C. S. Peirce

The 20th century philosopher Charles Sanders Peirce is America's greatest thinker so far. He was a logician, specialized in semiotics, a realist, renouncer of Kantianism, and was vigorously anti-Cartesian. See:

• C. S. Peirce's 5 famous The Monist papers
• John N. Deely's "Charles Sanders Peirce and the Recovery of the Signum" and "The Impact of Semiotics on Philosophy"
• Arisbe: The Peirce Gateway
• Dictionary of Peirce's Terms
• Institute for Studies in Pragmaticism
• Peirce.org
• physicist Peder Voetmann Christiansen's papers on applying Peirce's thought to physics (quantum semiotics)
• cf. also A Triadic Theory of Elementary Particle Interactions and Quantum
• and the related U.S. Patent 6819474.

Medieval scientists presentation by J. Hannam

“God’s Philosophers: the Medieval World and the Foundations of Modern Science”, Dr James Hannam - 18th October 2012

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Physics & Metascience (Metaphysics)

George Mason University physicist (and author of The Theory of Almost Everything) Robert Oerter, discussing act in potency in in physics, writes "it seems to me that the concepts of time and change are metaphysically prior to those of potentiality."

My response:

The French physicist, philosopher and historian of physics Pierre Duhem would agree with you, Dr. Oerter, that physical theories do not depend upon a choice of metaphysics. Duhem masterfully shows this, with many historical examples, in his classic philosophy of science work The Aim and Structure of Physical Theory (excerpt). He also treats this in "Physics & Metaphysics," "Physics of a Believer," and this excerpt from To Save the Phenomena.

His reply:

Thanks, that's very helpful. From the second link:

"That Physics Logically Precedes Metaphysics

...We cannot come to know the essence of things except insofar as that essence is the cause and foundation for phenomena and the laws that govern them. The study of phenomena and laws must therefore precede the investigation of causes."

That's what I was groping for in my attempts to answer Feser.

However, I think there's a distinction that must be made between the metaphysical essences that Duhem is talking about and the metaphysical principles that Feser is talking about. Don't we need concepts of cause and change before we can even begin a physical investigation?

My response:

Your question appears to be a question on the method and division of the sciences. Boethius, following Aristotle, proposed that the "Speculative sciences may be divided into three kinds: physics, mathematics, and metaphysics.":

1. Physics [(the natural sciences)] deals with that which is in motion and material [(ens mobile or "mobile being")].
2. Mathematics deals with that which is material and not in motion [(∵ mathematical objects, or "mathematicals," do not move or change)].
3. Metascience deals with that which is not in motion nor material.

(cf. §II of his De Trinitate)

In this context, Thomas Aquinas writes in his Division and methods of the sciences, a commentary on Boethius's De Trinitate questions V and VI (my adapted translation follows):

q. 5 a. 1 objection 9: That science on which others depend must be prior to them. Now all the other sciences depend on metascience because it is its business to prove their principles. Therefore Boethius should have placed metascience before the others.

reply to objection 9: Although metascience is by nature the first of all the sciences, with respect to us the other sciences come before it. For as Avicenna says, the position of metascience is that it be learned after the natural sciences, which explain many things used by metascience, such as generation, corruption, motion, and the like [(e.g., actuality, potentiality, matter, form, etc.)]. It should also be learned after mathematics […]. […] Nor is there necessarily a vicious circle because metascience presupposes conclusions proved in the other sciences while it itself proves their principles. For the principles that another science (such as natural philosophy) takes from first philosophy [(i.e., from metascience)] do not prove the points which the first philosopher [(metascientist)] takes from the natural philosopher, but they are proved through other self-evident principles. Similarly, the first philosopher does not prove the principles he gives the natural philosopher by principles he receives from him, but by other self-evident principles. So there is no vicious circle in their definitions. Moreover, the sensible effects on which the demonstrations of natural science are based are more evident to us in the beginning. But when we come to know the first causes through them, these causes will reveal to us the reason for the effects, from which they were proved by a demonstration quia [(i.e., a demonstration a posteriori, a demonstration from effects to causes)]. In this way natural science also contributes something to metascience, and nevertheless it is metascience that explains its principles. That is why Boethius places metascience last, because it is the last relative to us (quoad nos).

See The Way toward Wisdom by Benedict Ashley (read the first chapter, this excerpt, John Deely's review). His main theses are that:

1. the natural sciences are epistemologically prior to metaphysics  
2. metaphysics, which he proposes we term "metascience," is the true philosophy of science.

Pragmatism or Realism?

Realism opposes a relativism of truth and upholds absolute truth. Realism says that truth is the "adequation of intellect and thing." Pragmatism says something is true insofar as it is useful. While utility might be a sign that something is true, as, e.g., the usefulness of Newtonian mechanics in inventing new technologies is a sign that it is a true explanation of the natural world, utility does not necessitate it to be true, for there might be radically different yet accurate explanations of the natural world, like quantum mechanics, which employs a completely different conceptual and philosophical framework than Newtonian mechanics.

Why must scientists return to a realist and not pragmatist definition of truth? Garrigou-Lagrange, O.P., a correspondent with the French physicist Pierre Duhem, proves that a realistic definition of truth opens one up to lines of reasoning inaccessible with a pragmatist definition of truth:

In sciences, physical and physico-mathematical, those facts which exist independently of our mind are considered certain, as laws which express constant relations among phenomena. Postulates, hypotheses, are defined by their relation to the truth to be attained, not as yet accessible or certain. To illustrate. On the principle of inertia, many scientists hold that inertia in repose is certain, meaning that a body not acted upon by an exterior cause remains in repose. But others, H. Poincare, for example, or P. Duhem, see in this view a mere postulate suggested by our experience with inertia in movement, which means that "a body already in motion, if no exterior cause acts upon it, retains indefinitely its motion, rectilinear and uniform." Experience suggests this view, because as obstacles diminish, the more is motion prolonged, and because "a constant force, acting on a material point entirely free, impresses on it a motion uniformly accelerated," as is the motion of a falling body. But the second formula of inertia, as applied to a body in repose, is not certain, because, as Poincare [La science et l'hypothese, pp. 112-19. of French original] says: "No one has ever experimented on a body screened from the influence of every force, or, if he has, how could he know that the body was thus screened?" The influence of a force may remain imperceptible.

Inertia in repose, then, remains a postulate, a proposition, that is, which is not self-evident, which cannot be proved either a priori or a posteriori, but which the scientist accepts in default of any other principle. The scientist, says P. Duhem, has no right to say that the principle is true, but neither has he the right to say it is false, since no phenomenon has so far constrained us to construct a physical theory which would exclude this principle. It is retained, so far, as guide in classifying phenomena. This line of argument renders homage to the objective notion of truth. We could not reason thus under truth's pragmatic definition.

—Reality Chapter 57: Realism And Pragmatism, III. Pragmatic Consequences

A Vatican scientist

What is metaphysics?

Metaphysics, according to the Aristotelian Thomistic meaning, is several things:

1. The science of being as being
2. The "First Philosophy" (first in the sense of "ultimate", but last in the order of our learning)
3. "Beyond physics"
4. The study of "one"

Modern philosophy, however, gives a much broader definition of metaphysics: "The branch of philosophy that deals with the first principles of things or reality, including questions about being, substance, time and space, causation, change, and identity (which are presupposed in the special sciences but do not belong to any one of them); theoretical philosophy as the ultimate science of being and knowing." (OED).

For a Thomist, "questions about" "time and space, causation, [and] change" are parts of natural philosophy, not metaphysics.

St. Thomas says of "metaphysics":

1. "one" which is convertible with being is a metaphysical entity and does not depend on matter in its being. (ST I q. 11 a. 3 ad 2)
2. …the highest of [the sciences], viz. metaphysics… (ST I q. 1 a. 8 c.)
3. …acquired knowledge about Divine things, for instance, the science of metaphysics… (ST II-II q. 9 a. 2 arg. 2)
4. …metaphysics, which treats of being or substance… (Post. Anal. I lec. 41 b)
5. Metaphysics at once studies being in general and first being, which is separated from first matter. (De generatione proem.)
6. It is called metaphysics inasmuch as it considers being and the attributes which naturally accompany being (for things which transcend the physical order are discovered by the process of analysis, as the more common are discovered after the less common). (In Meta. proem.)
7. metaphysics, which deals with divine things, is the last part of philosophy to be learned (CG I a. 4)

St. Thomas says of "physics" (natural philosophy, natural science, or philosophy of nature):

1. …physics, which treats of mobile body [i.e., changeable bodies]. (Post. Anal. I lec. 41 b)

Basically, if there are no such things as immaterial beings, physics would be the ultimate or first science (In Meta.VI lec. 1 [1170]):

if there is no substance other than those which exist in the way that natural substances do, with which the philosophy of nature deals, the philosophy of nature will be the first science. But if there is some immobile substance, this will be prior to natural substance, and therefore the philosophy which considers this kind of substance, will be first philosophy.

Also, check out the 8 tenets of River Forest / Aristotelian Thomism, which are elaborated in The Way toward Wisdom (vide the first chapter, this excerpt, John Deely's review) by Benedict Ashley, O.P., which discusses the question "What is metaphysics?"

The ultimate goal of the natural sciences is to show the existence of immaterial being(s).

The Scale of the Universe 2

The Scale of the Universe 2

Trends in Philosophy & Physics

Physics remains of interest in philosophy: But philosophy does not remain of as much interest in physics: Although philosophy is more of interest in astronomy: Thomism is, unfortunately, becoming of slightly less interest in philosophy:

Modern Physicist Oerter & Philosopher Feser

Edward Feser: Oerter on universals and causality

and

Oerter contra the principle of causality
and
Natural theology, natural science, and the philosophy of nature

"Big Bang, Evolution, Creation and Belief in God" by Fr. Bill Stoeger

From the Tucson Catholic Physician Guild's February 2012 meeting:

Homeschooling is Education's Future

Created by: CollegeAtHome.com
Via: DegreeSearch.org

Pope Pius XI wrote in his 1929 encyclical on Christian education, Divini Illius Magistri, regarding "family education" (homeschooling):

73. Nevertheless, Venerable Brethren and beloved children, We wish to call your attention in a special manner to the present-day lamentable decline in family education. The offices and professions of a transitory and earthly life, which are certainly of far less importance, are prepared for by long and careful study; whereas for the fundamental duty and obligation of educating their children, many parents have little or no preparation, immersed as they are in temporal cares. The declining influence of domestic environment is further weakened by another tendency, prevalent almost everywhere today, which, under one pretext or another, for economic reasons, or for reasons of industry, trade or politics, causes children to be more and more frequently sent away from home even in their tenderest years. And there is a country where the children are actually being torn from the bosom of the family, to be formed (or, to speak more accurately, to be deformed and depraved) in godless schools and associations, to irreligion and hatred, according to the theories of advanced socialism; and thus is renewed in a real and more terrible manner the slaughter of the Innocents.

Historical Method in Teaching Physics

The French physicist Pierre Duhem wrote:

The legitimate, sure and fruitful method of preparing a student to receive a physical hypothesis is the historical method. To retrace the transformations through which the empirical matter accrued while the theoretical form was first sketched; to describe the long collaboration by means of which common sense and deductive logic analyzed this matter and modeled that form until one was exactly adapted to the other: that is the best way, surely even the only way, to give to those studying physics a correct and clear view of the very complex and living organization of this science [emphasis added] (Duhem, P.: 1905/1954, ‘The Aim and Structure of Physical Theory’, Princeton University Press, Princeton, NJ, p. 268).

Ernst Mach also advocated the history and philosophy of science (HPS) teaching method:

A person who has read and understand the Greek and Roman authors has felt and experiencedmore than one who is restricted to the impression of the present. He sees how men, placed in different circumstances, judge quiet differently of the same things from what we do today. His own judgments will be rendered thus more independent (Mach, E.: 1886/1986, ‘On instruction the Classics and the Sciences’, In: ‘Popular Scientific Lectures’, Open Court Publishing Company, La Sale, IL., p. 347).

Igal Galili, author of "Experts’ Views on Using History and Philosophy of Science in the Practice of Physics Instruction," wrote to me that the historical method "presents a great controversy in university physics textbooks of physics."

Arnold B. Arons, in his Teaching Introductory Physics, opposes the HPS teaching method; he thinks something "goes wrong if you suspend judgment (page I-229) in order to retrace historical footsteps."

Why is this? Do you agree or disagree? Is the historical method a "legitimate, sure and fruitful method of preparing a student to receive a physical hypothesis"?

Cf. this StackExchange discussion of this topic.

Mathematical Nominalism vs. Mathematical Realism

From the comments to the posting here:

Of course we want to hear about mathematics!

You should do some posts on Thomism and mathematics. The literature out there on St. Thomas's conception of mathematics seems very sparse. I especially would like to see some studies of how a Thomist views calculus, infinitesimals, etc.

There are some things, for example: My quotes of St. Thomas on mathematics; ch. 6 of Mullahy's Thomism & Mathematical Physics (PDF pgs. 264 ff.) is entitled "The Nature of Mathematical Abstraction"; "A neglected Thomistic text on the foundation of mathematics" by Armand A Maurer; and St. Thomas on the object of geometry by Vincent Edward Smith. These are all online for free.

Also, if you don't know about Augustin-Louis Cauchy, read this Dictionary of Scientific Biography article on him. I quote it: "More concepts and theorems have been named for Cauchy than for any other mathematician (in elasticity alone there are sixteen concepts and theorems named for Cauchy)." In his Cours d'Analyse, he proved the Fundamental Theorems of Calculus and Algebra, described partial fraction decomposition, devised convergence tests, and was the first to devise the ε-δ formulation of the limit (cf. this article by a prominent Cauchy historian; I love how it begins! A proper understanding of calculus is absolutely vital for understanding the power and limits of modern mathematical physics.). Of course Cauchy is also famous for complex integrals. Since he was a devout Catholic, I've been wondering if he was well-versed in Thomism. He studied classics before becoming a mathematician, so it's possible. I'm not sure he wrote any treatise on the philosophy of mathematics, though.

My follow-up:

Definitely read St. Thomas's In Boethium De Trinitate, q. 5, a. 3: "Does Mathematics Treat, Without Motion and Matter, of What Exists in Matter?". (Questions 5 and 6 of In Boethium De Trinitate are also called St. Thomas's Division and Methods of the Sciences.) Cf. also St. Thomas's commentary In II Phys. lect. 3.

From what I have read, it seems that Aristotelian philosophy of mathematics does well making sense of the everyday mathematics your average person on the street uses, e.g. arithmetic, combinatorics, geometry, and other discrete disciplines.

Aristotle and St. Thomas certainly distinguished discrete and continuous quantity (cf. Summa I q. 3 a. 3: "punctum non est principium nisi quantitatis continuae, et unitas quantitatis discretae": "a point is the principle of continuous quantity alone; and unity, of discontinuous quantity").

However, like you say, it would be interesting to see if an account of infinitesimals, calculus, the larger infinities, etc. could be given, while remaining a realist (rather than nominalist) theory of mathematics.

St. Thomas, in his commentary on Aristotle's Physics, deals very well with the "mathematical nominalist objection" to actual infinities in nature (be they infinitely large {cardinalities of Cantor sets}, infinitely small {infinitesimals}, etc.): From In III Phys. lect. 7:

[...] [Aristotle] says that it is impossible for the infinite to be separated from sensible things, in such a way that the infinite should be something existing of itself, as the Platonists laid down. For if the infinite is laid down as something separated, either it has a certain quantity (namely, continuous, which is size [magnitudo], or discrete, which is number [multitudo]), or not. If it is a substance without either the accident of size or that of number, then the infinite must be indivisible—since whatever is divisible is either number or size. But if something is indivisible, it will not be infinite except in the first way, namely, as something is called “infinite” [viz., "not finite"] which is not by nature susceptible to being passed through [better translation: "which is not surpass-able"], in the same way that a sound is said to be “invisible” [as not being by nature susceptible to being seen], but this is not what is intended in the present inquiry concerning the infinite, nor by those who laid down the infinite. For they did not intend to lay down the infinite as something indivisible, but as something that could not be passed through, i.e., as being susceptible to such, but with the passage having no completion.

So, it appears the mathematical nominalists are correct when it comes to mathematicals indirectly "separated [abstracted] from sensible things" (e.g., ∞, א, irrationals, etc., which are only ens rationis, "beings of reason" or "mind-dependent beings"), but they are incorrect in claiming that mathematicals of discrete (e.g., the number 2) and continuous quantity (e.g., a regular dodecahedron) can only be ens rationis (or our names of those ens rationis). The issue boils down to whether or not actual infinities exist in nature (cf., e.g., the whole Physics lecture above or the Summa questions: "Whether an actually infinite magnitude [magnitudo] can exist?" and "Whether an infinite multitude [multitudo] can exist?").

Also, Pierre Duhem—an early 20th century French, Catholic, Thomist physicist, philosopher of physics, and founder of the discipline of the history of medieval physics—wrote, contrary to Poincaré, that mathematical induction can be reduced to a finite syllogistic process.

Happy Easter!

Review of Hannam's God's Philosophers

Igal Galili is an excellent physics education researcher who believes the history and philosophy of science (HPS) must be incorporated into physics education—something Duhem advocated, too, in his Aim and Structure of Physical Theory. See, e.g., Galili & Hazan (2001).
Last year Galili wrote an excellent review of James Hannam's book God's Philosophers: How the Medieval World Laid the Foundations of Modern Science:

Book Review
James Hannam: God’s Philosophers. How the Medieval World Laid the Foundations of Modern Science?