Jeff, List: JD: On my interpretation of the text, the law of inertia functions as the third correlate in the triadic relation.
Are there any passages in Peirce's writings where he *explicitly *presents a triadic relation that has a law as one of its correlates? JD: We can analyze the relation in a number of ways, here is a simple version: A determines B to accelerate in accord with LI. How would you diagram this as an Existential Graph? JD: A fuller analysis would involve a closer look at LI. Newton's account of this law takes the following form: Force of inertia=mass*acceleration. A mathematical equation is a diagram of a *hypothetical *state of things. We effectively *define *force and mass in accordance with this equation, which is why it includes no arbitrary constants. The equation for the force due to gravity *requires *such a constant in order to make it *compatible *with this one, and the *value *of that constant must be determined *empirically*. It seems to me that *this *is why the one "is taken to be unchanging in its form," while the other "might be evolving"; we have to keep checking the calculations to confirm that the constant is *really * constant. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Tue, May 14, 2019 at 2:29 PM Jeffrey Brian Downard < jeffrey.down...@nau.edu> wrote: > Jon S, Gary F, John S, List, > > Let me offer a brief response to the objection Jon S. raised earlier. > > JD: I take the expression of the conditional (i.e., expressed in the EGs > by a scroll) to involve a genuinely triadic relation because there is a > law that governs the relation. > > Jon S: What is the warrant for taking *every *relation that is governed > by a law to be *genuinely triadic* on that sole basis? On the contrary, > most (if not all) *dyadic *relations that we encounter in experience are > governed by laws in some way, but we still classify them as dyadic because > they have *exactly two* correlates; the law itself is *not *a third > correlate. > > CSP: Any dynamic action--say, the attraction by one particle of > another--is in itself *dyadic*. It is governed by a law; but that law no > more furnishes a correlate to the relation than the vote of a legislator > which insures a bill's becoming a statute makes him a participator in the > blow of the swordsman who, in obedience to the warrant issued after > conviction according to that statute, strikes off the head of a condemned > man. (CP 6.330; 1908) > > Jon S: Even a *degenerate *dyadic relation is governed by a law; e.g., > the hardness of a diamond consists in the truth of the conditional > proposition that if it *were *to be rubbed with another substance, it > *would *resist scratching. Are there any passages in Peirce's writings > where he characterized a relation with *exactly two* correlates as > triadic? > > Jeff D: Most of the relations that we encounter in experience are rich > and complex. Consider the experience of one billiard ball A colliding > with another B in accordance with the law of inertia LI. We can abstract > from the law of inertia and attend solely to the dynamical relation > between A and B as existing individuals. There is a fact about each. A is > in motion, and then it collides with B, which was stationary. As a > result, B moves. That can be treated as a dynamical dyadic relation that > is formally ordered such that A is agent and B is patient. Considered in > this way, we treat the dyadic relation between them as a mere matter of > brute force. > > Alternately, we can consider the relation between the fact that A was > moving and B was stationary, and then the later fact that B was put into > motion as a result of the collision as being governed by the law of inertia > (LI). According to Peirce's classification of relations in "The Logic of > Mathematics,...), this is a genuinely triadic relation of fact. All such > genuinely triadic relations of fact are governed by some kind of law. On my > interpretation of the text, the law of inertia functions as the third > correlate in the triadic relation. We can analyze the relation in a number > of ways, here is a simple version: A determines B to accelerate in accord > with LI. > > A fuller analysis would involve a closer look at LI. Newton's account of > this law takes the following form: Force of inertia=mass*acceleration. > How does the law of inertia govern the relations between the facts > concerning A and B? The first fact attributes qualities to each (i.e., each > billiard ball has a position at the first time, such that A is in motion > heading towards the other ball and B is not in motion). The second fact > attributes a different set of qualities to each. The law governs the > changes in those facts so that there is a general regularity that governs > other possible interactions between any masses of this type. > > Notice what Peirce says about inertia as a dynamical law insofar as it is > explained by Newton in his theory of physics: > > As to the common aversion to recognizing *thought *as an active factor in the > real world, some of its causes are easily traced. In the first place, > people are persuaded that everything that happens in the material > universe is a motion completely determined by inviolable laws of > dynamics; and that, they think, leaves no room for any other influence. > But the laws of dynamics stand on quite a different footing from the laws > of gravitation, elasticity, electricity, and the like. The laws of dynamics > are very much like logical principles, if they are not precisely that. They > only > say how bodies will move after you have said what the forces are. They > permit any forces, and therefore any motions. Only, the principle of the > conservation of energy requires us to explain certain kinds of motions by > special hypotheses about molecules and the like. Thus, in order that the > viscosity of gases should not disobey that law we have to suppose that > gases have a certain molecular constitution. Setting dynamical laws to > one side, then, as hardly being positive laws, but rather mere formal > principles, we have only the laws of gravitation, elasticity, electricity, > and chemistry. Now who will deliberately say that our knowledge of these > laws is sufficient to make us reasonably confident that they are > absolutely eternal and immutable, and that they escape the great law of > evolution? > > The main difference that I see between the law of inertia and the law of > gravity is that, on Peirce's account, the former is governed by (if you > will) a logical law of deductive demonstration. As such, the law is taken > to be unchanging in its form. > > The law of gravity, on the other hand, might very well continue to evolve. > For instance, gravitational "constant" in Newton's version of the law might > be evolving. Furthermore, it's being an inverse square law and not an > inverse of a 2.1 power might not be fixed. Rather, the inverse power > relation (as a function of distance) might be evolving. > > The fundamental law governing the evolution of the law of gravity is, on > Peirce's account, the one law of mind. On my reading of this text, we can > understand that law to be an objective manifestation of the one law of > logic. In this case, the third clause that is governing the law of gravity > is not one of deductive demonstration. Rather, it is one that brings abductive > and inductive patterns of inference to bear on the ongoing formation of > the spatial and temporal habits in their relations to the distribution > of mass both locally and globally (e.g., understood in terms of the paths > that are possible through a given space). > > There appears to be a difference between the operation of these laws. The > law of inertia is, at this point in the history of the universe, relatively > static and dead. For the most part, it operates in an > efficient, mechanical, linear, conservative manner. The law of gravity, on > the other hand, continues to evolve. As a law, it appears to have some sort > of life. > > Is the claim that the law of inertia seems to govern the motions of masses > in a manner that is akin to a form of logical demonstration, while the law > of gravity seems to govern the relations between space and mass in a manner > that is akin to a form of logical abduction and/or induction testable as a > hypothesis? My hunch is that it is a testable hypothesis. > > Yours, > > Jeff > > Jeffrey Downard > Associate Professor > Department of Philosophy > Northern Arizona University > (o) 928 523-8354 > >>
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