propositions
which are formed correctly according to the rules of syntax and grammar
and yet are self-contradictory. The main problem with this proposal is
that it makes it difficult to make use of Aristotle's Law of the Excluded
Middle: for as we have seen, the fact that the first premise was shown
to be false did not imply that its negation was true.
Because every statement must be either "true" or "false",
that the man's claim must be either "true" or "false".
However, if it is "true",
then it is not "a lie" (for a lie is a "false statement")
and the statement is "false",
which is the opposite of what we assumed.
Hence this premise is contradicted by absurdity.
Similarly, if it is "false",
then it is "a lie"
and the statement is "true",
which is the opposite of what we assumed.
Hence this premise is contradicted by absurdity.
Hence the statement is neither "true" nor "false",
and neither is the statement:"the man is lying".
I prefer to take the following view. An idea is true if it corresponds
to some thing that is objectively real. It is false if it claims such a
corresponence but in fact does not so correspond. The statement "This statement
is a lie" never makes reference to any thing, but only to itself. All that
can truly be said of the statement is that it is a correctly formed statement.
It does not have an truth value on its own account. Moreover, it
can not attain one spontaneously, but would somehow have to be given one,
and there is no means by which this can occur. The statement exists in
a universe of its own. Hence, the statement cannot possibly be true, simply
because it is never established in relationship to the Cosmos, which relationship
alone could validate it. The statement is merely "a noise". Similarly,
the statement is not "a lie" because a lie has to refer (falsely) to some
supposed real thing, but this statement does not do so.
In brief, the statement is false (i.e. not true: it does not correspond
to any real thing) and yet it is not a lie (because it does not wrongly
correspond to - or contradict - any real thing).
The paradox can be reformulated in an attempt to frustrate this analysis
as follows: consider a man who says "This statement is false." However,
the flaw in the paradox now becomes apparent. What can is mean to say that
the statement "is false" when it isn't a statement about any real thing?
From the point of view of the value to be attributed to the statement,
it is clearly "false" in the sense that it does not refer to any real thing,
yet this does not then justify us allowing its self-referential claim.
The propagation of truth
The excellence of this system is simple.
This means that truth can be propagated from a small set of premises to
a wide range of conclusions. This is a central activity of mathematics,
which is basically the exploration of the consequences that result when
some set of premises - generally known as axioms - is postulated as being
true. In mathematics, this process is relatively unproblematic.
axioms are true just because they are axioms. Manifestly, the idea
of the axiom corresponds precisely to the reality of the axiom, simply
because the reality of the axiom is nothing other than the idea of the
axiom! The only difficulty is that it can be shown that some propositions
can be unknowably true. Whereas they follow from the adoption of
the axioms, their truth can in no way be established by any process of
deduction. These propositions are rather like offshore islands, with no
bridge or causeway or ferry service linking them to the mainland of truth.
This result is known as Goedel's Theorem.
an argument that conforms to Classical Inference links them to some conclusion
Aristotle's rules of inference are valid
that conclusion is just as true as the premises.
The origin of truth
In the physical world, deduction is up against a formidable problem. Where
can it start from? How does one come by true premises, in the first place;
from which true conclusions may be deduced? Moreover, how can one know
that the very process of Classical Inference is valid? Conventionally,
these questions are answered by two additional proposals.
Traditionally, the Church has assumed that still a third category of truths
are only attainable with the exercise of faith. All of this strikes me
Some premises are self-evidently true and
Other premises can be established as true on the evidence of experience
by the process called "induction".
The idea of "self-evident truth" is a dangerous conceit, according to which
the human intellect is supposed to be able to grasp that certain propositions
are absolutely necessary. Now, in the history of human endeavour, whenever
it has been thought that something is "just obvious" it has later transpired
that this thing was in fact false. The Galileo story
is instructive in this regard. Moreover, such an entrenched view has typically
resulted in the stagnation of th(os)e area(s) of knowledge to which it
Those truths which may seem to be self-evident are, I suspect, nothing
more than axiomatic syllogisms. "One plus One equals Two" is true, by definition,
within a simple system of abstract integer arithmetic. It does not follow
that it is true in the sense of "corresponding with physical reality".
Indeed, as far as the physical universe is concerned: the more that "plus"
signifies anything, the less accurate is the equation. The interactions
between the first "One" and the second "One" (think of the masses of two
electrons) tend to affect the value of the "Two". Much of physics is concerned
with accounting for such interactions, on the basis that they can be analysed
in terms of other delineable and non-interacting things. So: masses
do not add because of forces; velocities do not add because
of relativity; volumes of liquids do not add because of surface
tension, and so on. The root problem here is that while on the one hand
the only real numbers are the positive integers (no-one could ever see
"five thirds of a Zebra") on the other hand the only things that are properly
characterized by the positive integers are particles, and these are exactly
the kind of things for which association implies significant interaction.
Popper has shown that "inductive reasoning" is invalid, on a number of
grounds [The Logic of Scientific Discovery (1934,
1968)]. In brief, Popper points out that no matter how much clear
and incontestable evidence may exist that is consistent with (and supports)
some proposition, as soon as a single piece of clear incontestable evidence
is discovered that is inconsistent with that proposition, then that proposition
is immediately known to be false. Hence, it cannot be that "the more
evidence there is in favour of some proposition, the more certain we can
be that it is true." In practice, he asserts, induction is never
used in developing models. It is
often thought to be used in this
way, because it is easy to confuse it with the method that is actually
used, namely that of "Conjectures and Refutations"
[Popper (1963)]. This process is described and discussed below.
Cause for epistemological
We see the world in terms of edges of objects because our retinas and optical
cortex are preconfigured to detect and emphasize (straight) lines. We perceive
faces in arrangements of shapes because we are especially interested in
faces and pre-disposed to see them even where they do not objectively exist.
Similarly, we hear rhythms because our ears hunt them out in preference
to random sequences. We interpret the words and actions of others in terms
of our past experiences: projecting motivations and extrapolating outcomes.
When we decide to act, our decisions are flavoured by the relative importance
and detailed significance we give to various factors: our personal security;
the pleasure or pain anticipated; the long term effect on inter-personal
relationships and so on. This is where our choices are either well ordered
or disordered. Our decisions are also affected by other mental characteristics
or habits (vices and virtues) like impetuosity, compassion, complacency,
trust, cynicism or credulity. As we act, our actions are limited by our
capabilities: for example, our propensity to fumble; stutter; forget a
minus sign, guess, imagine and inspire.
How then does one ever learn anything? How can
one grasp what is true? What use are physics experiments, if the results
obtained are themselves always subject to interpretation and diverse resolution?
The answer is simple. One should not expect immediate and absolute answers
call. "Human knowledge" is never absolute "episteme":
either an immediate knowledge of a thing by intuitive apprehension of its
inner form, or certainty obtained by remorseless induction. It is always
and inevitably subjective and provisional, obtained by a process of continual
approximation. The best kind of knowledge
that anyone can ever have of anything is confused at least by one's one
subjective assumptions and prejudices. This kind of knowledge is called
"doxa" in Greek and "belief" in English. Sometimes, one's belief can, with
some good accuracy, correspond to objective reality. In such a case, the
belief is "true", and the Greek adjective "ortho-doxa" is appropriate.
Conjecture and Refutation
Popper argues that induction is un-necessary. The way in which we gain
knowledge of the real world is via "conjecture and refutation", as first
demonstrated by Plato in "Meno". When
confronted with an open question, the researcher tends to guess an answer:
based on intuition, hope and prejudice (as it may be - the origin of the
hypothesis really doesn't matter!) and then checks, using deductive
reasoning, whether the conjecture is consistent with experimental observations
and other propositions currently accepted as true.
Any guess that fails is provisionally rejected as being false.
The first hypothesis that stands up to a lot of testing is provisionally
adopted and graced with the description "Theory".
If after a while, when no proposition has been found that answers the question
in a manner consistent both with experimental evidence and those propositions
that have previous been accounted to be true,
then this background knowledge
is itself subjected to scrutiny.
The question is asked:
"Is it possible to modify the system of premises
according to which I currently evaluate my experience,
in such a manner as to admit an answer to the new
without detracting from my ability to respond consistently
to those questions that I have previously had success
If this - extremely difficult and sophisticated
- process succeeds,
it will result in a type of revolution or catastrophe:
a paradigm shift,
in which the system of interpretative premises that
had previously formed
the researcher's world view is exchanged for a different
It is as if a person trying to get to the centre
of a maze has had to admit
that at some point they took a wrong turn and has
been forced to retrace
their steps in order to try an alternative way forward.
If this process fails, a crisis situation develops.
The researcher is confronted with a question that
simply cannot be answered.
The Scientific Method
The process just outlined is roughly what is meant by "The Scientific Method".
It should be noted that it can never unequivocally establish truth. This
for two reasons. First, the interpretation of any observation is richly
influenced by the theoretical perspective and expectations of the observer.
Hence the significance of some fact may be either over- or under-rated,
or even entirely misconstrued. Second, no number of confirmations of a
theory can amount to its certain proof. There might always be some as yet
unexplored or even unenvisaged circumstance in which it fails.
In order to give a break from the relentless presentation
of my own viewpoint, I next comment on parts of a correspondence that I
received a while back.
"Life is big. It is really big!
It is so big and complex that we can not hope to comprehend it all
in our lifetimes, or even in the lifetime of the entire human race. We
are lucky if we can comprehend even a small amount of it, enough to survive
and even thrive. Because life is so big the first thing that we do as individuals,
societies and a species is hack out a working model that will allow us
to function on a day-to-day basis. As our needs become more complex so
do the models we make to meet our needs."
I largely agree with these comments. However, I take exception to the negative
evaluation associated with making models. The process is described as "hacking
out"; the epithet "working" is added
to the word "model" and the purpose of a "model"
is said to be "to allow us to function on a day-to-day
basis" and "to meet our needs". As
a Physicist, I want to be more positive. First, I would distinguish between:
Theories are always inadequate, but as we progressively refine them by
"conjecture and refutation" we can hope that they will tend towards the
limit that is "episteme". The development
of theory should always be reckoned as an activity that is aspirational
after truth (Episteme) rather than just expedient and "make do". There
is no need to be negative regarding this process, even if it should prove
to be a Never Ending Quest!
theories, on the one hand:
attempts at an authentic description of objective reality;
and models, on the other:
pragmatic (possibly phenomenological) rule sets, or
conscious simplifications of a theory that is too complex to apply in some
Moreover, I am unhappy with the simplistically Utilitarian slant of
the paragraph. Theories are not only changed in response to an increase
in the complexity of our functional needs, but also in response to the
growth in our understanding of the world and as our experience widens and
deepens. Obviously, these processes are associated with each other: science
and technology go hand-in-hand; but General Relativity did not in any way
arise "as our needs became more complex",
neither was it proposed in order "to meet our needs".
"Models are abstractions of the human
mind. They exist as a tool used by humans beings to impose order on our
environment so that we can function on a daily basis as individuals, and
as cultures and societies. Our models reflect how we understand ourselves
and our world."
A "subjectivist-relativist" spin is introduced
here. This view tries to turn epistemology into anthropology. It is deeply
damaging to any notion of truth. Models - still less theories - do not
order on our environment". Rather they enable us to make predictions
about it. Our environment doesn't change or cease to be disordered just
because we invent some model or other. Our models and theories do not reflect
rather precisely are our understanding of ourselves and
our world. Our models and theories reflect (imperfectly) what is
objectively the case about ourselves and our world.
"So far, so good. The next question,
or rather set of questions is how are our models developed, how closely
do they reflect reality and how often are they updated? Models, and by
extension, traditions are not bad per se if they are developed and maintained
in a responsible manor."
All models and (human) traditions are provisional, by the very nature of
what they are. However, the Apostolic Ecclesial
Tradition (The Gospel) is not. No more is Physical
Reality. Of course, our understanding of Apostolic Tradition
in a similar manner to our understanding of Physical Reality: but The Gospel
Tradition and Physical Reality are both objective, not culturally based
"They are necessary if we are to be a
cohesive body and not fall into anarchy and, ultimately, become extinct.
However, they are bad and they do damage when they are maintained in spite
of contradictory evidence. And that seems to be the case with certain
Again, the justification for a model (or tradition) is given in terms of
expedience. This is true as far as it goes, but is inadequate. Manifestly,
if a theory is wrong it will give rise to wrong predictions and will mislead
its adherents. This may result in their extinction; but even if it doesn't
they will not prosper in the way that they would if they were better informed
about the world in which they lived. Moreover, many of the deepest theories
of Physics are of no practical use and have no impact on the survival prospects
of the human race. In the terms of this paragraph they are not "necessary"!
Needless to say I deplore such a negative judgement of physics theories
such as QED, QCD, GR etc. etc.
Finally, I argue below that it
is generally wise to maintain an established theory for a while "in
spite of contradictory evidence".
Certain dynamic processes internal to a complex organism may represent
analogues of external systems. These will be more than just memories or
impressions of observables, but amount to theoretical models of reality.
They will yield predictions of future phenomena. A theory that makes
many accurate and pertinent predictions is worthwhile: it may enable the
life-form that has developed it to anticipate external threats and opportunities
and so "live long and prosper". It is a "correct belief": "ortho-doxa".
A theoretical model that makes a single wrong prediction, while perhaps
being still of some (great) utility (e.g. Newtonian Mechanics or Gravity)
is "falsified" and must be replaced, according to the process of "conjecture
While it is much easier to falsify a theory than prove it; even disproof
is problematic. What constitutes falsification is itself theory laden.
What may at first appear to be a falsification of some theory may in fact
turn out to be the disproof not of the theory that was meant to be under
test, but of some piece of "back-ground
knowledge" that was presumed to be true and was not meant to be under
investigation at the time. Discerning the significance of experimental
evidence is an art form in its own right!
It is commonly thought that Science deals with certainties, whereas
Religion deals with matters of sentiment. Nothing could be further
from the truth! Natural Science never deals with proofs, but only with
disproofs. No scientific proposition is definitive or certain. All are
provisional and subject to reformulation if not rejection, with the passing
of time. Even the most deeply held principles of Physics, such as relativity,
are subject to continual re-evaluation, doubt and dispute: and rightly
so. It is by their being held to account against experiment that they are
tested and exonerated: or not! As a theory successfully withstands more
and more provocative and stringent tests, then one's confidence (faith
or belief) that it is trustworthy (note the religious language) builds
up. Once a certain (arbitrary) point is reached, one tends to dispense
with a previous or competing theory which is known to be inadequate and
to adopt the successful theory as part of one's paradigm of nature. This
sudden transition (paradigm shift or "leap of faith") is an example of
a "catastrophe": a discontinuous response to a slow build-up of data.
Hysteresis in Physics
Hysteresis is a phenomenon generally encountered in physics and mathematics.
An every-day example is the electrical light switch. This has two states
"on" and "off" and it is possible to switch between these two states by
pressing a small lever. The lever resists small forces, however. An internal
spring is arranged in such a way that the lever is held in place until
a fairly large force is applied. In order to grasp the idea of hysteresis,
first consider the process of "turning on" a switch which is originally
At first the switch is off and no force is being applied.
Then a small downward force is applied to the lever.
The spring resists this force.
The lever does not move significantly
and the switch remains "off".
Then a moderate downward force is applied to the lever.
The spring continues to resist this force.
The lever moves significantly
but the switch remains "off".
Then a large downward force is applied to the lever.
The spring is not strong enough to resist this force and buckles.
The lever suddenly flips its position and the switch turns "on".
As the force is removed
the spring holds the lever in its new position
and the switch remains "on".
At first; when no force was being applied, the switch was in its
but now; when no force is being applied, the switch is in its
Hence, for this simple system, the present stimulus or "input" does not
determine its present state or "output".
Only if the force applied is greater than the strength of the restraining
spring does it unequivocally determine the state of the switch.
In order to be able to predict the present state of the switch (or understand
why it is what it is) it would be necessary to know the past history of
the stimulus back to a moment in time when
the stimulus was sufficiently large that it did definitely determine
the state of the system was otherwise specified.
even moderate changes in stimulus cause no change in the state of the
a very small change causes a dramatic (technically a "catastrophic")
change in the state of the system.
This means that there is a discontinuity in the relationship between
steady-state input and steady-state output.
This behaviour is characteristic of systems with "positive feedback".
These are systems which "prejudice themselves" by taking part of their
input from their output.
This inclines them to favour (and so tend to remain in) whichever state
they are currently in.
A large contrary stimulus is required in order to overcome this bias.
In electronics, the simplest such circuit is the Schmitt Trigger.
It is not necessary that the output of such a system is strictly binary.
Some systems behave like a light switch soaked in "goo".
For these, the catastrophic change is smoothed out; and no discontinuity
The applied force must always be changed (a little) in order to change
the angle of the lever a little.
The lever is stable in any orientation.
The most familiar example of this kind of behaviour is the magnetization
of an iron core by a solenoid.
In all cases, "hysterical" behaviour is characterized by a graph with a
"loop" in it.
The response of the system to a smoothly decreasing stimulus is not to
retrace its response to a smoothly increasing stimulus.
The discrepancy is indicated by a gap that opens up between the two plots
of "response" vs "stimulus".
If the system is continually cycled between extreme positive and extreme
then the plot of its "output" vs its "input" will be a "hysteresis
loop" of some kind.
Epistemological hysteresis is a result of memory. Memory makes present
and allows to be taken into account past experience and evidence, so that
a truly balanced judgement can be made. Indeed physical systems that exhibit
hysteresis are sometimes described as having a memory and may be used to
implement memory functions in computers.
Other aspects or names for "epistemological hysteresis" are "conviction",
"loyalty" and "faith". These all speak of the maintenance of some stance
against present (short-term) difficulties or positive incentives to change
that stance. The man with little hysteresis in his decision making is either
ignorant (and so has no past information to justify any stance) or foolish
(and so unwilling to grant any significance to evidence of any kind: past
or present). The fool will be a "vicar of Bray" personality: willing to
go along with the latest fad, wishing only to please either those in authority
over him or the latest person that he happens to meet. He has a backbone
of straw and will be utterly unreliable and faithless.
Faith and Certainty
Religious faith is no different in species than any
other kind of belief. It is a compelling opinion concerning matters that
are sufficiently important and which is held with sufficient conviction
as to motivate action. At the heart of faith there must be both doubt (for
else faith becomes fanaticism) and love (for else faith becomes faint-hearted).
Though belief is never absolute certainty, it can and should be
"certain enough for action". Faith involves the
will as well as the reason.
There is a close correspondence between the scientific method and the
life of faith. Both Science and Religion are based on evidence. In neither
case is the evidence conclusive. In both it is natural and necessary to
adopt as working certainties conclusions that are not formally certain
[Newman, "Grammar of Assent" (1870)]. In both is it necessary to
remain open to other, as yet unimagined, possibilities if progress is going
to be made. The basic difference between Science and Religion is that it
is not generally possible, practicable, admissible or appropriate to conduct
controlled experiments to test religious theories. It is for a similar
reason that it is not possible to conduct psychological experiments on
a friendship or romantic relationship: to
do so would call into question its basis, and so destroy the very thing
that one was attempting to investigate. Human relationships have to be
conducted on the basis of faith and trust and sincerity: not according
to "double-blind" controlled laboratory conditions!
Establishing a view of the world is not a neat process. Induction is
invalid and potentially misleading. Deduction, though valid, requires axioms:
which are not available! Knowledge advances, but always within a Cloud
of Unknowing. Progress can only be made by guess-work and intuition.
Empiricism is an act of faith. It is based on the conviction that the world
is comprehensible and coherent, unlike a nightmare or "Tom and Jerry" cartoon.
This metaphysical conviction is empirically justifiable in no way,
that it works: it is the basis of all Western Civilization's science
and technology. In every form of human inquiry faith necessarily precedes
knowledge. Physics is as dependent on faith as is Theology.
Rather than three categories of knowledge:
I contend that there are only two:
which pertains to the Cosmos: which is
which can be "observed"
by an interchange of mass-energy.
These differ only in their subject matter, not in their species.
which pertains to God: who is
beyond the Cosmos,
and with whom physical interaction is impossible.
The astute reader will note that my first
problem remains. At the start of the process of learning, it would
seem that one knows nothing: in which case the process of conjecture and
refutation cannot be employed and no knowledge can be gained. This problem
was first addressed by Plato in "Meno",
where he asked how it could be possible either to inquire into something
of which one was ignorant or something of which one had knowledge. In the
first case one has no means of beginning to learn and in the second case
one has nothing to learn!
Meno: Why, on what lines will
you look, Socrates, for a thing of whose nature you know nothing at all?
Pray, what sort of thing, amongst those that you know not, will you treat
us to as the object of your search? Or even supposing, at the best, that
you hit upon it, how will you know it is the thing you did not know?
Faced with this paradox, Plato refused to conclude that learning was an
impossibility and instead proposed the hypothesis (which he later makes
clear he was not absolutely committed to) that all learning was a form
of remembrance of what had been temporarily forgotten. To make this proposal
intelligible, he was forced to further propose that each human soul is
pre-existent and was omniscient before it was made corporeal. This inevitably
made the fact of human corporeality a great sadness as being the occasion
of the loss of knowledge and the cause of ignorance and hence wickedness.
Socrates: I understand the point you would
make, Meno. Do you see what a captious argument you are introducing - that,
forsooth, a man cannot inquire either about what he knows or about what
he does not know? For he cannot inquire about what he knows, because he
knows it, and in that case is in no need of inquiry; nor again can he inquire
about what he does not know, since he does not know about what he is to
Meno: Now does it seem to you to be a
good argument, Socrates?
Socrates: It does not.
Meno: Can you explain how not?
Socrates: I can; for I have heard from
wise men and women who told of things divine that -
Meno: What was it they said ?
Socrates: Something true, as I thought,
Meno: What was it? And who were the speakers?
Socrates: They were certain priests and
priestesses who have studied so as to be able to give a reasoned account
of their ministry; and Pindar also and many another poet of heavenly gifts.
As to their words, they are these: mark now, if you judge them to be true.
They say that the soul of man is immortal, and at one time comes to an
end, which is called dying, and at another is born again, but never perishes.
Consequently one ought to live all one's life in the utmost holiness.
For from whomsoever Persephone
shall accept requital for ancient wrong,
the souls of these she restores
in the ninth year to the upper sun again;
from them arise glorious kings
and men of splendid might and surpassing wisdom,
and for all remaining time
are they called holy heroes amongst mankind.
[Pind. Fr. 133 Bergk]
Seeing then that the soul is immortal and has
been born many times, and has beheld all things both in this world and
in the nether realms, she has acquired knowledge of all and everything;
so that it is no wonder that she should be able to recollect all that she
knew before about virtue and other things. For as all nature is akin, and
the soul has learned all things, there is no reason why we should not,
by remembering but one single thing - an act which men call learning -
discover everything else, if we have courage and faint not in the search;
since, it would seem, research and learning are wholly recollection. So
we must not hearken to that captious argument: it would make us idle, and
is pleasing only to the indolent ear, whereas the other makes us energetic
and inquiring. Putting my trust in its truth, I am ready to inquire with
you into the nature of virtue. [Plato "Meno"
An alternative view is now possible, which Plato did not conceive of. This
is based on Darwinian evolutionary theory. Every new-born infant has innate
knowledge hard-wired into its brain. This is analogous to the "monitor
program" and "boot sector" of a computer. In the case of a brain, it is
genetically determined and manifests itself in terms of innate behaviours
and dispositions. In the case of human and other animals with a significant
ability to learn and adapt to changes in their environment, these instincts
are the result of a breeding history that partly selected for those individuals
who were best able to gain knowledge of their environment and use it to
develop expertise that enhanced their ability to survive and breed.
The learning process is bootstrapped by this innate knowledge of "processes
that work", and can be viewed as the unfolding of the implications of the
truth of these processes. In a sense, Plato was exactly right. When we
are born, we are gifted with a basic knowledge, expectation or anticipation
of the kind of world in which we are to live, and the process of learning
is the working out of the implications of this basic knowledge as applied
to the experiences of life. This anticipation of the world is, however,
not inherent in our "spiritual
soul" and does not testify to its pre-existence. Rather, it is held
in the physiological construction of our brains and is the legacy
of our evolutionary struggle: the births, lives and deaths of our ancestors.
Episteme and Doxa
Plato was committed to the notion that Doxa, even Orthodoxa, was no good
and that only Episteme was worthwhile. I have argued that Episteme is unattainable
and that only Orthodoxa is available to mortals. How can I do this as a
Hence, I would expect Plato to agree with the analysis that I have presented
here as differing insignificantly from his intent and in fact amounting
to nothing more than a clarification of his own epistemology.
Well, first of all it is necessary to face up to unpleasant facts.
I concur with Plato that a smattering of Episteme - were it to be available
- would be indefinitely superior than large dollops of Orthodoxa.
However, if some good thing is unavailable, then one must make do as best
one can with what is to hand.
Next, I contend that Plato was too disparaging of Orthodoxa.
He only really conceived of Orthodoxa as an accidentally correct belief.
His problem with such a form of knowledge was that its possessor would
have no reason for committing themselves to it and would as likely reject
it at some point in favour of error as maintain it.
Plato thought that Orthodoxy could not be based on the question "why" or
an "understanding of the way things were" but only on an acquiescence in
authority or a serendipitous stumbling on an answer which could then only
be parroted without any comprehension.
Much of what Plato took to be Episteme was, in fact, scientific or metaphysical
Doxa with (I believe) a high verisimilitude (degree of correspondence with
reality): obtained by precisely the method of conjecture and refutation
only recently codified by Popper.
Finally, I contend that Scientific Orthodoxa is indistinguishable from
The method of conjecture and refutation can be hoped to result in Doxa
that tends ever closer to Orthodoxa.
The difference between "Scientific Orthodoxa" and "Socratic Orthodoxa"
is that the latter is conceived as being accidental and arbitrary, whereas
the former arises as the limit of a sceptical process of critical learning
Knowledge of the good
The ethical problem that faces the typical human being is two-fold. First,
there is a temptation to ignore the dictates of reason; and second, one
certain and clear knowledge of what is good. The first
part of the problem can be treated as an aspect of the latter; for if one
clearly that some conclusion was reasonable and that no other was possible,
then one would not be "tempted to ignore the dictate of reason". One might
earnestly wish that some other conclusion was possible, but given that
knew clearly that it wasn't; one would necessarily have
to accept, no matter how reluctantly, that "A is A" and make the best of
it. I have dealt with the question: "Why do the good thing, when one knows
what it is?" in more depth elsewhere.
The Platonic account of internal moral conflict is framed in terms of "wishful
thinking". Whereas the most plausible view of a question might be "such
and such", there are always alternative possibilities which simply cannot
be excluded, given the partial and ambiguous nature of human knowledge.
It is always open to the moral agent to choose to ignore the most plausible
conclusion as to what is good and so the prudent course of action;
in favour of some other conclusion that is preferable, according
to some (perhaps in itself reasonable, noble and proper) metric. So, a
husband faced by a midwife with the medical dilemma "save the mother or
save the unborn child" might personally desire one objective above the
other and so be motivated to favour this conclusion whatever the dictates
of reason told him was the proper action.
Absolute right and Absolute
It is important to note that the most important aspect of moral dilemmas
is not the practical outcomes associated with choices but rather the metrical
outcomes. This is what people mean by referring to "the thin end of the
wedge" or "a slippery slope" when debating ethical questions. It may be
that a certain choice - viewed in glorious isolation - might be clearly
the advantageous one for all the parties concerned, however it may involve
the breaching of a general "rule of conduct" that it is overwhelmingly
advantageous to maintain. As soon as this "rule" is breached once then
it will inevitably be breached again and again, with each infringement
being more easily justified on the basis of precedent than the last. The
ethical metric against which questions of right and wrong is measured will
start to slip. In the end, the "rule" will become inoperative and the overwhelming
advantage that resulted from its maintenance be entirely lost.
An example will best serve to explain what I mean. It is a general principle
of ethics that: "the intentional taking of innocent life is always wrong",
and in fact utterly reprehensible. I take the rational basis for maintaining
this to be obvious. Now consider the case when the lives of very many people
could only be saved by the intentional and direct killing of some innocent
person who is not willing to die in this way. If an exception is made to
our principle in this case, then it will lead: by a process of rational
extension, to the most horrendous practices; for example: the intentional
sacrifice of many innocent lives to save the life of some single (supposedly
important) individual. The true long-term outcome of infringing such a
rule is indefinitely terrible and this fact "trumps" all other considerations.
This is what is meant when we say that some act is "absolutely and always
Note that this is not the same as the idea that some acts are intrinsically
evil. The kind of ethical principle that I have indicated always has a
context associated with it. In the example considered it was the taking
of innocent life that was at issue, not all or any life without
condition. Often, those - like pope John-Paul II - who wish to say that
certain acts are intrinsically evil give examples which are true by construction:
murder, suicide, slavery etc. etc.; for these all contain the judgement
of wrongness within the definition of the act.
It is wrong to take the life of another unjustly, for this is murder.
Otherwise it might be:
defence of the weak and oppressed;
a "coup de grace" or
a noble act of warfare.
It is wrong to take one's own life out of despair, for this is suicide.
Otherwise it might be:
a noble act of self-sacrifice [Socrates];
a rational acknowledgement of one's own weakness.
It is wrong to require another human being to work for no significant remuneration
and to curtail their freedom to that end, when this is unjust: for
this is slavery.
Otherwise it might be:
due punishment for criminality;
a form of taxation "in kind".
Once one starts to favour conclusions because they are more attractive,
convenient or pleasant, rather than because one believes they are right,
then one has adopted a false metric for what is right. This is the
Platonic version of concupiscence
and can be seen to correspond to St Paul's account of the matter just as
well as the Aristotelian version. In fact this disformation of the will
be identified with "the sin living within
me" referred to by the Apostle [Rom 7:20],
as also the "law at war with the law of my mind ....
law of sin, which dwells in my members" [Rom
7:22] and "the flesh which serves the law
of sin" [Rom 7:25].
On the other hand, the Apostle's language in earlier verses of his Epistle
to the Romans is altogether more confused: "I do
not do what I want to" [Rom 7:15] "nothing
good dwells within me .... I can will what is right, but I cannot do it"
7:18] Indeed, taken at face value, these verses are self-contradictory:
for "to will" some act is the same as "to do" it. Nevertheless, most people
would acknowledge a large degree of sympathy with the Apostle's description
of his experience of concupicense. Many people feel that although they
often know what the right thing to do is, this doesn't mean that they do
it. Frequently, their judgement is clouded by the overwhelming attraction
of another imprudent choice. Faced with a substantial and obvious
immediate benefit (or disbenefit), most people find it very difficult to
act rationally; in accordance with their long term advantage. "jam
tomorrow"[Lewis Carrol] is nowhere
near as compelling a motive as "bread today", when you are hungry.
Even when one is pretty sure that a first course of action will result
in sustained well-being and a second will result in ruin, the latter will
be very attractive if coupled with a definite short term benefit or pleasure.
In effect, one gambles on something else "turning up" that will make it
possible to avoid the ruin of the second option, once its benefit has been
obtained. This is, of course, opportunism or "wishful thinking"; otherwise
known as greed or avarice: "I want it all, and I
want it now!" [Queen]. It isn't so
much that one "cannot do" what is right - this is hyperbole - but rather
that the habit has been set of choosing short-term benefits over long-term
The rational basis of concupiscence should be obvious. The ability to
predict outcomes reliably declines rapidly as events further and further
in the future are considered. Hence, if one action is expected to produce
an immediate benefit and a remote disaster, while another is expected to
produce immediate suffering and an eventual triumph; it is not altogether
obvious that the second action is the better choice. The immediate benefit
is pretty certain and may lead to other unenvisagable favourable possibilities.
In every case, there is a judgement to be made in which future outcomes
should be discounted according to the confidence associated with them.
Manifestly, this is bound to produce disagreement among moral agents faced
with the same dilemma; for even if they agree about the immediate and long-term
consequences, it is highly implausible that they are going to agree about
the likelihood associated with each predicted outcome. An additional complicating
factor is the certain prospect of death,
which means that the longest term considerations are of no
rational interest to any moral agent that does not believe in "Eternal
"I think that a general factor of a temporal
discount - standard in reward theory - is involved when deciding what is
best: if I gain immediate benefit but put off problems to the future, the
negative value of the problem is discounted compared to an immediate problem
or reward. Maybe this all relates to the further something is in the future,
the less sure we can be that it will eventually materialize (the revolution
may come first!) so it is rational in some sense.
This Platonic analysis has the distinct advantage of not referring to the
undefined concept of "will-power". On this view, while concupiscence is
a defect of the will, it is not some mysterious weakness that is to be
overcome by exercise. Rather, it is a disformation to be overcome by education,
meditation, encouragement and enlightenment. This is not to say that discipline
does not have a valid role in the correction of concupiscence. Confrontation
with objective reality is a most effective way for "wishful thinking" to
be brought to brook! Eventually, the person who spends money profligately
will have to stop, simply because they run out of funds. If they do not,
they will have to take up a life of crime to finance their extravagance
and, hopefully, they will be caught, prosecuted, convicted and punished.
St Paul tells us that God disciplines those who He loves.
Hence the importance of bringing up kids in a
stable household (so that they get used to being able to predict rewards
and punishments reliably) and a stable economy/culture (incentive to sacrifice
now for a more certain future good) etc." [Dr
P. Miller: private correspondence (March 2005)]
The notion of "blame" or "culpability" can be identified with the objective
fact of a disordered will. When a person systematically adopts a self-satisfied,
complacent or conceited metric for what is right, then that metric is the
proximate cause of whatever evil actions he or she perpetrates: their disordered
will is "to blame", and it is appropriate for them to be punished so as
to "bring them to their senses", and persuade them to adopt a more objective
Evil is sickness
It follows from this view that personal evil is always a species of sickness.
One way or another, a person has got into a state where they have an improper
view of what is right and wrong. Their wickedness is simply this disformation
of the will. It evolved out of natural predispositions, under the influence
of external events and random mental processes, in other words by their
"Free Will". It is not the fault
of the person that "they are evil", it is just a fact about them.
They were not "born bad". If their concupiscence can be rectified, then
the fact that they used to be evil is no longer of any importance: it was
no more their fault (for which they should carry guilt) that they were
evil than it is their merit that they are no longer so. The fault lies
in the past: in the evil will that they have lost. The virtue lies in the
present: in the good will that they have gained. Hence the Judaeo-Christian
view that repentance (which means the changing of an evil will into a good
will) automatically calls for immediate and unqualified forgiveness.
Prudence and Temperance: How
deep does wickedness go?
A corespondent wrote to me after reading a first version of this paper:
"I have one thing to discuss; on the
idea of sinning out of not knowing. I think there is some truth in what
you say, but I think that sometimes people deliberately choose to avoid
knowing the truth. For example, people may choose to drink a lot when having
an affair for example, to deliberately dull their mind to the knowledge
that what they are doing is wrong so that it doesn't surface to spoil the
Dr Miller rightly insists that there are levels of wickedness. Every imprudent
act that is executed on the basis of a disformed will is only marginally
wicked. The fact that the will is already disformed mitigates the culpability
of the act. It is the progressive disinformation of the will that is truly
sinful: but this only occurs by repeated decisions that amount to a continued
erosion of a prudential outlook. As Our Blessed Lord said:
I see what you call sin or wrongdoing, not as
a lack of knowledge (which I call a mistake) but at the deeper level of
resisting new knowledge whether by avoidance, by drugs, or by building
up "rationalizations" which are rarely rational." [Dr
P. Miller: private correspondence (March 2005)]
"And he called the people to him and
said to them: 'Hear and understand, not what goes into the mouth defiles
a man; but what comes out of the mouth: this defiles a man.' ....
Nevertheless, I maintain that all wickedness is a form of ignorance. Negative
ignorance: the mere absence of truth, is only the possibility of wickedness.
Positive ignorance: the presence of falsehood, is the habituation of wickedness
and the legacy of sin.
'Do you not see that whatever goes into the mouth
passes into the stomach, and so passes on? But what comes out of the mouth
proceeds from the heart, and this defiles a man. For out of the heart come
evil thoughts, murder, adultery, fornication, theft, false witness, slander.
These are what defile a man; but to eat with unwashed hands does not defile
a man.'" [Mat 15:10-11,17-20]
There is no possible original rationale for evil. By definition, sin
always is contrary to the well-being of the sinner. This not because of
some extrinsic punishment, but because of an intrinsic, inevitable
and sad necessity. Satan is the master of lies and there is no truth within
him beyond the truth that holds him in being. The same choice always lies
before the moral agent: to "choose life" and act according to his best
judgement or to "choose death" and act according to a self-deception. I
suppose that such an act could result from over hasty judgement or carelessness:
but even these "explanations" would not explain anything if the moral agent
knew that the decision facing him or her was important, with potentially
Once someone has chosen to act imprudently, it is only too plausible
that as part of their resolve they will take care to mitigate or evade
all evidence and considerations that they have already decided to discount.
They will do so in order to reduce the present cost of non-compliance with
their best judgement: the fear that they will suffer as a result of their
exercise of free-will. As Dr Miller may be understood to imply, this is
an aspect of "psychological hysteresis",
and is truly wicked in itself because it tends to habituate the "death
wish" represented by the original imprudential choice.
Education in virtue
Plato was very conscious that it was difficult to educate people into being
kind, just and brave. While he believed that all virtue was a form of wisdom
and wisdom was a type of knowledge, he took the fact that virtuous men
were notoriously unsuccessful in passing on their virtue - even to their
sons - as evidence against his conviction. I believe that he was mistaken
in this self-criticism. It seems to me that the fact that it is difficult
to inculcate virtue in a pupil would only indicate that virtue is not a
form of knowledge, if knowledge was always attainable by a continuous process
of incremental learning in which one idea was calmly established on the
foundation already laid down by previous study or dialogue. However this
is not the case.
Learning is not
Even in the impersonal field of abstract mathematics, individuals regularly
commit themselves to idiosyncratic accounts and explanations of formalism
or technique. Perhaps this is inevitable for all people and all subjects,
perhaps it is a personal failure in many cases: no matter, it happens.
Whenever an understanding to which a pupil has committed themselves proves
to be inadequate, a struggle ensues.
The student will generally try very hard to maintain his/her current understanding:
after all a lot of effort went into developing it! Only after a good deal
of persuasion, will they consent to give it up. This can be a frightening
experience for them. Whereas they had thought that they understood something:
and perhaps they did, up to a point; now they are forced to face up to
their ignorance. If they are fortunate, help will be on hand in the shape
of a ready-made better account which they can adopt: first, on the authority
of a teacher; and then come to grasp and understand by inspecting it from
all angles and applying it in practice.
In the field of ethics, the situation is much worse. The evidence is always
more equivocal, the arguments always more contentious, the outcomes more
significant and the degree of personal
commitment to cherished hypotheses or attitudes much higher. Hence
the process of persuasion is liable to be much less smooth than that which
is characteristic of less emotive topics of study. In the most extreme
cases, individuals will resist the most intense educational process: seeing
it (rightly or wrongly) as a form of indoctrination or brain-washing, and
to be rejected at all costs. It is then normal for the educator to "give
up" on the pupil and to discount him or her as incorrigible, when all that
was perhaps required was a different approach.
Sometimes an individual will experience the standard hysteresis catastrophy
in the field of personal ethic or outlook on life. If so they are liable
to describe this in terms of a "conversion experience", for that is truly
what it is.
What I have argued is that:
Knowledge comes in two forms: theoretical and practical.
The Scientific Method of "Conjecture and Refutation" is the sole systematic
means of arriving at truth.
Both are based on truth.
Truth is correspondence with Objective Reality.
Classical Inference is necessary as a means to attaining truth.
Plato's theory of "learning as recollection" can be re-interpreted on a
Ethics springs from epistemology:
This is based on the notion of falsification rather than proof.
Scientific Orthodoxa is identical with Episteme, as the limit of a convergent
Psychological hysteresis - faith - is an essential aspect of learning.
to the extent that a moral agent
and has clear knowledge of what is just
that agent will certainly do what is just.
Concupiscence is a disformation of the will:
incorrect habitual "knowledge" of what is of benefit or disbenefit.
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