Popper, falsifiable statements & mathematics
Paul Bramscher
yet they often contain tautological (and irrefutably provable)
mathematical underpinnings, what does this do to the holistic status of
science with regard to mathematics and falsifiable statements?
Can we say that math (and perhaps chemistry and physics) is
non-scientific, in that when it includes balanced or provable formula
(provable by tautology) that it is a non-science?
Or are we really saying that if we observe a particular phenomena and
say it works like this because X + X = 2X and it turns out that while
our math is correct, it was actually a case of X + Y = X + Y? In both
cases, the math is correct but the statement is falsifiable.
So if we wish to retain math is a tool of Popperian science, it seems
that we must mean "falsifiable" in more than one sense. That is, a
statement can be false because it has an internal flow problem. But it
may be false in the sense that -- while true at explaining some events
-- it is not true in explaining this event. And hence, it's both true
and untrue, depending on the scope of the problem.
Ponder this.
Abakus
"Paul Bramscher" <brams00...@tc.umn.edu> wrote in message
news:cdmg04$f6l$1...@lenny.tc.umn.edu...
Maths is a branch of logic, it is not an empirical discipline. Mathematical
and logical statements are unfalsifiable, because they are tautologies. For
example, "all blue things are blue" is a necessarily true statement which
does not involve any knowledge of the world.
The way that mathematical theorems are proven involves reducing them to
tautologies, which can be proven as true given the axioms of the system or
reducing the negative to a contradiction.
regards
Abakus
John Wilkins
Popper did not think logic or maths were sciences. Many things are not
sciences and are still useful - language, for example. Popper was not a
logical positivist and did not restrict all that can be known to
science.
Moreover, as falsification takes place in virtue of the use of logic, if
not maths, it cannot itself be the demarcation of science from
non-science.
--
John Wilkins
john...@wilkins.id.au http://wilkins.id.au
"Men mark it when they hit, but do not mark it when they miss"
- Francis Bacon
Immortalist
"John Wilkins" <john...@wilkins.id.au> wrote in message
news:1ghbfki.18esdyu3dlm69N%john...@wilkins.id.au...
> Paul Bramscher <brams00...@tc.umn.edu> wrote:
>
> > So, if making scientific statements requires that they are falsifiable,
> > yet they often contain tautological (and irrefutably provable)
> > mathematical underpinnings, what does this do to the holistic status of
> > science with regard to mathematics and falsifiable statements?
> >
> > Can we say that math (and perhaps chemistry and physics) is
> > non-scientific, in that when it includes balanced or provable formula
> > (provable by tautology) that it is a non-science?
> >
> > Or are we really saying that if we observe a particular phenomena and
> > say it works like this because X + X = 2X and it turns out that while
> > our math is correct, it was actually a case of X + Y = X + Y? In both
> > cases, the math is correct but the statement is falsifiable.
> >
> > So if we wish to retain math is a tool of Popperian science, it seems
> > that we must mean "falsifiable" in more than one sense. That is, a
> > statement can be false because it has an internal flow problem. But it
> > may be false in the sense that -- while true at explaining some events
> > -- it is not true in explaining this event. And hence, it's both true
> > and untrue, depending on the scope of the problem.
> >
> > Ponder this.
>
> Popper did not think logic or maths were sciences. Many things are not
> sciences and are still useful - language, for example. Popper was not a
> logical positivist and did not restrict all that can be known to
> science.
>
Can you point to where Paul Bramscher promotes logical positivism? Is it the
irrefutable tautology?
> Moreover, as falsification takes place in virtue of the use of logic, if
> not maths, it cannot itself be the demarcation of science from
> non-science.
> --
...the growth of our knowledge is the result
of a process closely resembling what Darwin
called 'natural selection'; that is, the
natural selection of hypotheses...
--Karl Popper
Popper started with the old idea that knowledge grows by trial and error, or in
more learned terms, by conjecture and refutation. He generalised this theory to
encompass all forms of learning and problem-solving, including the evolution of
life on earth. On his account every organism, from the amoeba to Einstein, is
constantly engaged in problem solving. In the plant and animal world this
involves the production of new reactions, new organs, new forms of life. For
humans it involves the production of new ideas. When these forms of life or
theories appear they confront selective pressures. These may come from the
biological environment or from competing forms of life. Ideas meet the
competition of alternative theories, critical arguments and experimental tests.
The central motif of Popper's evolutionary epistemology is the four-step
problem-solving schema:
P ---> TS ---> EE ---> P
The starting point is a problem, which evokes tentative solutions. These are
subjected to the process of error elimination by way of critical discussion and
experimental testing. In the course of these activities new problems emerge.
http://www.the-rathouse.com/poptheoryknow.html
the view that culture originates and changes over time in a manner analogous to
the cumulative trial and error of biological evolution has become increasingly
popular among social scientists. As anthropologist John Reader explains:
The farmers who founded and refined the wet-rice system and maintained its high
levels of production for centuries knew nothing of nitrogen cycles and oxygen
transportation in plants. They worked purely by trial and error. In the process,
however, they acquired a sound appreciation of just what made the system work,
and of how to keep it working.[8]
It cannot be doubted that the Balinese farmers are successful in cultivating
rice, but is it actually the case that they "acquired a sound appreciation of
just what made the system work"? For the traditional farmers it is observance of
Dewi Sri's calendar together with participation in the many religious activities
that are responsible for their success. Yet it can be easily shown that such
religious observances are in no way essential to obtaining continued good rice
harvests, since good harvests are obtained elsewhere in the world where the
biological requirements of the rice plant are met and Dewi Sri and her calendar
are totally unknown. So clearly a fit exists between Balinese farmers'
agricultural practices and the requirements of the rice plant, although
individual farmers may not know (and need not know) the underlying scientific
reasons for it.
Regardless of a lack of technological or scientific understanding of rice
cultivation, the society in which the rice farmer lives is structured in such a
way to ensure continuation of the farming practices found over the centuries to
be effective. By making it appear that these practices have divine origin and
guidance, it is less likely that an individual farmer would challenge the system.
So although daily rice offerings to the gods and frequent temple ceremonies in
themselves have no direct causal link to the success of the crop, these
traditional activities are well adapted in a larger sense since they ensure that
traditional agricultural methods which have proved effective over the centuries
will continue.
Does his lack of scientific understanding mean that the traditional Balinese
farmer is in any way irrational or illogical in his adoption of the centuries-old
methods of rice cultivation? Hardly, since for him rice cultivation and religious
practices form one integrated system. It would be well nigh impossible for him to
determine which particular aspects of his way of life are essential for obtaining
continued good harvests and which are not. Indeed, such experiments (for example,
refusing to participate in religious activities to see if this reduces rice
yield) would possibly result in the radical farmer being ostracized from his
community and make it impossible for him to obtain the water supply on which his
crop depends. Instead, there are important advantages for individuals to adopt
the agricultural and other traditional practices of the majority of their
community.[9]
So since many aspects of traditional rice cultivation are not individually
testable, we should not be surprised to find that some of them are not functional
or are even maladapted to the requirements of rice production. The difficulty
that an individual would encounter in attempting to analyze which aspects are
actually well adapted and which are not, save for the fact that they may play
important social functions, also argues for the rationality of accepting and
observing the total cultural package.
http://faculty.ed.uiuc.edu/g-cziko/wm/10.html
Because Galileo couldn't devise a frictionless circular path around the Earth to
prove his concept of inertia to be fact, he had to come up with some other way to
demonstrate that inertia was, in fact, a fact.
Half a century before Galileo was carrying on all of these ruminations, a
practical trial and error advocate named Tartaglia had gone out onto the proving
grounds and shot off cannonballs at different angles in order to come up with the
angle that would cause the cannonball to travel the furthest distance. After much
banging around, he determined that the optimum angle was forty-five degrees.
Galileo allowed the balls that had rolled down the inclined plane to roll off the
end of his workbench and measured the same angle, at forty-five degrees, the
inclined plane produced the maximum trajectory.
He then said he had, in the confines of his study, by mathematics alone, proven
that which was proven by trial and error on the proving grounds. It was
acceptable procedure, then, to use mathematics to prove facts that were not
capable of being directly measured.
Of course, Tartaglia had actually shot real cannonballs out of real cannons to
produce real measurements. By duplicating the facts in his study, Galileo had not
proven a fact that was not capable of direct measurement, he had just measured
the same fact in a different way, measuring real balls that had rolled down a
real inclined plane rolling off the end of a real workbench.
He hadn't proven anything let alone a concept, inertia, to be a fact.
Concepts about factual relationships can be demonstrated by measurement to be
fact.
Concepts, however, can never be proven to be facts
http://www.copernican-series.com/sss/induct.html
On Popper's account, the central problem of moral and political philosophy is to
formulate and criticise standards which act as 'rules of the game' in social
life. These rules of the game occur in all groups and they may be enforced
informally or by due process of law. The question we have to face is not whether
we will have rules but whether we will try to improve them by critical discussion
and trial and error. This approach cuts through the verbalism that bogs down
academic discussions of moral and politics and it is constantly in touch with
practical problems and their possible solutions.
http://www.the-rathouse.com/poppurpose.html
This volume adds weight to Bartley’s claim that Popper is on the right track but
has not received due credit because his ideas have suffered from misreading and
other mishaps. In Logik der Forschung (1934) Popper challenged the theory that
scientific knowledge grows by a process of induction from accumulated
observations. He advanced a theory of conjectural objective knowledge that grows
by trial and error, controlled by criticism and by empirical tests. He also
presented the now-famous falsification criterion for the demarcation of
scientific statements from those of metaphysics and pseudoscience. This criterion
was widely criticised as an attempt to solve a completely different problem,
namely to define meaningful statements. This misreading obscured his achievement
for some decades and books are still being written about the logical positivists
(called logical empiricists in the US) without mention of Popper. In the 1930s he
wrote a series of papers to refute various theories that contributed to the
collapse of civilisation in the holocaust. Mind, the most prestigious organ of
analytical philosophy, did not accept them. Eventually they appeared in the
journal Economica and later in book form as The Poverty of Historicism (1957).
http://victorian.fortunecity.com/beardsley/700/dwarf.html
...During this process, the individual learner attempts a trial solution. The
learning processes is trial and error for which the learner is responsible.
This is an evolutionary epistemology. Creation and elimination (or modification)
works hand in hand. Problem formulation takes precedence over observation and
there is an emphasis on the value of refutation and the falsification of
theories. Hence the development of critical thinking, a dialectical process of
continuous reflection and the testing of current assumptions to extend
understanding is vital. Popper recognises that criticism by experimental testing,
the consideration of other peoples argument, reason and compromise, the deduction
of consequences and the emphasis on the fallibility of science are important
components in. the objectification of knowledge. These are key strategies in the
critical rationalist methodology and might become more firmly embedded in the
ecological curriculum.
The fallibilist conception of ecological theories and knowledge requires teachers
to encourage students to develop the appropriate traits, attitudes and
dispositions to begin the essential process of critical thinking. Students of
ecology, as well as the scientists themselves, need to refine these skills,
construct, identify, analyze and evaluate arguments, rather than to accept too
readily dogmatic beliefs.
http://www.hamar.fsnet.co.uk/teg/6/DoUndergrads.html
[conjecture and refutation (trial & error)]
...Some of this confusion [about education] arises from the clash to two
antagonistic notions of scientific activity which may be called the romantic and
the rational or the poetic and the analytical. This clash involves the opposition
of activities which are in fact complementary and it is resolved by the mode of
thought which travels under the unfortunately cumbersome title of the
'hypothetico-deductive' model of scientific activity. Popper has called this the
method of conjecture and refutation, a high-falutin' name attached to the
old-fashioned method of trial and error. This is not entirely original and it can
be traced in the work of thinkers such as Whewell, Peirce and the French
physiologist Bernard. The leading modern exponent is Popper who has added some
wrinkles of his own, notably in rejecting 'justified belief' as the terminus of
scientific or philosophical activity.
It can be very difficult to understand philosophical ideas without understanding
the problem that the ideas were supposed to solve. Often these problems arise
outside philosophy itself, in science, religion, politics, art etc. Popper's
first major problem was 'When should a theory be ranked as scientific?' or 'Is
there a criterion for the scientific status of a theory?'
We can understand how this arose by a study of Popper's biography. He was born in
1902 and he grew up in Vienna with the air full of the exciting ideas of Freud,
Adler and Marx. These men formulated impressive schemes that appeared to explain
anything and everything that happened. There was an explanation for everything,
albeit different explanations. It seemed that nothing could contradict them and
in this respect Popper noted that Einstein had a very different attitude to his
equally revolutionary theory. This was put to the test by Edington's eclipse
observations in 1919 and Einstein had announced that a negative result would
suggest a need to reconsider his theory. In this way Einstein provided Popper
with the hint for his falsification criterion for science. This scenario provides
a rational explanation for Popper's motivation in formulating his criterion,
unlike the suggestion that he embraced falsificationism in the reckless and
irrational spirit of the Jazz Age.
=== The Line of Demarcation ===
A statement may be considered to be scientific if it is conceivable that publicly
available evidence maybe produced to show that it is false. In other words we
have to be able to look for some kind of evidence that would clash with our
statement or our theory. For example the statement "There are no students in the
library" can be refuted by the discovery of a student in the library. Similarly,
the laws of science, formulated in universal terms along the lines 'All ravens
are black' can be refuted by the discovery of a white raven. The point is, to
make progress we need to locate weak spots in our theories in order to stimulate
the production of new ideas. This means we have to take the risk of being wrong
by making assertions that can be checked against evidence.
The criterion of testability is not a criterion of truth, meaning or even of
importance, and it shows that we should not take the word 'science' too
seriously. On the science side of the line we have descriptive statements which
say something about the world. They may be true or false and they may be refuted
by evidence. They may also be supported by evidence but this is a great deal more
problematic because for some theories, everything that happens counts as
supporting evidence (as Popper found with the followers of Marx and Freud).
On the 'non-science' side of the line are several categories of statements, among
them the statements of pseudosciences such as astrology, which claim to be based
on evidence but can never be refuted; the 'ought' statements of morals and
ethics; theories of method (such as the falsification criterion); and also,
incidentally, nonsense statements.
Some more needs to be said about morals, values, ethics and political ideals.
These can be formulated as proposals for various kinds of behaviour or action. In
this way they can be contrasted with propositions which state matters of fact
(this is the language used by Popper in Chapter 5 of The Open Society and its
Enemies). We may argue about the truth or falsity of propositions but we cannot
claim that proposals are true or false. Our acceptance or rejection of proposals
is a matter of decision, though matters of fact (and hence considerations of
truth and falsity) will arise in considering the consequences. The element of
decision in relation to moral 'oughts' and political proposals has been
interpreted to mean that these decisions are irrational or arbitrary, as indeed
they may be, especially if they are made under the influence of a theory that
these matters cannot be subjected to reasonable discussion. As indicated in
Critical Preference in Science and Ethics we can critically examine alternative
moral or political codes and we can form critical preferences that can be
modified in the light of evidence and new arguments.
Attempts to derive values from facts cannot be achieved logically, though there
have been many efforts to do so in the belief that such a derivation would
produce rational or scientific ethics. This was considered to be a defence
against unreason at a time when rationality was supposed to apply in science but
not on the other side of the line of demarcation, for example in religion, morals
and aesthetics. However, attempts to provide a 'positive' basis for morals are
likely to lead to dogmatism, quite likely linked to conservatism by appealing to
the official or prevailing laws or morals at the time.
Popper's line of demarcation should affect the way the way we look at science in
relation to other subjects because it cuts across the bounds that are supposed to
exist between 'the sciences' and 'the rest'. Statements in any subject such as
history or literary criticism may be considered to be scientific if they can be
supported or refuted by evidence. The convention applies to statements, not to
areas of activity.
It should not matter how a student defines the subject, because it is very much
more important to be clear about the problem that is being investigated. A
serious attempt to work on a problem should drive the student into a whole range
of subjects or disciplines, thereby making nonsense of the narrow definition of
subjects and over-specialisation. Too much focus on subjects and examinations can
make the problems and themes invisible, but problems and themes should provide
the backbone and the organising principles amidst the mass of information that
confronts the student and the researcher.
If we lost sight of genuine problems, or never find them, it is virtually
impossible to contribute to the growth of knowledge. This brings us to another
philosophical problem - how does our knowledge grow? Popper has suggested that
our knowledge grows as a result of our attempts to solve problems by trial and
error, a process that he has compared with the evolution of life on earth. If we
are going to talk about the growth of knowledge, we seem to imply that there is
something to grow towards, presumably the truth. But how does this come about,
and what is the truth?
...The advance of science is not due to the fact that more and more perceptual
experiences accumulate in the course of time. Nor is it due to the fact that we
are making ever better use of our senses...Bold ideas, unjustified anticipations,
and speculative thought, are our only means for interpreting nature, our only
instruments for grasping her, and we must hazard them to win our prize.
A fierce battle has raged over the problem of induction which is closely related
to the matter of the line of demarcation because it is sometimes suggested that
the criterion of science is its inductive, or maybe its experimental method, as
against the speculative or creative or expressionistic method of the arts, the
intuitive method of psychology, the sociological imagination, the historical
method etc. Everything depends on what is meant by induction, and if it is used
to mean the guess or the imaginative leap, then this does not distinguish science
from any other activity that involves thinking. However it usually refers to a
methodical or logical process for proceeding from the particular to the general,
or from the observation of facts to the formulation of laws. This type of
induction is not logically or psychologically defensible and it cannot be
retrieved by the use of the probability calculus to assign numerical
probabilities to theories.
=== Conclusions ===
Scientific knowledge is capable of growing by the detection and correction or
error, though its growth can never be completed. It does not grow in a
disciplined, orderly or predictable way, but rather by unjustified leaps of
imagination, controlled by the use of logic, critical analysis and experimental
tests.
Our knowledge in a given field does not consist of a mass of facts or a set of
verified laws, it consists of a body of hypotheses along with an account of the
tests and other arguments that have been used in attempts to refute them. There
is no opposition between imagination and reason because they have different (and
complementary) roles to play. There is no antagonism between theorising and fact
finding provided that we have a clearly formulated problem in mind when we start
looking for facts.
This theory of knowledge has some political implications. The
positivist-empiricist-inductivist may have thought that he did not need to
actively make decisions about his subject matter. The task of the scientist was
to collect and collate information to steadily record the tale told by the book
of nature. However, this idea of the passive observer-collector cannot be
sustained. If the scientist wants to advance the frontier of knowledge, even to
the smallest degree that the average honours student should aspire to achieve, he
has to make an effort and bring into action both the imagination and the critical
faculties. There is also the consideration that the findings are quite likely to
be used and the scientist (or at least the community of scientists) is morally
responsible for warning of potential dangers and monitoring any dubious
applications.
Scientists can only approach the truth by conjectures and by critical tests, and
if they accept their social responsibilities they will carry their critical
attitude out of the laboratory, to participate, like everyone else, in a
continuous process of non-violent cultural revolution.
http://www.the-rathouse.com/poprevtheory.html
At the same time I realized that such myths may be developed, and become
testable; that historically speaking all-or very nearly all-scientific theories
originate from myths, and that a myth may contain important anticipations of
scientific theories. Examples are Empedocles' theory of evolution by trial and
error, or Parmenides' myth of the unchanging block universe in which nothing ever
happens and which, if we add another dimension, becomes Einstein's block universe
(in which, too, nothing ever happens, since everything is, four dimensionally
speaking, determined and laid down from the beginning). I thus felt that if a
theory is found to be non-scientific, or "metaphysical" (as we might say), it is
not thereby found to be unimportant, or insignificant, or "meaningless," or
"nonsensical." it cannot claim to be backed by empirical evidence in the
scientific sense-although it may easily be, in some genetic sense, the "result of
observation."
http://www.cla.calpoly.edu/~fotoole/321.1/popper.html
Popper, too, locates the beginning of science in the advent of an attitude, the
appearance of the "critical" beside the "dogmatic." These are for him
psychological, not historical, categories, which are not distinguished by means
of their products or world-views. The dogmatic attitude, "an uncontrolled wish to
impose regularities" upon the world, is succeeded by the critical attitude,
"which shares with the dogmatic attitude the quick adoption of a schema of
expectations- a myth, perhaps, or a conjecture or hypothesis- but which is ready
to modify it, to correct it, and even to give it up." (6) Popper's scientist is
not entirely removed from praxis, but takes a different attitude to his products
and experiences. For example, he writes, "The method of trial and error is
applied not only to Einstein, but, in a more dogmatic fashion, by the amoeba
also. The difference lies not so much in the trials as in a critical and
constructive attitude towards errors... ." (7)
In the essay "Science: Conjectures and Refutations," Popper describes his
distinction as belonging to the psychology of experience, (8) while Husserl
describes his as the "genuine" history of philosophy, but in spite of this, each
ends up describing his respective "attitudes" in both historical and
psychological, or subjectivistic terms. Popper, despite his initial psychological
description, credits the Greeks with the "discovery of the critical method,"
indicating that the adoption of the critical attitude by the human psyche took
place at a specific point in history, namely with the Presocratics. (9) Husserl,
in turn, while being primarily concerned with historical description of the
origin of science among the Presocratics, ends up ascribing "prescientific"
properties to the minds of children, while scientific rationality is the mark of
a mature mind. (10) For Popper, the prescientific attitude is "characteristic of
primitives and children; and increasing experience and maturity sometimes create
an attitude of caution and criticism rather than of dogmatism." (11) In both
investigations into the origins of science, the scientific attitude ends up in
the hands of members of a certain society at a certain point in history, members
who have certain psychological characteristics, which make them relate to their
surroundings in an entirely novel way. Popper credits Thales, the first
scientist, with the institution of the critical attitude, which is "the attitude
of reasonableness, of rationality." Husserl marks with Thales, the first
philosopher, the advent of "a new humanity"-perhaps a more dramatic description
than Popper's, but one which results from the same sentiment: Thales, or rather
what he represents, is the beginning of the rationality, the very humanity, we
take to be proper to us today. (12)
http://www.bu.edu/wcp/Papers/Meth/MethGreb.htm
Popper's opposition to inductivism is well known. He repeatedly insisted that
there can be no successful algorithm for theory-formation. Popper likened the
position of the theorist to the
situation of a blind man who searches in a dark room for a black hat which
is--perhaps--not there. (15)
The theorist, like the blind man, proceeds by trial-and-error, coming to learn
where the hat is not, without ever reaching a certainty immune from rejection in
the force of further experience.
Popper is correct to emphasize the role of creative imagination in the
formulation of scientific hypotheses. The problem-situation does not dictate a
solution to the theorist. However, neither are hypotheses formulated
independently of the problem-situation. Popper's "black-hat image" is quite
misleading. Scientific conjectures are "blind" only in the sense that the outcome
of subsequent testing is unknown. They are not "blind" in Campbell's sense of
being "independent of the environmental conditions of the occasion of their
occurrence".
http://www.bu.edu/wcp/Papers/Scie/ScieLose.htm
> John Wilkins
> john...@wilkins.id.au http://wilkins.id.au
> "Men mark it when they hit, but do not mark it when they miss"
> - Francis Bacon
Abduction: A method of reasoning by which one infers to the best explanation.
Tron Furu
"Paul Bramscher" <brams00...@tc.umn.edu> skrev i melding
news:cdmg04$f6l$1...@lenny.tc.umn.edu...
> So, if making scientific statements requires that they are falsifiable,
> yet they often contain tautological (and irrefutably provable)
> mathematical underpinnings, what does this do to the holistic status of
> science with regard to mathematics and falsifiable statements?
>
> Can we say that math (and perhaps chemistry and physics) is
> non-scientific, in that when it includes balanced or provable formula
> (provable by tautology) that it is a non-science?
>
It all hangs on your definition of "science". If science is the art af
making true statements, then there is no science, as we do not even know
what truth is. If science is the ordering of concepts, propositions and
theorems for any given field of study, then math and logic are oobviously
sciences. If science is equated with empirical research in the field of
natural philosophy - i.e. "natural science" - then, by definition, math and
logic are not sciences, as they do not involve empirical study of nature.
Personally, I usually go for something like the second version.
T
Tron Furu
"John Wilkins" <john...@wilkins.id.au> skrev i melding
news:1ghbfki.18esdyu3dlm69N%>
...
> Moreover, as falsification takes place in virtue of the use of logic, if
> not maths, it cannot itself be the demarcation of science from
> non-science.
I don't know if I red this right:
A) Moreover, as falsification takes place in virtue of the use of logic, if
not maths, /falsification / cannot itself be the demarcation of science from
non-science.
B) Moreover, as falsification takes place in virtue of the use of logic, if
not maths, /logic/ cannot itself be the demarcation of science from
non-science.
I think it is A you mean; just checking. Still, I don't immediately
understand why falsification can't be a demarcation criterion just because
it involves the use of logic. Would that also be on account of logic, not
being empirical, is not science?
TiA,
T
Paul Bramscher
There are branches of math (such as discrete), and usages of math
(counting of physical objects), which arguably are empirical exercises.
However, I was trying to hint that if science is based on the building
of falsifiable statements, but uses (among its toolkit) an epistemology
which is not falsifiable (certain techniques in mathematics), then how
does this affect the falsification of the end result?
For example, "self-made millionaire" or "self-organization". If a
self-made millionaire employs other workers, invests in other companies,
buys products or services created or rendered by others, he cannot be
said to be truly self-made. His wealth was, at least, partially, the
result of others (same applies to the trendy "self-organization" term).
And so I question the depth of falsifiability in the context of
scientific statements which include the work of non-falsifiable
toolkits. For example -- theoretical physics since at least Einstein.
Without mathematical tautology we'd still be left largely with Newtonian
mechanics (at best).
And if not math, why not astrology? We might devise a completely
internally consistent version of astrology with tight tautology and
rational internal mapping. And if we introduced this back into
astronomy could we call statements which relied upon it as "scientific"?
Perhaps we could -- so long as they were falsifiable?
BuddhaThu
A=A is false if there is no existential "A" out there. We do not
assign empty variables as much as we do not look for fairies and
goblins. There must be something out there that we call "A". We are
not platonic mystics. Remember that. There is no mysterious realm
where there is an ghostly A floating around.
A=A can also be false due a circularity problem. No one can prove or
confirm it from the outside, for to prove or to confirm it on the
outside would change the identity thesis to A=B. This is not a pure
identity thesis. It is identity according to usage, linking likes to
liks together that are not self-equated to each other in an isomorphic
relationship. It is a great tool to be used to train similar and
abstract concepts together that cannot be readily pointed out
empirically. But in the end, they are only ***normative
abstractions,*** or abitrary connections, or assocations in a Humean
sense.
Isomorphic tautologies signal a limitation on science according to the
quantum scientist and philosopher Herman Weyl. He was an intutionist
that denies the law of the excluded middle in logic. In other words,
he is Brouwerian. Brouwer, Weyl and Popper were into the science of
creativity and intuitionistic discovery of science. Math to them was a
free creation of the human mind, (just like art), that helps us
express *our truth*, not THE TRUTH. So be free to use your imagination
and free your mind.
Concepts, although, expressing the free creativity of human mind are
essential to doing "objective science." Without concepts preceding our
experiments, there is no way to collect data and evaluate it. This is
what Rush Rhees called miracles. Events beyond concepts cannot be
proven by science, (either true or false), for science work on
concepts that precede the event. For if an event that has no concept,
then science will be at a lost until it can rig its own models and
concepts. They do not go out there and blindly collect data. They need
concepts to limit and isolate the boundaries of their data. Such is
the nature of scientific provability.
Your posting reminds me of an MIT linguistics prof. who visited us
last semester. (Yable, I think was his name.)In it, he talked about
the nature of Russell's statement "The present King of France s bald."
Russell thought that the statement is false. Strawson thought that the
statement is unprovable, neither true nor false. This lecturer could
not understand the difference between them.
I told him the difference is simple if we recast them in terms of
"knowledge by acquaintance" and "knowledge by description." One
expresses knowledge by actual experience, -- (that is that we actually
travelled to France and found that the King of France does not exist,
but until then, it is ***unprovable,*** -- not true nor false.) The
other is taken from a norm adherence to mean that it is taken within
our society as general knowledge that there is no King of France, and
therefore false. We did not have to travel to France to check it out.
The difference between them is as distinct as kennen and wissen.
***Both, however, can change like the wind.***
I recommend you Robert Nozick. He is a philosopher who died recently.
He is famous for his externalist account of knowledge in terms of
"tracking the truth." In this model, truth changes, contrary to what
the Greek classical philosophers thought. How I am now, may not be
true as to how I am later. So we track it and gauge the changes moment
to moment. It is kind of Popperian, in that it favors a much more open
instance of doing scientific research. The approach is that it moves
scientific research in both its logic and empirical approaches toward
tracking the changes of an event, rather to look for truth within its
finality. In this, it is more realistic than much older accounts.
It is my view that mathematical statements, in order to be closer to
the truth, must be seen in this instance. They are tools that
***describes*** truth within this instance, and untruth in another
instance. It need not be constant. This is a much more realistic
application of mathematics and bears a greater relationship to the
world that we study.
Concepts as math together with experience go hand in hand with each
other. They do not exist within a hiearchial relationship. The
relationship is symbiotic, and as the relationship is symbiotic, both
sides can express change and affect one another.
I am sorry for being so longwinded. There is more, but I have to go.
Paul Bramscher <brams00...@tc.umn.edu> wrote in message news:<cdmg04$f6l$1...@lenny.tc.umn.edu>...
Immortalist
Epistemology has it's very own version of the theory of falsifiability called
"negation by contradiction." I like Kants example; "a square has five sides" is
falsifiable in the sense that the subject "square" covertely contains the
proposition by definition that a square has four sides and a predicate that
contradicts this by claim more or less sides is prooved false by Aristotle's
handy little law that claims analitycally that it is false that (A = not A) but
true that (A = A)
Craig Franck
> "John Wilkins" wrote
> > Moreover, as falsification takes place in virtue of the use of logic, if
> > not maths, it cannot itself be the demarcation of science from
> > non-science.
>
> I don't know if I red this right:
>
> A) Moreover, as falsification takes place in virtue of the use of logic, if
> not maths, /falsification / cannot itself be the demarcation of science from
> non-science.
>
> B) Moreover, as falsification takes place in virtue of the use of logic, if
> not maths, /logic/ cannot itself be the demarcation of science from
> non-science.
>
> I think it is A you mean; just checking. Still, I don't immediately
> understand why falsification can't be a demarcation criterion just because
> it involves the use of logic. Would that also be on account of logic, not
> being empirical, is not science?
I think the problem is just using falsification as a criterion leads to
scientism, the view that all meaningful questions are scientifically
determinable to be true or false, at least in theory.
According to the verification theory of meaning, on which falsification
it is based, "I have 35 cents in my right pant pocket" is meaningful in
that you know how to verify/falsify it. It involves math and logic, but
not the scientific method. So there must be some other test for whether
a statement or question is scientific or not.
--
Craig Franck
craig....@verizon.net
Cortland, NY
Immortalist
"BuddhaThu" <softspok...@yahoo.com> wrote in message
news:d984cfeb.04072...@posting.google.com...
> Tautologies are not a safe haven for scientists.
>
> A=A is false if there is no existential "A" out there. We do not
> assign empty variables as much as we do not look for fairies and
> goblins. There must be something out there that we call "A". We are
> not platonic mystics. Remember that. There is no mysterious realm
> where there is an ghostly A floating around.
>
> A=A can also be false due a circularity problem. No one can prove or
> confirm it from the outside, for to prove or to confirm it on the
> outside would change the identity thesis to A=B.
But can we confirm it from the inside by definition at least in some cases?
For instance the statement; "cars have wheels" is true by the law of
non-contradiction.
Definition cars; 4 wheels, oil, engine, brakes, lights, gasoline, etc...
Subject cars
Predicate have 4 wheels
[more old Kantian veiws on this]
Craig Franck
> Abakus wrote:
> > Maths is a branch of logic, it is not an empirical discipline. Mathematical
> > and logical statements are unfalsifiable, because they are tautologies. For
> > example, "all blue things are blue" is a necessarily true statement which
> > does not involve any knowledge of the world.
>
> There are branches of math (such as discrete), and usages of math
> (counting of physical objects), which arguably are empirical exercises.
>
> However, I was trying to hint that if science is based on the building
> of falsifiable statements, but uses (among its toolkit) an epistemology
> which is not falsifiable (certain techniques in mathematics), then how
> does this affect the falsification of the end result?
That things like the scientific method, naturalism, and verification theory
were not themselves verifiable was what caused Logical Positivism to
cannibalize itself. Any system of knowledge must rely heavily on things
that are external to it.
Concepts such as a reasonable, unverifiable belief and tacit knowledge
(non-discursive knowledge directly given by experience) are equally
required for science and mysticism.
> And so I question the depth of falsifiability in the context of
> scientific statements which include the work of non-falsifiable
> toolkits. For example -- theoretical physics since at least Einstein.
> Without mathematical tautology we'd still be left largely with Newtonian
> mechanics (at best).
>
> And if not math, why not astrology? We might devise a completely
> internally consistent version of astrology with tight tautology and
> rational internal mapping. And if we introduced this back into
> astronomy could we call statements which relied upon it as "scientific"?
>
> Perhaps we could -- so long as they were falsifiable?
Whether is would pass as science or not might come down to how well
it generated useful hypotheses. If you buy the thesis that occult sciences
were our unconscious minds projected onto nature, you might be able
to generate a Jungian astrology. But it would probably be a bunch of
generalities that were fine-tuned for each individual.
Abakus
Maths is not an empirical discipline. You can certainly apply certain
equations to physical phenomena. Whether a given equation "describes" well
the behaviour of a given physical process can be falsified, within certain
limits.
> However, I was trying to hint that if science is based on the building
> of falsifiable statements, but uses (among its toolkit) an epistemology
> which is not falsifiable (certain techniques in mathematics), then how
> does this affect the falsification of the end result?
It doesnt affect it at all.
> For example, "self-made millionaire" or "self-organization". If a
> self-made millionaire employs other workers, invests in other companies,
> buys products or services created or rendered by others, he cannot be
> said to be truly self-made. His wealth was, at least, partially, the
> result of others (same applies to the trendy "self-organization" term).
I beg your pardon?
> And so I question the depth of falsifiability in the context of
> scientific statements which include the work of non-falsifiable
> toolkits. For example -- theoretical physics since at least Einstein.
> Without mathematical tautology we'd still be left largely with Newtonian
> mechanics (at best).
Without mathematical tautology we'd still be in the bronze age probably.
> And if not math, why not astrology? We might devise a completely
> internally consistent version of astrology with tight tautology and
> rational internal mapping. And if we introduced this back into
> astronomy could we call statements which relied upon it as "scientific"?
You're not getting the point. Astrology is empirical (if empirically
bullshit): it makes statements about the world. Its statements are synthetic
statements, not analytic, ie they are reducible to tautologies.
> Perhaps we could -- so long as they were falsifiable?
Astrology is indeed falsifiable. And it has been falsified over and over.
regards
Abakus
Paul Bramscher
Well, here's a way to extend your example. Someone makes the claim that
he has 35 cents in his right pant pocket, and 'twice what is in the left
as is in his right.' It turns out, for example, that there are several
ways the claim on the contents of the left pocket may be falsified:
1. He might have only 34 cents in his right and (for example) 68 in his
left. He is wrong in the statement that he had 35 in his right, but he
is still correct in asserting that he has twice 'what in the left as in
the right'. So, in this case, a tautology (X + X = 2X) claim holds true
in describing right, but the initial quantity of X is wrong.
2. He might have 35 in his right, and 71 in his left. Right claim for
the first pocket, bad math (or bad counting) for the second. Or perhaps
he claims that 35 + 35 does indeed equal 71. We can prove formally
(beyond falsifiability) that this is not the case.
3. He might have none in his right, in which case 0 + 0 = 2(0) = 0 and,
in a perverted sense, he's still correct about the quantity in his left
pocket.
There are other scenarios. Science and observables are built on
dependencies and assumptions. It's interesting to see how they interact
with math and logic.
Abakus
"John Wilkins" <john...@wilkins.id.au> wrote in message
news:1ghbfki.18esdyu3dlm69N%john...@wilkins.id.au...
>
> > So, if making scientific statements requires that they are falsifiable,
> > yet they often contain tautological (and irrefutably provable)
> > mathematical underpinnings, what does this do to the holistic status of
> > science with regard to mathematics and falsifiable statements?
> >
> > Can we say that math (and perhaps chemistry and physics) is
> > non-scientific, in that when it includes balanced or provable formula
> > (provable by tautology) that it is a non-science?
> >
> > Or are we really saying that if we observe a particular phenomena and
> > say it works like this because X + X = 2X and it turns out that while
> > our math is correct, it was actually a case of X + Y = X + Y? In both
> > cases, the math is correct but the statement is falsifiable.
> >
> > So if we wish to retain math is a tool of Popperian science, it seems
> > that we must mean "falsifiable" in more than one sense. That is, a
> > statement can be false because it has an internal flow problem. But it
> > may be false in the sense that -- while true at explaining some events
> > -- it is not true in explaining this event. And hence, it's both true
> > and untrue, depending on the scope of the problem.
> >
> > Ponder this.
>
> Popper did not think logic or maths were sciences. Many things are not
> sciences and are still useful - language, for example. Popper was not a
> logical positivist and did not restrict all that can be known to
> science.
I'm slightly puzzled by this last statement. Ayer, for instance, discusses
in detail the case of the analytical propositions of maths and says, that as
they are tautological dont fall under the verifiability principle. What I'm
saying that I tend to think that even if Popper had been a positivist (which
he wasnt) this fact didnt have to necessarily impinge on his views on
mathematics and logic.
regards
Abakus
Abakus
"Craig Franck" <craig....@verizon.net> wrote in message
news:QbTLc.23$T9.13@trndny05...
So observing that there are a number of things you call "coins", that these
coins are in a place you call "pocket" and that these coins are a certain
amount involves "just maths and logic". And you even agree that you are
verifying an hypothesis. Fascinating.
regards
Abakus
-
Abakus
> "Paul Bramscher" wrote
>
> > Abakus wrote:
>
> > > Maths is a branch of logic, it is not an empirical discipline.
Mathematical
> > > and logical statements are unfalsifiable, because they are
tautologies. For
> > > example, "all blue things are blue" is a necessarily true statement
which
> > > does not involve any knowledge of the world.
> >
> > There are branches of math (such as discrete), and usages of math
> > (counting of physical objects), which arguably are empirical exercises.
> >
> > However, I was trying to hint that if science is based on the building
> > of falsifiable statements, but uses (among its toolkit) an epistemology
> > which is not falsifiable (certain techniques in mathematics), then how
> > does this affect the falsification of the end result?
>
> That things like the scientific method, naturalism, and verification
theory
> were not themselves verifiable was what caused Logical Positivism to
> cannibalize itself. Any system of knowledge must rely heavily on things
> that are external to it.
The problem with positivism was the principle of verification. The
scientific method and naturalism have nothing to do with positivism. You
are getting mixed up.
> Concepts such as a reasonable, unverifiable belief and tacit knowledge
> (non-discursive knowledge directly given by experience) are equally
> required for science and mysticism.
Science and mysticism? How about steam engines and ballroom dancing?
regards
Abakus
Abakus
"Tron Furu" <tron...@frisurf.no> wrote in message
news:0CPLc.4872$Mq3....@news4.e.nsc.no...
To use a definition of science from a book I happen to be currently reading,
by Michael Shermer, which is as good as any: "science is a set of cognitive
and behavioural methods to describe and interpret observed or inferred
phenomena, past or present, aimed at building a testable body of knowledge
open to rejection or confirmation" .
regards
Abakus
Craig Franck
> "Craig Franck" wrote
> > That things like the scientific method, naturalism, and verification
> > theory
> > were not themselves verifiable was what caused Logical Positivism to
> > cannibalize itself. Any system of knowledge must rely heavily on things
> > that are external to it.
>
> The problem with positivism was the principle of verification. The
> scientific method and naturalism have nothing to do with positivism. You
> are getting mixed up.
The scientific method and positivism were inextricable linked.
http://www.philosophypages.com/hy/6q.htm
Carnap begins with an account of the methods and procedures by
means of which we employ sensory observations to verify (or at
least to confirm) the truth of scientific hypotheses about the operation
of the physical universe. Using the formal methods of mathematical
logic, then, the goal is to construct a strictly scientific language that
perspicuously represents the structure of the world as a whole. The
details are highly technical, of course, but it is only with the detailed
treatment that the difficulties of the procedure become evident. The
fundamental problem is that empirical generalizations are themselves
incapable of direct support within such a system.
> > Concepts such as a reasonable, unverifiable belief and tacit knowledge
> > (non-discursive knowledge directly given by experience) are equally
> > required for science and mysticism.
>
> Science and mysticism? How about steam engines and ballroom dancing?
My point is that belief in Naturalism requires a fundamental insight
into the nature of reality that goes beyond our ability to articulate.
Craig Franck
> "Craig Franck" wrote
> > I think the problem is just using falsification as a criterion leads to
> > scientism, the view that all meaningful questions are scientifically
> > determinable to be true or false, at least in theory.
> >
> > According to the verification theory of meaning, on which falsification
> > it is based, "I have 35 cents in my right pant pocket" is meaningful in
> > that you know how to verify/falsify it. It involves math and logic, but
> > not the scientific method. So there must be some other test for whether
> > a statement or question is scientific or not.
>
> So observing that there are a number of things you call "coins", that these
> coins are in a place you call "pocket" and that these coins are a certain
> amount involves "just maths and logic". And you even agree that you are
> verifying an hypothesis. Fascinating.
I'm not sure how to take that, but I don't believe it's actually a scientific
hypothesis since it doesn't explain anything. It's just a statement that may
or may not be true.
If I set off a metal detector and developed the theory that I forgot to take
the change out of my pockets, that would be a different matter. It functions
within a larger framework.
--
Abakus
A statement that may or may not be true, and whether it is true or not can
be falsifiable, is a hypothesis. When you find the statement to be true you
verify the hypothesis. It doesnt get much more scientific than that, really.
Your hypothesis of the coins is not very different from, eg, "there are no
eagles in the north pole", or "poppies contain morphine" or "there is a gene
for schizophrenia". You go and check and come back with an answer.
Additionally, most scientific disciplines, particularly in the early stages
of a certain field of study, involve long periods of data-collecting and
analysis, without much of a hypothesis put forward. One single example, and
there are many, would be the study of natural products: a lot of the
literature on natural products involves papers describing the chemicals
found in plants. What you learn from that is that chemical X is present in
plant Y. This may be boring science but it is science. Some purists may
call it "protoscience". And a lot of science also works by trial and error.
And a lot of science works by lets-see-what-happens-when-we-do-this; you
find many articles in the literature where they find that a certain drug has
some interesting effect on certain cells. And you wonder, why did they try
this chemical at all? Well, they probably tried many that they had on their
shelves and one day they got lucky. This is what is called somewhat
derogatorily "shelf biochemistry"; but sometimes it produces great results.
There is not just one single scientific method, there are many, in the same
way that there are many ways in which we make inferences from the data
available in our everyday lives. Because science doesnt have any peculiar
methodology: the methods of science are simply fine-tunings of the ways we
operate in our everyday lives.
And falsificationism is not a criterion for "scientism", it is a criterion
for scientific hypotheses.
regards
Abakus
Abakus
> "Abakus" wrote
>
> > "Craig Franck" wrote
>
> > > That things like the scientific method, naturalism, and verification
> > > theory
> > > were not themselves verifiable was what caused Logical Positivism to
> > > cannibalize itself. Any system of knowledge must rely heavily on
things
> > > that are external to it.
> >
> > The problem with positivism was the principle of verification. The
> > scientific method and naturalism have nothing to do with positivism.
You
> > are getting mixed up.
>
> The scientific method and positivism were inextricable linked.
There may be. But the reason positivism declined was mainly the failure to
verify the verifiability principle, which is a metaphysical statement.
>
> > > Concepts such as a reasonable, unverifiable belief and tacit knowledge
> > > (non-discursive knowledge directly given by experience) are equally
> > > required for science and mysticism.
> >
> > Science and mysticism? How about steam engines and ballroom dancing?
>
> My point is that belief in Naturalism requires a fundamental insight
> into the nature of reality that goes beyond our ability to articulate.
I dont see why. Naturalism (which I prefer to call materialism) is the idea
that what there is belongs to the natural world. This is the view that the
only thing that exists is matter. In a modern context, "matter" should be
taken to extend to all scientifically observable entities such as energy,
forces, etc, in other words, the "material world".
regards
Abakus
Craig Franck
> "Craig Franck" wrote
> > I'm not sure how to take that, but I don't believe it's actually a
> > scientific
> > hypothesis since it doesn't explain anything. It's just a statement that
> > may
> > or may not be true.
> >
> > If I set off a metal detector and developed the theory that I forgot to
> > take
> > the change out of my pockets, that would be a different matter. It
> > functions
> > within a larger framework.
>
> A statement that may or may not be true, and whether it is true or not can
> be falsifiable, is a hypothesis. When you find the statement to be true you
> verify the hypothesis. It doesnt get much more scientific than that, really.
I've been taught a hypothesis must function as an explanation. The problem
I have is you appear to be making a hypothesis its own target of explanation.
http://www.philosophypages.com/dy/h9.htm#hyps
http://www.philosophypages.com/dy/e9.htm#expl
http://www.philosophypages.com/lg/e15.htm#expl
> Your hypothesis of the coins is not very different from, eg, "there are no
> eagles in the north pole", or "poppies contain morphine" or "there is a gene
> for schizophrenia". You go and check and come back with an answer.
I think the first example is different from the other two. It's a hypothesis for
why we see no eagles at the north pole, but it doesn't add any information.
So it really explains nothing. "There is a gene for schizophrenia" is not a
trivial restatement of facts. "Poppies contain morphine" is a terrible hypothesis
for why we find morphine in poppies, but a good one form why they act
as an analgesic.
I agree one could take any statement of the form you described and turn it
into a hypothesis. But the quality of a hypothesis is measured by how well it
functions as an explanation.
> There is not just one single scientific method, there are many, in the same
> way that there are many ways in which we make inferences from the data
> available in our everyday lives. Because science doesnt have any peculiar
> methodology: the methods of science are simply fine-tunings of the ways we
> operate in our everyday lives.
I'd say when someone mentions the scientific method, they are specifically
referring to the steps outlined in the last link.
Craig Franck
> "Craig Franck" wrote
> > The scientific method and positivism were inextricable linked.
>
> There may be. But the reason positivism declined was mainly the failure to
> verify the verifiability principle, which is a metaphysical statement.
That I can agree with.
> > My point is that belief in Naturalism requires a fundamental insight
> > into the nature of reality that goes beyond our ability to articulate.
>
> I dont see why. Naturalism (which I prefer to call materialism) is the idea
> that what there is belongs to the natural world. This is the view that the
> only thing that exists is matter. In a modern context, "matter" should be
> taken to extend to all scientifically observable entities such as energy,
> forces, etc, in other words, the "material world".
But how is this opinion formed? Materialism makes heavy use of
scientific realism. When someone says they absolutely know that
external objects of perception are real and mind independent entities,
one wonders how this can be the case if it's not a form of intuitionism.
(A scientific explanation of this could be that the basic reality testing
skills of a sound mind appear to be functioning at the unconscious
level; it's just apparent to people "things are a certain way.")
Also, if as some people claim over at talk.origins, there has never been
a non-naturalistic event in the entire history of the universe, while it
might be the case, I get the impression that they are going beyond
induction or logic when they form this conclusion.
Abakus
> "Abakus" wrote
>
> > "Craig Franck" wrote
>
> > > I'm not sure how to take that, but I don't believe it's actually a
> > > scientific
> > > hypothesis since it doesn't explain anything. It's just a statement
that
> > > may
> > > or may not be true.
> > >
> > > If I set off a metal detector and developed the theory that I forgot
to
> > > take
> > > the change out of my pockets, that would be a different matter. It
> > > functions
> > > within a larger framework.
> >
> > A statement that may or may not be true, and whether it is true or not
can
> > be falsifiable, is a hypothesis. When you find the statement to be true
you
> > verify the hypothesis. It doesnt get much more scientific than that,
really.
>
> I've been taught a hypothesis must function as an explanation. The problem
> I have is you appear to be making a hypothesis its own target of
explanation.
A hypothesis is an idea or proposition about the natural world, that can be
tested by observations or experiments. An hypothesis may indeed serve as an
explanation, and frequently in science or in our everyday lives hypotheses
are proposed as explanations for certain phenomena. For instance,
continuing with your simple case of the coins in your pocket, the hypothesis
"I have coins in my pocket" could be a proposed explanation for the
phenomenon "something is bothering my leg", or for the phenomenon "there
is a funny clinking sound when I walk". In such cases the hypothesis "I have
coins in my pocket" would serve -if verified by observation- as a possible
explanation for those phenomena.
> > Your hypothesis of the coins is not very different from, eg, "there are
no
> > eagles in the north pole", or "poppies contain morphine" or "there is a
gene
> > for schizophrenia". You go and check and come back with an answer.
>
> I think the first example is different from the other two. It's a
hypothesis for
> why we see no eagles at the north pole, but it doesn't add any
information.
> So it really explains nothing. "There is a gene for schizophrenia" is not
a
> trivial restatement of facts. "Poppies contain morphine" is a terrible
hypothesis
> for why we find morphine in poppies, but a good one form why they act
> as an analgesic.
Hypotheses of course come in many forms and shapes, in the same way that
ideas and propositions come in many forms and shapes. Any statement about
the world which can be tested by observation or experimentation is an
hypothesis. The three statements I gave above are statements about the
world, and the three are testable by observation or experimentation, ergo
the three are bona fide hypotheses.
> I agree one could take any statement of the form you described and turn it
> into a hypothesis. But the quality of a hypothesis is measured by how well
it
> functions as an explanation.
You dont have to turn them into hypotheses. They are -by definition-
hypotheses. I dont know what you mean by the "quality " of a hypothesis. If
the hypothesis is confirmed by the data then it is correct and if it is not
confirmed then it is not. That is the only classification for hypotheses
that is worth making. Of course, you can value hypotheses in terms of the
significance of the knowledge we may gain by testing them, and in this
context it is doubtless far more likely that the Nobel committee will pay
more attention to those individuals who spend time testing the hypothesis
"there is a gene for schizophrenia" (especially if they find the damn gene)
than to those who spend time testing the hypothesis "there are coins in my
pocket" -but this is a different story altogether.
> > There is not just one single scientific method, there are many, in the
same
> > way that there are many ways in which we make inferences from the data
> > available in our everyday lives. Because science doesnt have any
peculiar
> > methodology: the methods of science are simply fine-tunings of the ways
we
> > operate in our everyday lives.
>
> I'd say when someone mentions the scientific method, they are specifically
> referring to the steps outlined in the last link.
When someone mentions "the scientific method" there are two possibilities.
One, they know what they are talking about and are sacrificing accuracy for
the sake of brevity and conciseness, ie, they are speaking in a form of
shorthand, in the assumption that their audience (especially if the audience
is composed of scientists) knows what they mean ; two, they are ignoramuses
who have no idea what science is and how it works. The latter is, without a
shadow of a doubt, the most frequently encountered usage of the expression
"scientific method", for the very simple reason that there are far more
ignoramuses of science than people who know what science is about.
Somebody who knew what science was about was one Percy Bridgman, a
physicist. Nobody much remembers his name, but most people do recognize one
line of his book "reflections of a physicist". In the chapter titled "on
scientific method", this gentleman stated: "No one standing on the outside
can predict what the individual scientist will do or what method he will
follow. In short, science is what scientists do, and there are as many
scientific methods as there are individual scientists. "
Another distinguished scientist, thinker and Nobel prize winner, Sir Peter
Medawar (most of whose collected essays can be found in the brilliant book
"Pluto's Repulic" which I wholeheartedly recommend reading to anybody with
an interest in science), said the following:
"Laymen and philosophers who have been brought up to think that scientists
wield a weapon known as "the scientific method" may well wonder how I could
allow myself to fritter away my time as I did, but there is not such thing
as as the scientific method and I don't regard my own messings-about as any
more discreditable than those of a writer who, before writing the novel or
play which makes his reputation, spends his time on potboilers and
half-finished manuscripts."
And finally, another scientist, Prof Lewis Wolpert (one of whose very
enjoyable lectures I had the pleasure of attending last year) wrote, in his
book The Unnatural Nature of Science:
"No one method, no paradigm, will capture the process of science. There is
no such thing as as the scientific method".
regards
Abakus
>
Abakus
> "Abakus" wrote
>
> > "Craig Franck" wrote
>
> > > The scientific method and positivism were inextricable linked.
> >
> > There may be. But the reason positivism declined was mainly the failure
to
> > verify the verifiability principle, which is a metaphysical statement.
>
> That I can agree with.
>
> > > My point is that belief in Naturalism requires a fundamental insight
> > > into the nature of reality that goes beyond our ability to articulate.
> >
> > I dont see why. Naturalism (which I prefer to call materialism) is the
idea
> > that what there is belongs to the natural world. This is the view that
the
> > only thing that exists is matter. In a modern context, "matter" should
be
> > taken to extend to all scientifically observable entities such as
energy,
> > forces, etc, in other words, the "material world".
>
> But how is this opinion formed? Materialism makes heavy use of
> scientific realism. When someone says they absolutely know that
> external objects of perception are real and mind independent entities,
> one wonders how this can be the case if it's not a form of intuitionism.
Materialism is the oldest philosophical tradition in Western civilization.
It started with the good old Greeks of the VI century BCE who came up for
the first time with the idea that the world is not the playground of the
gods but tht it is governed by laws and these laws are knowable. This is the
root of scientific thinking. Of course materialism is not itself an
empirical science. It rests on assumptions that are ultimately
metascientific, but not metaphysical in the Aristotelian sense, ie, the
assumptions of materialism go beyond empirical science, but not beyond
physical reality.
Materialism is however rooted in solid empirical evidence and has as a
result always had its metascientific hypotheses scientifically confirmed,
because the basic assumption of valid science has also always been that
nature is governed by knowable physical laws
> (A scientific explanation of this could be that the basic reality testing
> skills of a sound mind appear to be functioning at the unconscious
> level; it's just apparent to people "things are a certain way.")
There are many hypotheses which are consistent with our observations. Maybe
we are just a head in a vat and what we see and experience is something like
"the matrix". Maybe Berkeley was right and there is no external world and
god is projecting this film we call reality in our heads. Maybe we are
asleep and everythng is a dream. Maybe we dont exist and we are just
somebody else's dream. Of all these possible explanations the simplest is
that there is an outside world and we are a bunch of mammals farting around
in it.
> Also, if as some people claim over at talk.origins, there has never been
> a non-naturalistic event in the entire history of the universe, while it
> might be the case, I get the impression that they are going beyond
> induction or logic when they form this conclusion.
If something happens and it happens in the universe,then it is by definition
a natural phenomenon. The problem with non-natural (or supernatural ) things
is that we have a word for them but we dont have any examples of what a
supernatural thing may be like. What would be a non-tautological definition
of a supernatural entity or event? How can something actually be
supernatural?
regards
Abakus
BuddhaThu
Yes, but what you are simply doing is re-asserting my main thesis. You
are still confirming it from the outside according to usage.
Take the classic example of A=A and in "All unmarried men are
bachelors." This is not a true A=A. It is A=B, identity being asserted
by usage. It is how I use "unmarried men" in similar usage to what is
a "bachelor." Similarity does not mean same, or different. This is
only an approx. relationship by the fact that they are different
words.
To me, there is no learning of a language or of a concept in A=A. If
you say "All unmarried men are unmarried men", then you are not saying
much to help me learn what the heck is an unmarried man. :-) Nothing
is really justifying the usage of the word. This is the same as "cars
have 4 wheels."
Again, certainty is never in a tautological existence. The
tautological existence exerts only paradox and limitation upon your
existence.
"Immortalist" <Reanima...@yahoo.com> wrote in message news:<DamdnSfaHfu...@comcast.com>...
Craig Franck
> Materialism is however rooted in solid empirical evidence and has as a
> result always had its metascientific hypotheses scientifically confirmed,
> because the basic assumption of valid science has also always been that
> nature is governed by knowable physical laws
That's true, but I think it's clear that the materialism of Thales and
Democritus was not based on scientific observation. 2,500 years ago,
some form of Panpsychism was probably the most likely explanation
for the world around us.
Today, I believe a combination of event-based process philosophy and
animism is a far better metaphysical basis for scientific thinking than
materialism. But such a strong prior commitment to materialism is hard
to shake off. The most you can say is materialism is the result of the
statistical fallout of quantum mechanical events, the nature of which we
really aren't sure.
> Of all these possible explanations the simplest is
> that there is an outside world and we are a bunch of mammals farting around
> in it.
I agree with this. There was a monster thread recently over on talk.origins
called "Epistemological pluralism" in which I concluded that scientific
realism simplifies science exponentially, and that is its main value.
But there is a need to explain why naive realism is the default metaphysics
of so many non-scientifically minded individuals. There is also the fact that
scientific realism is representational in nature. We perceive the world around
us through representations in our brain. Our visual field is in fact several maps
inside our visual cortex. But we think it's the outside world. Would you
agree that this "out there" conclusion is "intuitively given"?
The fact that we believe something that is scientifically false proves that our
hard wiring for perception trumps logical thinking. I think this demonstrates
that it is not unreasonable to postulate an unconscious bias toward seeing the
world as totally mental or totally physical, rational arguments notwithstanding.
> If something happens and it happens in the universe,then it is by definition
> a natural phenomenon. The problem with non-natural (or supernatural ) things
> is that we have a word for them but we dont have any examples of what a
> supernatural thing may be like. What would be a non-tautological definition
> of a supernatural entity or event? How can something actually be
> supernatural?
It's very hard to say, since a supernatural event should scientifically be
classified as a naturalistic event with no current explanation.
One possibility is "supertasks": an infinite number of naturalistic events
in a finite period of time. This has the advantage of being logically coherent
with naturalism.
Abakus
> "Abakus" wrote
>
> > Materialism is however rooted in solid empirical evidence and has as a
> > result always had its metascientific hypotheses scientifically
confirmed,
> > because the basic assumption of valid science has also always been that
> > nature is governed by knowable physical laws
>
> That's true, but I think it's clear that the materialism of Thales and
> Democritus was not based on scientific observation. 2,500 years ago,
> some form of Panpsychism was probably the most likely explanation
> for the world around us.
It was certainly based on observation and experience. We could say that
science did not exist at the time, but that is not relevant.
> Today, I believe a combination of event-based process philosophy and
> animism is a far better metaphysical basis for scientific thinking than
> materialism. But such a strong prior commitment to materialism is hard
> to shake off.
Animism? Why would animism be a better basis for scientific thinking than
materialsm? The history of science is the history of the demise of vitalism,
animism, dualism and all similar views.
>The most you can say is materialism is the result of the
> statistical fallout of quantum mechanical events, the nature of which we
> really aren't sure.
The most you can say of materialism is that so far it seems to fit all the
perceptual and experiential data.
> > Of all these possible explanations the simplest is
> > that there is an outside world and we are a bunch of mammals farting
around
> > in it.
>
> I agree with this. There was a monster thread recently over on
talk.origins
> called "Epistemological pluralism" in which I concluded that scientific
> realism simplifies science exponentially, and that is its main value.
> But there is a need to explain why naive realism is the default
metaphysics
> of so many non-scientifically minded individuals.
Realism is the default position of all philosophers when they are off-duty,
as a philosopher said. It is also the default position of most
scientifically minded individuals.
>There is also the fact that
> scientific realism is representational in nature. We perceive the world
around
> us through representations in our brain. Our visual field is in fact
several maps
> inside our visual cortex. But we think it's the outside world. Would you
> agree that this "out there" conclusion is "intuitively given"?
Of course. I remember when I was a kid (I mean, when I was 100%
philosophically naive) I wondered whether my senses fooled me and that maybe
things were not quite as I perceived them, but I dont think that people
would very often come up with the idea that the world is all in their heads
and that they live in the matrix. I mean, you may come up with the idea but
like a sci fi plot.
> The fact that we believe something that is scientifically false proves
that our
> hard wiring for perception trumps logical thinking.
It is not scientifically false at all. It is simply scientifically
unprovable. It is a metascientific view.
>I think this demonstrates
> that it is not unreasonable to postulate an unconscious bias toward seeing
the
> world as totally mental or totally physical, rational arguments
notwithstanding.
> > If something happens and it happens in the universe,then it is by
definition
> > a natural phenomenon. The problem with non-natural (or supernatural )
things
> > is that we have a word for them but we dont have any examples of what a
> > supernatural thing may be like. What would be a non-tautological
definition
> > of a supernatural entity or event? How can something actually be
> > supernatural?
>
> It's very hard to say, since a supernatural event should scientifically
be
> classified as a naturalistic event with no current explanation.
Yes. Until the explanation emerges.
regards
Abakus
Craig Franck
> "Craig Franck" wrote
> > I've been taught a hypothesis must function as an explanation. The problem
> > I have is you appear to be making a hypothesis its own target of
> > explanation.
>
> A hypothesis is an idea or proposition about the natural world, that can be
> tested by observations or experiments. An hypothesis may indeed serve as an
> explanation, and frequently in science or in our everyday lives hypotheses
> are proposed as explanations for certain phenomena.
This might come down to semantics, but according to "The Encyclopedia
Britannica" and an Encyclopedia of Philosophy at my local library, it must
function as an explanation since it's the explanation part that makes it a
hypothesis. You need the context to evaluate the hypothesis.
So "I have change in my pocket" is a good hypothesis for why I hear a
faint jingling sound, but a bad hypothesis for why I have a headache. Without
knowing what it's supposed to explain, you can't evaluate it as a hypothesis,
just determine its truth value.
I remember repeated reading that you can't determine a hypothesis to be
absolutely true because it *must* go beyond the facts. By this reasoning,
heliocentricity is now a fact and not a hypothesis. NASA has pictures, they
can prove it beyond all doubt, so it's no longer a hypothetical explanation
as to why the planets move the way they do.
> Hypotheses of course come in many forms and shapes, in the same way that
> ideas and propositions come in many forms and shapes. Any statement about
> the world which can be tested by observation or experimentation is an
> hypothesis.
I've cited several sources for my belief that it must function as an explanation
to be considered a hypothesis. It would be helpful if you could cite a source
saying something similar to "Any statement about the world which can be tested
by observation or experimentation is an hypothesis." Otherwise, I don't know
what else to say.
> > I agree one could take any statement of the form you described and turn it
> > into a hypothesis. But the quality of a hypothesis is measured by how well
> > it
> > functions as an explanation.
>
> You dont have to turn them into hypotheses. They are -by definition-
> hypotheses. I dont know what you mean by the "quality " of a hypothesis. If
> the hypothesis is confirmed by the data then it is correct and if it is not
> confirmed then it is not. That is the only classification for hypotheses
> that is worth making.
I mean how well it functions as an explanation. All you seem interested in is
the truth value. Yes, Winona Ryder is 5' 4. No, that's not a good hypothesis as
to why she was convicted of shop lifting. Just confirming her height does not
validate the hypothesis since you don't know what it's a hypothesis for.
> > I'd say when someone mentions the scientific method, they are specifically
> > referring to the steps outlined in the last link.
>
> When someone mentions "the scientific method" there are two possibilities.
<snip comments and quotations>
This I can agree with. I've long suspected there was something funny
about a hard quantification of the scientific method because it contains
language like "invent a hypothesis," which is as helpful as putting "create
something" in a methodology of art.
Abakus
> "Abakus" wrote
>
> > "Craig Franck" wrote
>
> > > I've been taught a hypothesis must function as an explanation. The
problem
> > > I have is you appear to be making a hypothesis its own target of
> > > explanation.
> >
> > A hypothesis is an idea or proposition about the natural world, that can
be
> > tested by observations or experiments. An hypothesis may indeed serve as
an
> > explanation, and frequently in science or in our everyday lives
hypotheses
> > are proposed as explanations for certain phenomena.
>
> This might come down to semantics, but according to "The Encyclopedia
> Britannica" and an Encyclopedia of Philosophy at my local library, it must
> function as an explanation since it's the explanation part that makes it a
> hypothesis. You need the context to evaluate the hypothesis.
You are not making this very easy. First of all, if encyclopedias and
dictiionaries contained the sum total of the universe's knowlwdge then
courses and degrees and colleges and universities would be a waste of time
and money. Secondly, please note that any statement or proposition *is by
definition an explanation*: it explains the idea it contains. If you look at
what I wrote in my previous post you will see how it works.
> So "I have change in my pocket" is a good hypothesis for why I hear a
> faint jingling sound, but a bad hypothesis for why I have a headache.
Without
> knowing what it's supposed to explain, you can't evaluate it as a
hypothesis,
> just determine its truth value.
That goes without saying. If you say to somebody, "I have this mysterious
clinking sound in my pocket" and they reply "It is raining in Croatia", you
can infer that their proposition is probably not a good explanatory
hypothesis for the clinking sound.
> I remember repeated reading that you can't determine a hypothesis to be
> absolutely true because it *must* go beyond the facts. By this reasoning,
> heliocentricity is now a fact and not a hypothesis. NASA has pictures,
they
> can prove it beyond all doubt, so it's no longer a hypothetical
explanation
> as to why the planets move the way they do.
I agree with that. I fail to see the relevance of that statement to what we
were discussing, though. I doubt it has any.
> > Hypotheses of course come in many forms and shapes, in the same way that
> > ideas and propositions come in many forms and shapes. Any statement
about
> > the world which can be tested by observation or experimentation is an
> > hypothesis.
>
> I've cited several sources for my belief that it must function as an
explanation
> to be considered a hypothesis. It would be helpful if you could cite a
source
> saying something similar to "Any statement about the world which can be
tested
> by observation or experimentation is an hypothesis." Otherwise, I don't
know
> what else to say.
I dont either. Have a look in the web, or in books, I have no idea. And as I
said before, any proposition is an explanation for something, so we dont
disagree here.
> > > I agree one could take any statement of the form you described and
turn it
> > > into a hypothesis. But the quality of a hypothesis is measured by how
well
> > > it
> > > functions as an explanation.
> >
> > You dont have to turn them into hypotheses. They are -by definition-
> > hypotheses. I dont know what you mean by the "quality " of a hypothesis.
If
> > the hypothesis is confirmed by the data then it is correct and if it is
not
> > confirmed then it is not. That is the only classification for hypotheses
> > that is worth making.
>
> I mean how well it functions as an explanation. All you seem interested in
is
> the truth value. Yes, Winona Ryder is 5' 4. No, that's not a good
hypothesis as
> to why she was convicted of shop lifting. Just confirming her height does
not
> validate the hypothesis since you don't know what it's a hypothesis for.
Sane people dont normally go about uttering propositions for the sake of it.
They tend to be uttered with the intention of making a point or explaining
something or replying to something. If somebody tells you "it's one thirty"
it is probably because you asked them the time, not because you asked them
the height of Winona Ryder.
regards
Abakus
Immortalist
>
> Yes, but what you are simply doing is re-asserting my main thesis. You
> are still confirming it from the outside according to usage.
>
The principle of identity follows immediately upon the idea of being, and is
stated as follows: "A being is what it is." A negative statement of it would be:
"A being cannot both be and not be at the same time and under the same aspect."
Some would say that it is a meaningless statement, i.e. a tautology. It seems
that it can be heard as a tautology. But it can also be heard as the first
judgment of the intellectual life from which all reasoning must proceed and to
which no one can r eason.
For Aristotle this is just the first principle not only of knowledge but also of
reality. It proclaims the primal mystery of being and demands the subordination
of the mind to reality. It is the axiom of a being's irreducible diversity.
Having arrived at this first principle Aristotle believes that it is a judgment
that is held with absolute and changeless certitude. Two judgments follow
immediately upon the simple apprehension of the concept of being as such, and the
concept of non- being. As soon as a person experiences the concept "being as
such," and the concept of "non-being," the two judgments that "a being is what it
is," and that "a being cannot both be and not be at the same time under the same
aspect," are immediately asse nted to by the mind.
These judgments are the first principles of human reason; they are presupposed to
every other judgment that the human mind can make; they are beyond demonstration.
They are self-evident. They are valid both in the order of being and in the order
of k nowing.
It follows then that it is contradictory to hold that a person must prove by
demonstration, all that he holds to be true. He comes to these first judgments
that are in themselves, and in the knower, self-evident.
http://www.google.com/search?q=%22principle+of+identity%22
> Take the classic example of A=A and in "All unmarried men are
> bachelors." This is not a true A=A. It is A=B, identity being asserted
> by usage. It is how I use "unmarried men" in similar usage to what is
> a "bachelor." Similarity does not mean same, or different. This is
> only an approx. relationship by the fact that they are different
> words.
>
> To me, there is no learning of a language or of a concept in A=A. If
> you say "All unmarried men are unmarried men", then you are not saying
> much to help me learn what the heck is an unmarried man. :-) Nothing
> is really justifying the usage of the word. This is the same as "cars
> have 4 wheels."
>
An animal may contain in memory from experiences an array of features which it
considers very dangerous. If the animal sees a small number of the features like
a few particular curves and a color in nearby bushes it accesses the array
analytically and conpares. When the alarm goes of the compression of data has
saved the animals life for it did not have to have the entire array of features
in its mind but a way to compare tpes of features.
The trick of the evolutionary value of identity inferences is the quick access
without unfolding the entire array but having guideposts and turning points.
Similaraly embroyology works this way with bumper cones and axon guides that
respond to generalized chemical gradients. Thinking to hard today.
> Again, certainty is never in a tautological existence. The
> tautological existence exerts only paradox and limitation upon your
> existence.
>
heeeea! (low raspy voice)
I live to die
that's why I was born
kill or be killed
the law of the land
living through the violence
I'm just surviving - there's no way to end this(**)
one more dead, one survives
instinct to live
http://www.darklyrics.com/lyrics/sixfeetunder/haunted.html#6
(**) tautological existence exerts only paradox and limitation upon
Craig Franck
> "Craig Franck" wrote
> > This might come down to semantics, but according to "The Encyclopedia
> > Britannica" and an Encyclopedia of Philosophy at my local library, it must
> > function as an explanation since it's the explanation part that makes it a
> > hypothesis. You need the context to evaluate the hypothesis.
>
> You are not making this very easy.
I'm making it hard for you? I didn't expect that response. I went to the
reference section of my library and consulted two sources that one could
reasonably assume contained accurate information on the precise definition
of a technical term.
And you view this as somehow an obstacle to this discussion
> First of all, if encyclopedias and
> dictiionaries contained the sum total of the universe's knowlwdge then
> courses and degrees and colleges and universities would be a waste of time
> and money.
But you would expect them to contain accurate definitions of basic terms.
People who get degrees often look up words in dictionaries of science and
technological terms, so it's not an either or situation. I would only be
mistaken in my pursuit if I looked up a scientific term in a general-language
dictionary.
> Secondly, please note that any statement or proposition *is by
> definition an explanation*: it explains the idea it contains. If you look at
> what I wrote in my previous post you will see how it works.
I don't agree. If all it does is explain the idea it contains then the statement
explains itself. That is trivially true and does not constitute a hypothesis.
> > I remember repeated reading that you can't determine a hypothesis to be
> > absolutely true because it *must* go beyond the facts. By this reasoning,
> > heliocentricity is now a fact and not a hypothesis. NASA has pictures,
> > they
> > can prove it beyond all doubt, so it's no longer a hypothetical
> > explanation
> > as to why the planets move the way they do.
>
> I agree with that.
Now I'm confused. You agree that "The sun is at the center of the solar
system" is a fact and not a hypothesis? If that's the case, then we agree
with each other.
> I fail to see the relevance of that statement to what we
> were discussing, though. I doubt it has any.
I think you missed the relevance.
> > I've cited several sources for my belief that it must function as an
> > explanation
> > to be considered a hypothesis. It would be helpful if you could cite a
> > source
> > saying something similar to "Any statement about the world which can be
> > tested
> > by observation or experimentation is an hypothesis." Otherwise, I don't
> > know
> > what else to say.
>
> I dont either. Have a look in the web, or in books, I have no idea.
I've looked. Everything I've found agrees with my contention that a
hypothesis must function as an explanation for something. And that
something must be explicitly stated. The fact that you have no idea
where to back up your contentions is worrisome.
In fact, there is no way to move beyond opinion.
> And as I
> said before, any proposition is an explanation for something, so we dont
> disagree here.
We disagree as to whether:
"Any statement about the world which can be tested by observation
or experimentation is an hypothesis."
"Today is Sunday" is a proposition. But unless it explains something --
why the busses aren't running -- it's not functioning as an explanation.
So "Today is Sunday" is only the first half of a hypothesis. It's the answer
to an unknown question.
Abakus
The chunk of my previous post which you edited out contains all the answers
to your questions.
regards
Abakus