ONT Newton's Summmation
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
CSP = Charles Peirce
HP = Howard Pattee
IN = Issac Newton
JA = Jon Awbrey
JC = John Collier
JC: Speaking of old fashioned views, what's wrong with [Newton's Five Rules, vide infra].
Okay, let's toss Newton's particular, all too particlear marbles into the ring,
and look at them along with the other heuristics. I know what you're thinking,
"heuristicae non fingo", but never mind that now. I have heard of two popular
readings of Newton's auto-recusive claim, "hypotheses non fingo", one, that he
never pretended any hypothesis, which sounds to my ears as though it lighted
somewhere on the spectrum between the theorem of the absurd and the theatre
of the disingenue, but, two, a rather more charitable reading, says that he
simply meant that he was not speculating on the "underlain" being, essence,
ontos, substance, or substrate of the phenomena, but merely trying to put
salve on their superficial appearances, wherever their irruptions might
irritate the sooth of topical assurance the most. In this casuistic
and far less caustic interpretation, Newton is doing nothing more
radical than marking off physics from metaphysics, where all the
figments of ontology live, and putting off the latter til later.
So much depends on how you read him.
But I think that his touchiness on
the topic of hypothesis leaves us
in the lurch as to how it's done.
Jon Awbrey
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
JA, quoting CSP:
| Admitting, then, that the question of Pragmatism is the Question of Abduction,
| let us consider it under that form. What is good abduction? What should an
| explanatory hypothesis be to be worthy to rank as a hypothesis? Of course,
| it must explain the facts. But what other conditions ought it to fulfill
| to be good? The question of the goodness of anything is whether that
| thing fulfills its end. What, then, is the end of an explanatory
| hypothesis? Its end is, through subjection to the test of
| experiment, to lead to the avoidance of all surprise and
| to the establishment of a habit of positive expectation
| that shall not be disappointed. Any hypothesis,
| therefore, may be admissible, in the absence of any
| special reasons to the contrary, provided it be capable
| of experimental verification and only in so far as it is
| capable of such verification. This is approximately the doctrine
| of pragmatism. But just here a broad question opens out before us.
| What are we to understand by experimental verification? The answer to that
| involves the whole logic of induction. Let me point out to you the different
| opinions which we actually find men holding today, perhaps not consistently, but
| thinking that they hold them, upon this subject. (LOP 1903, 250; CP 5.197-198).
|
| Charles Sanders Peirce,
|'Pragmatism as a Principle and Method of Right Thinking',
| The 1903 Harvard 'Lectures on Pragmatism' (= LOP 1903),
| Patricia Ann Turrisi (ed.), SUNY Press, Albany, NY, 1997.
HP: This sounds perfectly normal, but why is Peirce given so much credit for this "normal" view?
Obviously, induction is important too, but "any hypothesis" is not generally "admissible".
What is missing in this approximate doctrine is mention of the aesthetic elements of
explanations: simplicity, beauty, fecundity, etc., and clues for "distinguishing
this beauty from merely formal attractiveness ... a test so difficult that it
may baffle the most penetrating scientific minds" (Polanyi).
JC: Speaking of old fashioned views, what's wrong with:
JC, quoting IN:
| RULE 1
| We are to admit no more causes of natural things, than such as are both true and
| sufficient to explain their appearances. To this purpose the philosophers say,
| that Nature does nothing in vain, and more is in vain, when less will serve;
| for Nature is pleased with simplicity, and affects not the pomp of
| superfluous causes.
|
| RULE 2
| Therefore to the same natural effects we must, as far as possible, assign the same causes.
| As to respiration in a man, and in a beast; the descent of stones in Europe and in America;
| the light of our culinary fire and of the sun; the reflection of light in the earth, and in
| the planets.
|
| RULE 3
| The qualities of bodies, which admit neither intension nor remission of degrees,
| and which are found to belong to all bodies within reach of our experiments, are to
| be esteemed the universal qualities of all bodies whatsoever. For since the qualities
| of bodies are only known to us by experiments, we are to hold for universal, all such as
| universally agree with experiments; and such as are not liable to diminution, can never
| be quite taken away.
|
| We are certainly not to relinquish the evidence of experiments for the sake of dreams
| and vain fictions of our own devising; nor are we to recede from the analogy of Nature,
| which is wont to be simple, and always consonant to itself. We no other way know the
| extension of bodies, than by our senses, nor do these reach it in all bodies; but
| because we perceive extension in all that are sensible, therefore we ascribe it
| universally to all others, also.
|
| That abundance of bodies are hard we learn by experience.
| And because the hardness of the whole arises from the
| hardness of the parts, we therefore justly infer the
| hardness of the undivided particles not only of the
| bodies we feel but of all others.
|
| That all bodies are impenetrable we gather not from reason,
| but from sensation. The bodies which we handle we find
| impenetrables and thence conclude impenetrability to
| be a universal property of all bodies whatsoever.
|
| That all bodies are moveable, and endowed with certain powers
| (which we call the forces of inertia), or persevering in their
| motion or in their rest, we only infer from the like properties
| observed in the bodies which we have seen.
|
| The extension, hardness, impenetrability, mobility, and force of inertia of the whole
| result from the extension, hardness, impenetrability, mobility, and forces of inertia
| of the parts: and thence we conclude that the least particles of all bodies to be
| also all extended, and hard, and impenetrable, and moveable, and endowed with their
| proper forces of inertia. And this is the foundation of all philosophy. Moreover,
| that the divided but contiguous particles of bodies may be separated from one another,
| is a matter of observation; and, in the particles that remain undivided, our minds are
| able to distinguish yet lesser parts, as is mathematically demonstrated. But whether
| the parts so distinguished, and not yet divided, may, by the powers of nature, be
| actually divided and separated from one another, we cannot certainly determine.
| Yet had we the proof of but one experiment, that any undivided particle, in
| breaking a hard and solid body, suffered a division, we might by virtue of
| this rule, conclude, that the undivided as well as the divided particles,
| may be divided and actually separated into infinity.
|
| Lastly, if it universally appears, by experiments and astronomical observations, that
| all bodies about the earth, gravitate toward the earth; and that in proportion to the
| quantity of matter which they severally contain; that the moon likewise, according to
| the quantity of its matter, gravitates toward the earth; that on the other hand our
| sea gravitates toward the moon; and all the planets mutually one toward another;
| and the comets in like manner towards the sun; we must, in consequence of this
| rule, universally allow, that all bodies whatsoever are endowed with a principle
| of mutual gravitation.
|
| For the argument from the appearances concludes with more force for the
| universal gravitation of all bodies, than for their impenetrability, of
| which among those in the celestial regions, we have no experiments, nor
| any manner of observation. Not that I affirm gravity to be essential to
| all bodies. By their inherent force I mean nothing but their force of
| inertia. This is immutable. Their gravity is diminished as they recede
| from the earth.
|
| RULE 4
| In experimental philosophy we are to look upon propositions collected by general induction
| from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses
| that may be imagined, till such time as other phenomena occur, by which they may either
| be made more accurate, or liable to exceptions. This rule we must follow that the
| argument of induction may not be evaded by hypotheses.
|
| Isaac Newton,
|'The Mathematical Principles of Natural Philosophy',
| translated by A. Motte, London, 1729.
|
| http://www.fordham.edu/halsall/mod/newton-princ.html
JA, quoting IN:
"Hypotheses non fingo"
JA, quoting CSP:
| Having discovered and demonstrated the grounds of the possibility of
| the three inferences, let us take a preliminary glance at the manner in
| which additions to these principles may make them grounds of proceedure.
|
| The principle of inference 'à priori' has been apodictically demonstrated;
| the principle of inductive inference has been shown upon sufficient evidence
| to be true; the principle of inference 'à posteriori' has been shown to be one
| which nothing can contradict. These three degrees of modality in the principles of
| the three inferences show the amount of certainty which each is capable of affording.
| Inference 'à priori' is as we all know the only apodictic proceedure; yet no one
| thinks of questioning a good induction; while inference 'à posteriori' is
| proverbially uncertain. 'Hypotheses non fingo', said Newton; striving
| to place his theory on a firm inductive basis. Yet provisionally we
| must make hypotheses; we start with them; the baby when he lies
| turning his fingers before his eyes is testing a hypothesis he has
| already formed, as to the connection of touch and sight. Apodictic
| reasoning can only be applied to the manipulation of our knowledge;
| it never can extend it. So that it is an induction which eventually
| settles every question of science; and nine-tenths of the inferences
| we draw in any hour not of study are of this kind.
|
| CSP, CE 1, 186.
|
| Charles Sanders Peirce, "Harvard Lectures 'On the Logic of Science'", (1865),
|'Writings of Charles S. Peirce: A Chronological Edition, Volume 1, 1857-1866',
| Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤