Rebirth of Reason

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Post 60

Sunday, March 27, 2011 - 6:57amSanction this postReply
In his review, Merlin remarked:
    Some comparison of his view of induction to those of Francis Bacon and William Whewell would have been nice, too. Both wrote extensively about induction. Harriman's idea of integration seems to have a good deal in common with Whewell's ideas of colligation and consilience.
A work of related interest is: The Philosophical Breakfast Club
Laura J. Snyder (Random House 2011)

From the publisher:
    The Philosophical Breakfast Club recounts the life and work of four men who met as students at Cambridge University: Charles Babbage, John Herschel, William Whewell, and Richard Jones. Recognizing that they shared a love of science (as well as good food and drink) they began to meet on Sunday mornings to talk about the state of science in Britain and the world at large. Inspired by the great 17th century scientific reformer and political figure Francis Bacon—another former student of Cambridge—the Philosophical Breakfast Club plotted to bring about a new scientific revolution. And to a remarkable extent, they succeeded, even in ways they never intended.

    Historian of science and philosopher Laura J. Snyder exposes the political passions, religious impulses, friendships, rivalries, and love of knowledge—and power—that drove these extraordinary men. Whewell (who not only invented the word “scientist,” but also founded the fields of crystallography, mathematical economics, and the science of tides), Babbage (a mathematical genius who invented the modern computer), Herschel (who mapped the skies of the Southern Hemisphere and contributed to the invention of photography), and Jones (a curate who shaped the science of economics) were at the vanguard of the modernization of science.

    This absorbing narrative of people, science and ideas chronicles the intellectual revolution inaugurated by these men, one that continues to mold our understanding of the world around us and of our place within it. Drawing upon the voluminous correspondence between the four men over the fifty years of their work, Laura J. Snyder shows how friendship worked to spur the men on to greater accomplishments, and how it enabled them to transform science and help create the modern world.

My own remarks so far on Mr. Harriman’s book are collected below. These are from endnotes lately added to my essay “Induction on Identity” (1991).
    11. David Harriman (2008) places the point at which the atomic theory was inductively proven sometime after Maxwell’s kinetic theory of gases (1866) and not later than the confirmation of Mendeleev’s prediction of gallium (1875). His is not a claim about when all knowledgeable scientists accepted the atomic theory, but a claim about when all the elements of a rational proof of the theory were at hand. I hope later in this thread to look into whether the additional evidence and theory to 1908, my point (in the 1991 essay) of definitive proof for the atomic theory, fits naturally and entirely within the criteria Mr. Harriman has proposed for inductive proof of a theory. Meanwhile, note that criteria for rational induction purportedly sufficient to establish scientific theory in chemistry go back to Jakob Friedrich Fries (1801, 1822).

    27. Contrast my representation of the hypothetico-deductive method in science with its representation by Harriman (2010, 145–46). I have not supposed that the method entails that hypotheses are mere guesswork, which is not the way the method has been employed by any research in physical science with which I am familiar. However much later philosophers of science took hypotheses to be guesswork, that was not the view of William Whewell (Snyder 2006).

    31. Broad causal mode: Identical existents, in given circumstances, will always produce results not wholly identical to results produced by different existents in those same circumstances. Narrow causal mode: Identical existents, in given circumstances, will always produce identically same results.
    . . .
    Harriman (2010) writes that the essence of the law of causality is that “an entity of a certain kind necessarily acts in a certain way under a given set of circumstances” (21). Does that formulation of the essence of the causal law coincide with causality in the broad mode or with causality in the narrow mode? Harriman’s statement is slightly ambiguous between the two, though it leans towards the latter mode. Indeed, in further elaboration, he states that future actions can be inferred from past actions because the past actions were effects of causes, and because “if the same cause is operative tomorrow, it will result in the same effect” (21). As I argued in the 1991 text above, application of the law of identity to action and becoming entails only the conception of causality in the broad mode, not the narrow, and taking the latter to apply to all existents is an error.
    . . .
    Mr. Harriman appeals to a brother of my principle of substantive propagation in maintaining that the “justification for inferring the future from the actions of the past is the fact that the past actions occurred . . . for a reason, a reason inherent in the nature of the acting entities themselves” (21). Harriman erroneously supposes this principle entails universal causality in the narrow mode. That is, for all the “forms, motions, combinations and dissolutions of elements within the universe” (Rand’s fine phrase), “if the same cause is operative tomorrow, it will result in the same effect” (21).

    With regard to generalizations about kinds of joined actions, such as push of a ball and its rolling, Harriman rightly says they are made true by “some form of causal relationship between the two” (21). C. S. Peirce wrote: “General principles are really operative in nature. This is the doctrine of scholastic realism” (1903, 193). Peirce famously was a proponent of scholastic realism in theory of universal concepts. Particularly, his realism was close to the realism of Duns Scotus, as informed by and as informing modern scientific practice. As applied to generalizations, Peirce saw realist concepts at work in the following way. Take any two occasions of releasing a stone from the hand and watching it fall. However much the two occasions are alike, between them there is any number—an infinity, denumerable or higher—of like possible occasions of its release allowing a stone to fall. A real relation of mediation unites the particular occasions, actual and possible, of the generalization “released stones fall.” Behind that uniformity of nature there must be not mere chance, like a run of straight sixes, but “some active general principle” (ibid.) Every sane person must accept that last statement, where it is understood that the principle does not merely accidentally coincide with moments in which one makes predictions based on it (ibid. See also Peirce 1901, chapter 18, and 1902, chapter 15).

    Rand’s theory of concepts is not what has traditionally been called realist. Rather, hers is an objectivist theory. Concepts are “produced by man’s consciousness in accordance with the facts of reality . . . [they are] products of a cognitive method of classification whose processes must be performed by man, but whose content is dictated by reality” (ITOE 54). That cognitive method of classification requires the ability to regard items as (at least) substitution units along a real dimension(s) shared by the items. Regarding things as units, whether as substitution units or also as measure-value units along shared dimensions,* is a “method of identification or classification according to the attributes which a consciousness observes in reality. . . . Units do not exist qua units, what exists are things, but units are things viewed by a consciousness in certain existing relationships” (ITOE 6–7).

    Rand’s objectivist theory of conceptual identification, set in her metaphysics, as supplemented by the principle of substantive propagation, is a strong competitor to Peirce’s realist way of tying inductive generalization to universal concepts.

    By four months of age, an infant expects objects to fall if not supported. This is an example of what Mill called eduction, inference from particular past cases to the next particular like case, rather than inductive inference from particulars to general. Animals also have the limited power that is eduction. Harriman writes that animals “cannot project from their percepts what future to expect” (28). While that is a slight overstatement, it is surely correct with respect to all the expectations we have from induction, which requires conceptual generalization.

    Harriman inclines to think that higher animals have direct experience of causation (cf. Enright 1991, §II). Like us, they “perceive that various actions they take make certain things happen. But they cannot go on to infer any generalizations from these perceptions” (28). The important thing is that Harriman rightly affirms that the human animal perceives some causal relations directly. (See “Hume – Experience of Cause and Effect” above* and Yale.) From those percepts, general causal principles (from “Pushed balls roll” to “Applied torque causes onset of rolling”) are formed after the general pattern of how universal concepts are formed from percepts. Harriman’s book is an attempt to spell out more specifically the abstraction process from elementary causal principles such as “pushed balls roll” to general scientific principles—the tremendous abstraction process that is ampliative induction—illustrated by episodes in the history of science.

Also, under another paper of mine “The Observational Cast of Science,” as follows:
    In his 2010 book on induction in physics, David Harriman writes:
      Ptolemy conducted a systematic study in which he measured the angular deflection of light at air/water, air/glass, and water/glass interfaces. This experiment, when eventually repeated in the seventeenth century, led Willebrord Snell to the sine law of refraction. But Ptolemy did not discover the law, even though he did the right experiment and possessed both the requisite mathematical knowledge and the means to collect sufficiently accurate data.
      . . .
      Ptolemy’s failure was caused primarily by his view of the relationship between experiment and theory. He did not regard experiment as the means of arriving at the correct theory; rather, the ideal theory is given in advance by intuition, and then experiment shows the deviations of the observed physical world from the ideal. This is precisely the Platonic approach he had taken in astronomy. . . . [Ptolemy] began with an a priori argument that the ratio of incident and refracted angles should be constant for a particular type of interface. When measurements indicated otherwise, he used an arithmetic progression to model the deviations from the ideal constant ratio.* (37)

      * Smith, A. M. 1982. Ptolemy’s Search for a Law of Refraction. Archive for History of Exact Sciences 26:221–40.

    Mr. Harriman’s citation is to one of the works of A. Mark Smith that I had earlier cited in the posts quoted above.* Before remarking on Harriman’s assessment of Ptolemy’s failure to discern the law of refraction, I need to show a little more physics and its history. Jerry Marion writes in Classical Dynamics (1965):
      Minimal principles in physics have a long and interesting history. The search for such principles is predicated on the notion that Nature always acts in such a way that certain important quantities are minimized when a physical process takes place. The first such minimum principles were developed in the field of optics. Hero of Alexandria [Heron], in the second century B.C., found that the law governing the reflection of light could be obtained by asserting that a light ray, traveling from one point to another by a reflection from a plane mirror, always takes the shortest possible path. A simple geometrical construction will verify that this minimum principle does indeed lead to the equality of the angles of incidence and reflection for a light ray reflected from a plane mirror. Hero’s principle of the shortest path cannot, however, yield a correct law for refraction. In 1657 Fermat reformulated the principle by postulating that a light ray always travels from one point to another in a medium by a path that requires the least time. Fermat’s principle of least time leads immediately, not only to the correct law of reflection, but also to Snell’s law of refraction. (216)

    Harriman states that Ptolemy’s most important obstacle to discovering the law of refraction was his incorrect view of the relation of theory and experiment. That proposition is not from Mark Smith. Harriman goes on to contend that Ptolemy’s science was “a logical application of Platonism” and that Ptolemy regarded experiment as “the handmaiden of intuition” (38). These contentions, too, are not squarely from Mark Smith.

    Professor Smith has argued that Greek science worked within a methodological framework of “saving the appearances.” This framework is rather at odds, I notice, with the strain in Plato of “pooh-pooh the appearances” (Rep. 509d–513c, 517b–518d); it is less at odds with Plato’s praise of measurement as opponent of false appearances (Prt. 356c–357a; Sph. 236b; Phlb. 66a–c). Whatever the relative weights of its debts to Plato and other Greek philosophers, Smith lays out the assumptions of the appearance-saving endeavor of Greek science (in optics that would be Euclid, Heron, and Ptolemy) as follows: All irregular change is merely appearance, illusion. “Beneath the appearances, there lies a real, intelligible world that is utterly simple, changeless, and eternal” (1982, 224). That world is a Euclidean locus in which things are not as in appearance, but stand in their true spatial relationships. “Moreover, the only real relationships are those most basic ones obtaining between and among points, and they are mathematically expressible in terms solely of distances and angles” (ibid.).

    What does it mean to save the appearances? What does such salvation amount to? It is the reduction of appearances “to the utter simplicity of uniformity. Such a reduction requires some absolutely simple and perfect gauge of uniformity, a salvans . . . . And what finally determines the perfection of the salvans is its conformance to what I have called the Principle of Natural Economy” (ibid.)

    Like his predecessors, Ptolemy thought of the visual ray as a physically real line
      through which the geometrical reality behind the visible appearances could be immediately construed. And the rectilinearity of that line was presumed to be a function of its absolute spatial brevity.

      We have already seen how successfully the ray-as-least-distance was employed in the salvation not only of direct vision, but, far more important, of reflection. Hero’s demonstration of the contingency of the equal-angles law upon the Principle of Least Lines is a clear testament to that success. In the case of refraction, though, the same sort of analysis will not work. The sine-law simply cannot be established on the basis of least distances but, as Fermat eventually showed, must be grounded upon least times. In other words, if it is to save refraction, the ray must be understood to represent a temporal, not a spatial, path.* The inadequacy of Ptolemy’s analysis of refraction was therefore due to the inadequacy of his ray-concept.

      * The basic flaw in Ptolemy’s refraction-analysis consists in the fact that the terms of his analysis are too concrete and specific. The spatial brevity that he supposed to be the fundamental governing principle of visual radiation is actually a function of a more profound temporal brevity. Likewise, the angular relationships that he thought governed refraction are actually functions of a more profound sine relationship. Thus, Ptolemy’s failure overall was due to his inability to conceive the phenomena more abstractly, to transcend the limitations of the simple spatial intuitionism that dictated his scientific approach. (Smith 1982, 239)

    Within a widened saving-the-appearances methodological framework, Ptolemy could have arrived at the correct sine law by expanding beyond the intuitive assumption that the deep true story of visual radiation is writ by spatial extent. By the times of Descartes and Fermat, a ray of light is just a trajectory of light from object to object, not the visual ray of the ancients. Then too, their accounts of optical paths were more abstract than Ptolemy’s failed attempt, which was all too bound to “spatial intuitionism” (Smith 1982, 240). That is not to say that Ibn Sahl or (much later) Snell needed to wait on any such accounts to learn the correct law from experiment.

    Ptolemy has been variously characterized by scholars as Platonist-Pythagorean, Aristotelian, Stoic, and Empiricist. Mark Smith concludes that “although the epistemological foundations of Ptolemy’s analysis may be legitimately characterized as ‘Aristotelian’, the structure of that analysis may no less legitimately be characterized as ‘Platonic’” (Smith 1996, 19; on the general Aristotelian empirical foundation, see p. 28).

    David Harriman’s portrayal of Ptolemy’s conception of experiment as the “handmaiden of intuition” does not refer to Ptolemy’s confinement to abstractions all-too-low in his analysis of experiment, the confinement that was detailed by Smith and was called by Smith “spatial intuitionism.” The extent to which Harriman’s characterization of experimentation in pre-Galilean physics as "handmaiden of intuition" is true and cogent will have to wait for another occasion.

(Edited by Stephen Boydstun on 3/27, 7:58am)

Post 61

Sunday, November 30, 2014 - 6:25amSanction this postReply

A quibble with Mr. Harriman, when he writes:

Aristotle induced his theory of deduction; he examined an enormous range of particular arguments and arrived at generalizations that identified the various types of valid and invalid structures. Then, ascending to an even greater level of abstraction, he asked: What is the common root of all invalid arguments? He found that all such arguments imply a contradiction, i.e., they imply that something is A and non-A at the same time and in the same respect. Thus he grasped (inductively) that the law of noncontradiction is the fundamental principle of valid thought. (236)

Citations from texts of Aristotle should be provided for such controversial claims about Aristotle's views, particularly the claim that Aristotle saw the law of noncontradiction as root of forms of valid inference (part of valid thought) such as:


All animals are mortal.

Socrates is an animal.

Therefore, Socrates is mortal.


Beyond Aristotle whatever, to the truth of the matter: From the thesis that contradiction is the root of all invalid inferences joined with the thesis that all inferences are either valid or invalid, one could glide with Harriman to his (and Aristotle’s?) conclusion that the law of noncontradiction is the fundamental principle of all valid inference. That is entering by a window, rather than the door. The less encumbered analysis of the root of such inferences as in the argument about Socrates would be direct appeal to the law of identity, as understood by Rand (Baumgarten, Bolzano, . . .): “A thing is what it is” or “A thing is something specifically.”


Aristotle did not connect the identity formula “A thing is itself” with our “A thing is something specifically.” He thought the former formula nearly empty and useless (Metaphysics 1041a10–24). He did realize that any existent not only is but is a what (1030a20–24).





(Edited by Stephen Boydstun on 11/30, 8:08am)

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