Friday, August 31, 2012

Acceleration, Ratio. Quotient

Though ratios are mathematically represented as quotients, there are important distinctions between the two relations.  First, 'is proportionate to', but not 'divided by', is a symmetrical relation.  Second, a ratio, unlike a quotient, does not reduce to a single numerical value, which means that a quotient with a ratio as either divisor or dividend is ill-formed.  Nevertheless, the standard Physics representation of Acceleration suppresses both these distinctions, beginning with its representation, as a quotient, Velocity, which, fundamentally is a ratio between measured Distance and measured Time, the symmetry of which is plain from the experiential equivalence of 'take less time' and 'cover more ground' as meanings of 'go faster'.  The representation of that ratio as a quotient, in turn, facilitates the further representation of it as part of a second quotient, i. e. in Velocity/Time.  So, that 'go faster' is easily comprehensible as an experiential concept only underscores that 'A = d/t-squared' is more contrived abstraction than insight.

Thursday, August 30, 2012

Acceleration, Uniformity, Velocity

Galileo's determination that Gravity is constant means not only that its effects on distinct objects are the same, but that its effects on a single object in the course of a single event is uniform.  So, insofar as Acceleration is defined as 'increase in Velocity', uniform Acceleration means uniform change in Velocity.  On the other hand, Velocity is defined as 'change of Distance in a Time-interval'.  Hence, it is conceived as an average, and, hence, as uniform in an interval.  Therefore, the notion of Velocity is problematic, if not contradictory, in a gravitational event, as well as in any another in which Acceleration is uniform.  So, the infinitesimal analysis that reduces an interval to instantaneity concomitantly minimizes the discrepancy between Velocity qua uniformly changing, and Velocity qua constant.  In such cases, mathematical precision can also be evasive abstraction.

Wednesday, August 29, 2012

The Mathematics of Acceleration

By means of Quotients, distinct unequal concrete motions, i. e. distinguished by an increase in Velocity, can be represented by the formula 'Acceleration = Distance/(Time-Unit)-squared'.  Furthermore, by means of Infinitesimals, that Time-Unit, which originally represents an interval, can be conceived as approaching instantaneity, in order to satisfy proportionality to Force, which, can, in principle, be exercised in an instant.  So, insofar as the Mathematization of Physics introduces precision into the representation of Nature, i. e. beginning with the formula 'F = ma', it does so only as abstract interpretation.  On the other hand, its representation of human artifaction, i. e. of Technology, can be not merely descriptive, but prescriptive.

Tuesday, August 28, 2012

Physics, Mathematics, Precision

Once Mathematical Physics is conceived as a practical enterprise, and not as an ontological discovery, the role of Mathematics in it, as the facilitation of precision in measurement, is plain.  For, its central notion, Force, can be grasped as an accelerant without exactitude, i. e. as simply an event that increases the velocity of some entity.  Likewise, Gravity, can be established both as an accelerant, and as constant, without specific quantification.  The virtue of Mathematics in such an enterprise can be inferred from its contribution to a different project, i. e. to cooking, in which precision in measurement can be decisive in its success.  In the context of Physics, that virtue is perhaps best evinced not merely insofar as Acceleration can be assigned a numerical value , but insofar as it can be expressed precisely, i. e. in terms of division, squares, and infinitesimals.

Monday, August 27, 2012

Experimental Reason and the Quantification of Experience

The enduring appeal of Pythagoreanism--that the world is intrinsically mathematical--has been so pervasive that even an Empiricist such as Locke accepts it, i. e. among his Primary Qualities,  But, the subsequent subjectivization of Mathematics by Berkeley and Hume, raises for Kant the problem of the legitimacy of the quantification of Experience, in general, and, of Mathematical Physics, in particular.  His 'Copernican' solution is to conceive Physics as a system of subjective appearances that, concomitantly, objectifies them, while remaining agnostic about things-in-themselves.  However, while that solution might suffice for Theory, its agnosticism is inadequate for Practice, which entails interaction with things-in-themselves.  In contrast, Locke, anticipating Pragmatism, briefly offers the insight that any correspondence between subjective Secondary Qualities and objective Primary Qualities is, ultimately, provisional, i. e. is a problem of ongoing adjustment.  So, to elaborate on that insight, the quantification of Experience, systematic, or otherwise, by Experimental Reason, is itself experimental, i. e. is validated by being effective until proven otherwise.

Sunday, August 26, 2012

Experimental Reason and Mathematics

Husserl's criticism, in The Crisis of European Sciences, of the replacement of "method" by "true being", could be interpreted as implicitly directed at Heidegger.  Regardless, its explicit target is the mathematization of nature, pioneered by Galileo, which obscures, according to Husserl, not only its origin as Method, but the "hidden reason" that constitutes that origin.  Now, if Husserl had pursued the latter formulation, instead of seeking to ground Mathematization in the Transcendental Ego of Phenomenology, he might have considered the possibility that that covert faculty is Experimental Reason.  As a mode of Experimental Reason, it is easy to argue that Mathematization, while an undeniably useful tool, is not co-extensive with it, e. g. that quantification is not involved in many ordinary experiences of 'What if?'  Also as such, it is easy to distinguish between the experimental production of events, and the subsequent interpretation of them, from which it can be inferred that the primary value to Science of Mathematization is technological precision, not theoretical idealization, despite the continued presumption, 400 years after Galileo, of the ontologizers of Mathematics, e. g. many prominent Physicists.

Saturday, August 25, 2012

Experimental Reason and Archimedes' Lever

Galileo, Copernicus, Newton, and Einstein are among the scientists usually cited as inspiring Modern Philosophy.  However, the most influential of all might be an Ancient scientist--Archimedes.  For, the acknowledged 'father' of Modern Philosophy, Descartes, in the Second Meditation, explicitly acknowledges the 'Archimedean Point' as exemplary for his quest for Certainty, characterizing that point as "firm and unmovable".  However, that characterization betrays both its own shortcoming, and that of the aspects of the Cartesian system that are modeled upon it.  The Archimedean Point may indeed be firm and unmoveable, but without the Lever of Archimedes' image, it is inert, as well,  Likewise, Descartes' 'I think' is, in itself, only an isolated point with no motive power.  On the other hand, a few years later, in the Passions of the Soul, he seems to discover his psychic Archimedean Lever--the pineal gland, in which "slight movements . . . may greatly alter the course" of behavior.  Furthermore, the most fundamental of these passions, according to him, is Wonder, which, as, has been previously discussed here, is the initial stage of Experimental Reason.  In other words, Experimental Reason is the Archimedean Lever of the Cartesian Soul, from which the 'I think' is an abstraction', and, hence, of the ensuing Philosophical tradition.

Friday, August 24, 2012

Experimental Reason and Examplification

As has been previously discussed, Experimental Reason produces not merely events, but appearances, i. e. evidence subject to further consideration.  Furthermore, such appearances are conceived as exemplary, i. e. as representative of other events, e. g. that a ball accelerates when experimentally rolled down an incline is conceived by Galileo as representative of all earthbound motion.  Now, the inference from arbitrary singular case to universal is warranted by the 'universal generalization' rule in contemporary Logic.  Here, that transition is classified as an instance of the process previously introduced as 'Examplification', i. e. as 'setting an example', a familiar notion in ordinary experience.  So, Experimental Reason entails Exemplification.

Thursday, August 23, 2012

Experimental Reason, Appearances, Freedom

According to Kant, 'nature' is a system of events, each of which is an appearance.  However, to cause to occur and to cause to appear are not equivalent.  For, the latter, but not the former, presupposes the existence of a perceiver to which an event might appear.  In other words, to cause to appear can  be onlypurposeful, and, hence, only extra-natural, i. e. only free causality, in Kant's doctrine.  Now, Experimental Reason produces not merely an event, but evidence, i. e. an appearance.  Hence, Experimental Reason entails free causality.

Wednesday, August 22, 2012

Experimental Reason, Physics, Nature

For Aristotle, 'physics' is derived from the Greek for 'nature', a kinship which his Teleological system reflects, i. e.  its fundamental principle of change is 'in the nature' of something.  Newton does not disagree with that kinship, contending only, in contrast, that mechanistic Efficient Causality, not Teleological, is what is in the 'nature' of 'physical' entities.  It is Kant, following the insights of Leibniz and Hume, who segregates 'nature' qua perceivable mechanistic changes, from 'nature' qua purposive in itself, i. e. Physics from Biology and Psychology.  So, contemporary Behaviorism, while celebrated for eliminating the 'Ghost' from the 'Machine', is less recognized as just another descendant of Newtonian Mechanics.  Now, one internal flaw in Newtonian Physics is its use of 'frames of reference', not so much because such a device is difficult to explain without Teleology, but because it effects an epoche in nature, i. e. it is opaque with respect to the incessant mechanism that presumably governs all events.  The experimental context is another such caesura in the presumed mechanistic concatenation, or, in other words, neither Newtonian Physics nor Behaviorism can adequately explain the operation of Experimental Reason.

Tuesday, August 21, 2012

Experimental Reason, Nature, Mutation

While the greatest contemporary rival to the Newtonian concept of 'nature' is typically regarded as Einstein's version, the more profound challenge to it is presented by Darwinism.  For, the process of Mutation entailed by the latter reduces easily neither to the Efficient Causality that governs both those versions, nor to the Teleological Causality that governs their Aristotelian ancestor.  Instead, Mutation is an instance of what has been previously introduced here as 'Material Causality', defined as 'Becoming-Diverse', and, thus, as not to be confused with the familiar, but vague, Aristotelian notion that goes by the same name.  Now, Experimental Reason can be conceived as both an instance of Material Causality, and of Mutation, and, hence, as a natural event that none of those prominent systems of 'nature' can recognize, unlike that of Lucretius, with its principle of Swerve.

Monday, August 20, 2012

Experimental Reason and Morality

Aristotle's definition of humanity as 'Homo Sapiens' carries the moral  implication that the Good consists in a state of Knowledge, i. e. in Contemplation.  Accordingly, a re-definition of humanity as 'Homo Faber' implies that the Good consists in some act of making, and, as 'Homo Ludens', in some playful performance.  Thus, the exercise of Experimental Reason, an expression of Homo Ludens, as has been previously discussed, can be morally, and not merely epistemologically or logically, significant, a significance that is difficult to appreciate in the compartmentalization typical of contemporary Academic Philosophy.

Sunday, August 19, 2012

Experimental Reason and Homo Ludens

Constructivism implicitly redefines Homo Sapiens as Homo Faber, i. e, because it holds that to know X is to construct X.  Now, insofar as, as has been previously argued, Experimental Reason entails Constructivism, it exceeds it, i. e. it further entails risk and uncertainty, which, in the artist, is a playful dimension.  In other words, in the exercise of Experimental Reason, humans are Homo Ludens, i. e. no longer passive constituents in or bystanders of a given world, but active participants in the creation of one.

Saturday, August 18, 2012

Experimental Reason and Sense Experience

Kant's characterization, in the footnote to B xxii of the 1st Critique, of the Copernican revolution as "contradictory to the senses", is misleading, at best.  The senses provide only appearances of the Sun at different locations of the sky, and that it is in motion is one theory of those changes, while that the spectator is in motion, is another such theory, i. e. the latter theory does not challenge the visual evidence itself.  Thus, Copernicus' rejection of Geocentrism no more entails a repudiation of Sense Experience than does Galileo's rolling a ball down an incline in order to determine if it accelerates.  More generally, the passage is at odds with one of the main themes of its context--that Experimental Reason involves the controlled modification of Sense Experience.

Friday, August 17, 2012

Experimental Reason and Philosophy

Plato, in the Theaetetus, says that the origin of Philosophy is a "sense of wonder", which, as has been previously discussed, can be characterized as Experimental Reason.  Now, the fundamentality of Experimental Reason is evinced by the fact that it can give rise to Dialectical, Deductive, and Inductive reasoning.  Thus, for example, theories of Dialectical Reason seem unable to explain the interrogative dimension of Wonder.  Likewise, the standard defense of Analytic Philosophy's claim that Philosophy and Deductive Logic are co-extensive--that other types of Reason are 'not Philosophy'--hardly meets its own standard of logical soundness.  So, in the absence of a more compelling counter-argument, Experimental Reason and Philosophizing can be conceived as one and the same.

Thursday, August 16, 2012

Experimental Reason and Propositions

To propose X is to wonder 'What if X?'  Thus, a proposition, like a proposal, has the interrogative and hypothetical connotations expressive of Experimental Reason, as has been previously discussed here.  However, Dewey, notably, aside, most contemporary Logicians treat 'propositions' as given as declarative.  Their Logics, thus, either abstract from the Experimental Reason that supplies them with their contents, i. e. from the original propositions from which declarative statements are derived, or else are inappropriately classified as 'Propositional'.  Similarly, any use of the term 'proposition' as equivalent to 'non-linguistic state-of-affairs' is problematic, at best.

Wednesday, August 15, 2012

Experimental Reason and Groundwork

Before the foundation of a building is laid, the ground upon which it is laid needs to be suitably tested and prepared.  In other words, groundwork precedes founding.  Thus, any presumed equivalence between 'The Groundwork of the Metaphysics of Morals' and 'The Foundations of the Metaphysics of Morals' is profoundly misleading.  Similarly, given the synonymy of 'reason' and 'ground', Experimental Reason can be understood as the groundwork phase of Reason.  Thus, for example, the Cartesian Doubt that precedes the establishment of his Epistemological foundation, is Experimental Reason doing its groundwork.

Tuesday, August 14, 2012

Experimental Reason--Constitutive and Regulative

Kant's distinction between 'constitutive' and 'regulative' Reason is his representation of the traditional 'Platonist' vs. 'Nominalist' contrast, i. e. whether Reason is ingredient in Existence, or is merely a human mental tool.  His pivotal innovation is to propose that the distinction pertains to Theoretical Reason only, for, Pure Practical Reason is both constitutive and regulative.  A similar argument can be made for Experimental Reason--even if it might not be constitutive for Theory, e. g. 'God does not pause to wonder', it is so for Practice, not merely for methodical scientists, but for a child curious to discover 'What if?'  Still, if, e. g. Lucretius is correct to propose that 'Swerve' is ingredient in Existence, then Experimental Reason, qua instance of Swerve, is constitutive for Theory, as well.  Hence, Experimental Reason eludes traditional classifications, and the debates predicated upon them.

Monday, August 13, 2012

Experimental Reason and Freedom

A main concern of Kant's is to establish that the Principle of Pure Practical Reason is a sufficient condition of Freedom.  In contrast, he seems less conscientious about whether or not that Principle is a necessary condition of Freedom, as well.  Thus, he seems to present no a priori argument against the possibility that Experimental Reason is another ground of Freedom, i. e. that the question 'What if?' can spontaneously initiate an efficacious course of action.

Sunday, August 12, 2012

Experimental Reason, Constructivism, Know-How

According to one version of 'Constructivism', one advocated by Cassirer, and confirmed by Gestalt theory, to 'know' X = to 'build' X.  In contrast, Spinoza distinguishes between the idea of how to draw a circle from the idea of a property of a circle, asserting that the former is more fundamental.  Now, the Schematism, which is the basis of Kant's Constructivism, provides a "rule of synthesis" (B 180), thus evincing Kant's allegiance to Spinoza's assertion.  Likewise, Experimental Reason formulates a procedure for the production of data.  In other words, the 'knowledge' of which such Constructivism is a theory is fundamentally that of Know-How.  The priority of this version is expressed, for example, in the thesis that Gestalt structuring is governed by genetic programming.

Saturday, August 11, 2012

Experimental Reason and Technology

With the advantage of greater historical hindsight, Kant might have characterized the inspiration of Galileo and Copernicus as leading him to seek not merely motion in the spectator, but action.  For, Experimental Reason entails not merely the entertainment of objects, but the controlled construction of events, as well.  So, with access to the later bountiful evidence of the technological fruits of the insights of those ingenious scientists, Kant might have better appreciated the systematic connection, entailed by Experimental Reason, between Theoretical Reason and Practical Reason.  He might also have noted that absent the question 'What if I were to act on that maxim?', his Principle of Pure Practical Reason remains an empty logical computation.

Friday, August 10, 2012

Experimental Reason, Fact, Artifaction

Whitehead's comment, that experimentation entails "cooking the facts", is unworthy of a book titled 'Adventures of Ideas', from one of the few philosophers for whom Creativity is a fundamental principle.  By implication, the comment is groundlessly dismissive of Constructivist Epistemology, according to which, a 'fact', by definition, is 'cooked'.  More generally, he fails to appreciate that experimentation is not an isolated anomalous practice.  For, all human artifaction, e. g. any transformation of raw materials for manufacturing purposes, constitutes a 'cooking of the facts'.  In other words, Whitehead seems to not appreciate the epochal significance in human history of the ascendancy of Experimental Reason--the era of rapid and pervasive technological advances.

Thursday, August 9, 2012

Experimental Reason and Universal Reason

Now, while Copernicus' hypotheses are well-recognized as transforming human knowledge, and, consequently, human culture, they are never conceived as transforming the objects of that knowledge, e. g. Heliocentrism is regarded as a discovery of what presumably already exists, not an alteration of it.  Hence, in general, on that presumption, Experimental Reason is never more than a contingent human event, and, hence, is not to be confused with the Reason that governs universal existence, often attributed to a deity.  Still, those moments that transform the human world are events in the history of universal existence, so, hence, must be governed by any such universal Reason.  So, either pivotal moments of human Wonder are governed by the laws of the latter, or else human Reason is the only species of  Rationality.

Wednesday, August 8, 2012

Experimental Reason and Wonder

Spinoza, in apparent response to Descartes, denies that Wonder is an emotion, arguing that it is an isolated concept that halts Mind, because of its lack of connection to any other concept.  An elaboration of that definition could further take into account that in Wondering, Reason seeks to not only discover such connections, but to actively create them, as well.  His model of Mind thus demonstrates how questioning is not, as some Logicians have it, a mere psychological attitude that is extrinsic to the proper functioning of Reason, namely, to draw inferences, but is, itself, an intrinsic mode of Reason.  Accordingly that model also shows how Experimental Reason, which wonders 'what if?', is a mode of pure Reason.

Tuesday, August 7, 2012

Experimental Reason and Disjunctive Reason

While the object of Doubt is some given circumstance, the object of the experimental question, 'What if?', is the subsequent proposal, the entertaining of which entails a doubt of the given only in the case of mutual exclusivity.  In other words, what questioning immediately effects is the generation of an alternative to some given.  Thus, the traditional Logical classification that best suits Experimental Reason is 'Disjunctive', i. e. Disjunctive Reason is the source of disjunctive propositions, and, hence, is presupposed by the Disjunctive Syllogism.

Monday, August 6, 2012

Experimental Reason, Inquiry, Creativity

Dewey's ongoing study of Logic, culminating in his characterization of it as 'theory of inquiry', expresses his appreciation of the experimental nature of Reason.  He also recognizes that an inquiry involves interrogation.  However, his attribution of "questionable"--"uncertain, unsettled, disturbed"--primarily to an objective situation, suppresses the subjective wonder of 'what if?' that can suddenly occur to anyone, thereby first creating a 'situation'.  In other words, Dewey's concept of Experimental Reason does not seem to appreciate the creativity that inspires an Archimedes or a Copernicus, who are not necessarily confronted with a disturbed situation.  To the contrary, as the case of Galileo exemplifies, such creativity can itself be a disruptive factor.

Sunday, August 5, 2012

Experimental Reason, Cartesian Doubt, Empiricism

Copernicus' question, 'What if the spectator were in motion, and the stars were at rest?', does not merely express a doubt of Ptolemaic Astronomy, but, further, initiates a novel investigation of celestial events.  Thus, more generally, implicit in Kant's advocacy of the Baconian experimental method is a rejection of the Cartesian method of Doubt, as intellectually insufficient.  He, therefore, distinguishes himself from not only his Rationalist predecessors, but from the Empiricists--Locke, Berkeley, and Hume--as well.  For, the adaptation of the experimental method entails that even the face value of a sense impression is subject to subsequent reconsideration, i. e. it entails a repudiation of the fundamental principle of that Empiricist tradition.

Saturday, August 4, 2012

Experimental Reason, As If, What If?

Kant describes his use of Experimental Reason as "hypothetical", and as "regulative" (B 674 ff).  That use has also been characterized as 'as if', because it represents problematic propositions as if they were assertoric.  But, as the 'if' indicates, such problematic propositions are, properly, hypotheses, ergo the classification of their use as 'hypothetical'.  Now, as Kant recognizes, the formulation of an hypothesis originates as a response to an inquiry, i. e. to the "questions" (B xiii) of the experimenter.  Hence, his 'as if' reasoning is grounded in the 'what if?' of Experimental Reason.

Friday, August 3, 2012

Experimental Reason and Constructivism

An experiment presents a controlled environment, the events of which are contrived.  Thus, those events are pre-planned, and involve entities insofar as they appear in the context, not insofar as they may be in themselves.  In other words, Experimental Reason entails a Constructivist theory of Knowledge.  In contrast, it is a weaker version of that relation that is represented in the Preface to the B edition of the 1st Critique, i. e. there, Kant characterizes his Constructivist system merely as the one with which he just happens to experiment.

Thursday, August 2, 2012

Experimental Reason and Hypothesis

'Experimental Reason' can be defined as the 'faculty of Hypotheses'.  Strangely, despite his praise of Copernicus' innovative hypothesis, in the B edition Preface to the 1st Critique, Kant's only intensive consideration of Hypotheses, at B 798ff, is relatively dismissive of their significance.  Thus, the latter characterization, i. e. that an hypothesis is no more than a conditioned guess, demeans not only the Copernican revolution, but his own, as well, a self-described "experiment" from which his entire doctrine issues forth.  So, while many B edition passages reflect Kant's new-found appreciation of Bacon, B 798ff is not among them.

Wednesday, August 1, 2012

Sufficient Reason, Experimental Reason, Imagination

Kant interprets the Principle of Sufficient Reason as the concept Causality, which he, more precisely, formulates, in the Second Analogy of the 1st Critique, as 'every event is an effect that is necessarily preceded by some cause'.  Now, this formulation is presumably mediated by a Schema, which is the source of the entailed time-ordering, i. e. it presupposes an analogous formulation of the PSR in the Schematism.  However, there, at B 183, Causality, and, hence, the PSR, is defined in terms of the efficacy of the Cause, from which "something else always follows", not in terms of the conditionality of the Effect.  In other words, the discrepancy between the formulations, which Kant seems to not notice, is an inversion, thereby suggesting, initially, at least, the distinction between a Theoretical and a Practical PSR, as has been previously discussed.  But, a second alternative to the Theoretical PSR, that has been previously proposed, might be an Experimental PSR, based on the concept of a Reason that Kant, in the B edition Preface, ascribes to the experimental method.  And, indeed, the prototypical example, in those passages, of that method, is the production of geometrical figures, the source of which, more precisely, is the same Productive Imagination that generates the Schematism.