Philip Catton - Academia.edu (original) (raw)

Papers by Philip Catton

Philosophy of Science, 1986

For the diagrammatic mode of reasoning in the classical mathematics of Euclid, think analogue, an... more For the diagrammatic mode of reasoning in the classical mathematics of Euclid, think analogue, and for the symbolically styled, algebraic mode of reasoning (that surged from the seventeenth century onward), think digital. Newton in such thinking seems like an inventor of an mp3 system, who thereafter champions vinyl. For he invented the calculus and then resolutely cleaved to diagrammatic reasoning, even fiercely arguing its superiority.

a shorter version of this was published in Ngā Kete a Rēhua: Inaugural Māori Research Symposium - Te Waipounamu Proceedings Book, 254-266., 2010

New Zealand has scarcely taken the first step towards genuinely bicultural dialogue, because no-o... more New Zealand has scarcely taken the first step towards genuinely bicultural dialogue, because no-one has indicated clearly what that first step must be.
Four general questions for NZ are introduced which broaden out into a search for definition of the needed first step.
(1) Does philosophy’s ‘Enlightenment ideal’ demarcate fairly, accurately and exhaustively what is genuine intellectual accomplishment by humans?
(2) Was NZ’s most famous philosopher, Karl Popper, correct to compare ‘tribal’ consciousness so invidiously with his vaunted ‘open society’?
(3) How might NZers best conceptualise the relationship between Matauranga Maori and science?
(4) How might philosophy best conceptualise its own cultural specificity, or thereby the cultural conditions that are necessary for the very existence of philosophy and theoretical science?
Because of its defining biculturalism, NZ possesses a particularly deep-lying institutional need to answer such questions both reflectively and well.
Suppose for the sake of argument that philosophy and science (a) were brought to NZ only within the heritage of those who arrived long after its indigenous people did, and yet, (b) themselves define, by the ideal to which they are beholden, what it is to reflect or dialogue truly well or ill. Then there is no coherence (in terms of any possible truly inclusive ideal dialogue within NZ) to NZ’s legally mandated biculturalism.
Such a dire realisation would be important if true, and it is equally important to diagnose and intellectually redress the error in it if it is false. New insights would result were NZers collectively to investigate this, which they largely have not done before now. NZ needs these insights as starting-point for true bicultural dialogue, if there is to be one.

G. Oppy and N.N. Trakakis (Ed.), A Companion to Philosophy in Australia and New Zealand. (paperback and on-line) (Pp. 435-440 of the print Companion.) Melbourne: Monash University Publishing., 2010

Principia Mathematica: Avello Publishing Journal Issue 1 Volume 3. Pp. 1-44. , 2013

Isaac Newton — theologian, alchemist, raging recluse, icon, mathematician, practical man, magicia... more Isaac Newton — theologian, alchemist, raging recluse, icon, mathematician, practical man, magician, measurer extraordinaire, and most profoundly, progenitor of physics as exact science — comes into coherent focus for us as he was in himself only when we recognise why his diagrams in Philosophiæ Naturalis Principia Mathematica are made by him to be not merely pedagogical, but instead indispensable to the reasoning itself.

Whether nature is or is not systematic sounds at first like an idle meta¬physical question, but c... more Whether nature is or is not systematic sounds at first like an idle meta¬physical question, but considered in relation to (i) the aims of science and (ii) the methods of appraisal of scientific theories, it can be given clear (and quite plainly empirical) content. We also ask the question in order to understand (iii) the relation of causation, laws of nature, and theoretical structure.

(i) Aims. The doctrines (1) that science aims to provide explanations, (2) that science achieves success in this aim, (3) that explanation involves unification, and (4) that the principles on which explanations, properly so-called, are based, must be true, together imply that nature is a system. For a kind of explanation she calls “causal”, Nancy Cartwright affirms (1), (2) and (3) but denies (4); for a kind of explanation she calls “theoretical”, Cartwright affirms (1), (2) and (4) but denies (3). I show by historical examples (in particular, in the work of Coper¬nicus, Kepler, Newton, Maxwell and Einstein) that Cartwright’s distinction between “theoretical” and “causal” explanation is often impossible to make out. I show, largely through discussions of Galileo and Newton, that Cartwright has a misleading view of the role of idealization in physical science, a view apt perhaps for physics before Newton, but not for Newtonian physics. I use my historical case studies to undermine numerous specific sceptical arguments by which Cartwright supports her novel conception of “theoretical” explanation.

(ii) Methods. I argue that the Newtonian, “bootstrap” method in terms of which Cartwright reconstructs low-level experiment- and measurement-based inferences to specific causal conclusions has its clearest and most cogent applica¬tions in inferences to high-level theoretical conclusions. Newton’s method, however, presupposes that nature is a system. Nature must be systematic in order to be well suited to study by the bootstrap method. I argue that the method has been notably successful, and that it consequently is appropriate to assimilate the method’s substantive presupposition concerning natural systemati¬city to what has been learned from the experience of the method’s successful application, and to say that we have evidence that this presupposition is true, that is, evidence that nature is systematic.

(iii) Causation, Laws, and Theory. Against Cartwright I defend a top-down, anti-metaphysical conception of this relation, and “internal realist” concep¬tion of theoretical structure. By highlighting some facets of the mathematics appertaining to fundamental physical laws presumed true, I argue that certain phenomena concerning scientific practice from which Cartwright’s metaphysical view of causes gains apparent strength in fact are conformable to my own account.

atlas-conferences.com

Consider (A1) intuitionistic logic, (A2) the Kantian pure intuition of time, (A3) constructive ... more Consider (A1) intuitionistic logic, (A2) the Kantian pure intuition of time, (A3) constructive mathematics, (A4) experience as a state of the subject. Consider furthermore, towards making four parallel comparisons, (B1) classical logic, (B2) the Kantian pure intuition of space [with a modification], (B3) classical mathematics, (B4) experience as the mode of a subject’s connecting to its public, intersubjective world.
Note that:
1. Intuitionistic logic, as Gödel firmly established, deserves our respect if classical logic does; but the converse is, as Gödel again firmly established, also true — classical logic deserves our respect if intuitionistic logic does.
2. Time is, in various ways that Kant points out to us, a deeper condition on experience than space; and yet in ways that Kant also points out the converse is also true — space is in various ways a deeper condition on experience than time is (a thesis that Kant establishes with arguments that are not touched by the usual criticism against Kant that his philosophy is embarrassed by non-Euclidean geometries). [My modification on B2 is to weaken Kant's assessment of the pure intuition of space, at least to the extent of its not encompassing Euclideanness of the metric, and perhaps so far as its not encompassing any more than topological structure.]
3. Constructive mathematics commands special respect as mathematics but the notion that it is uniquely worthy cannot be sustained; classical mathematics too has its place.
4. The private, what-it-is-like-for-the-subject aspect of experience commands special attention; but Kant established as well the converse point, that our right to view experience as a mode of the subject’s connecting to what it is not actually precedes our right to view experience as a state of the subject.
I argue that the parallelism between my various A1-B1, A2-B2, A3-B3 and A4-B4 comparisons is both perfectly strong, and significant -- it explains the inevitability of Brouwer's solipsistic tendency, identifies the special significance of mathematics that proceeds (according to Brouwer's prescription) out of constructions within the pure intuition of time, and at the same time identifies deep reasons to conclude that such a constructive approach cannot even potentially complete the whole of mathematics.

Philosophia Mathematica, Jan 1, 2012

Not simply set out in accompaniment of the Greek geometrical text, the diagram also is coaxed int... more Not simply set out in accompaniment of the Greek geometrical text, the diagram also is coaxed into existence manually (using straightedge and compasses) by commands in the text. The marks that a diligent reader thus sequentially produces typically sum, however, to a figure more complex than the provided one and also not (as it is) artful for being synoptically instructive. To provide a figure artfully is to balance multiple desiderata, interlocking the timelessness of insight with the temporality of construction. Our account of the diagram complements those of Manders and Macbeth by more strongly emphasizing practical synthesis. † We especially thank Catherine Legg, Koji Tanaka and Zach Weber for early critical input, Max Cresswell for his questions, Danielle Macbeth for her comments on an advanced draft, and two referees, John Mumma and Jessica Carter, for diligence, insight, and patience. Thanks also to Stephen Sharp.

NEW ZEALAND JOURNAL OF FORESTRY, Jan 1, 2007

As scientists, we endeavour to be objective concerning whether there is anthropogenic climate cha... more As scientists, we endeavour to be objective concerning whether there is anthropogenic climate change, and if there is, about how significant it will be.

Victoria, Jan 1, 2007

That elegance links to insight is original to mathematical practice and ineluctable from it. Yet ... more That elegance links to insight is original to mathematical practice and ineluctable from it. Yet this linkage is not well explained by modern epistemologists of mathematics. Two key tenets of modern epistemology are that a proposition is the content of a declarative assertion, ...

Newton and Einstein each in his way showed us the following: an epistemologically responsible phy... more Newton and Einstein each in his way showed us the following: an epistemologically responsible physicist adopts the most measured understanding possible of spacetime structure. The proper way to infer a doctrine of spacetime is by a kind of measuring inference  a deduction from phenomena. Thus it was (I argue) by an out-and-out deduction from the phenomena of inertiality (as colligated by the three laws of motion) that Newton delineated the conceptual presuppositions concerning spacetime structure that are needed before we can actually think coherently about these phenomena. And Einstein (I argue) very much recapitulated this argument pattern, twice over in fact, recolligating the phenomena first so as to add something from the laws of electromagnetism, and then so as to add everything about gravitation, into what he understood by inertiality. Notably, to deduce one's theoretical conclusions from phenomena is both more cautious and more cogent than to "infer to the best explanation". And in the context of the development of a doctrine of spacetime, deductions from phenomena lay before us formal rather than causal understanding. Deductions from phenomena tell us, in this context, not what things or what causes there are, but rather what our concepts should be like. The more measured the inference is, however, the more definitively it tells us this. For these reasons the most measured understanding of spacetime lies on a line between conventionalism and realism, between relationalism and absolutism, and indeed (as I demonstrate) between empiricism and rationalism. Spacetime is understood as neither merely immanent in material goings-on, nor truly transcendent of them either. In order to explain this understanding as adequately as I can and in order to remark its excellences most fully, I consider some respects in which the tertium quid between metaphysical realism and strict empiricism about spacetime is wise in the sense of practical wisdom. The wisest understanding of spacetime illustrates, I argue, an original and fundamental connection that epistemology has with ethics.

Presented by The Australasian Association of Philosophy. Home &gt; Papers &gt; Ph... more Presented by The Australasian Association of Philosophy. Home &gt; Papers &gt; Philip Catton.Philip Catton. Immanence and Ideality Philip Catton Philosophy &amp; Religious Studies, University of Canterbury. Full text: Not available Last modified: May 30, 2005. ...

Karl Popper: Critical Appraisals

Karl Popper: critical appraisals, Jan 1, 2004

Aristarchus, Harvey, Wegener, Newton and Einstein all made significant scientific progress in whi... more Aristarchus, Harvey, Wegener, Newton and Einstein all made significant scientific progress in which they overturned the thinking of their predecessors. But Popper's model of conjectures and refutations is a poor guide to fathoming the accomplishment of these scientists. By now we have a better model, which I articulate. From its vantage point, I criticise Popper.

Philosophy of Science, Jan 1, 1999

Dialogue, Jan 1, 1989

Marx called a social pattern "contradictory" if the conditions of its maintenance are also key in... more Marx called a social pattern "contradictory" if the conditions of its maintenance are also key ingredients for its demise. The science of ecology, too, studies patterns the conditions for whose maintenance are also key ingredients for their demise. The historical materialist notion of contradiction has a close counterpart in the ecological notion of succession. Succession is a process by which the structure of a biological community --both niche structure and species structure --changes as a result of each species' modification of the habitat. Just by living, each species member alters its environment, and in non-climax communities these effects, summed over all living things, constitute disequilibria. The habitat changes, and with it the niche structure. Gradually the species structure of the community changes. Each seral stage, with its distinctive species structure, requires for its maintenance the ongoing existence of living members of each species in the structure; yet this condition is the key ingredient for succession, for the demise of the seral stage.

Philosophy of Science, Jan 1, 1988