A Rambling Brain Dump on Material and Formal Logic

This is a rambling brain-dump from an e-mail today.

Historically, I'm not completely clear on the division.  (I have this vague memory of T. Noone mentioning something by Ashworth on it.)  It establishes itself by the 16th century and is, of course, present incipiently in texts like Aquinas's introduction to the Posterior Analytics commentary.  (Yet, that's a dangerous text to wield if you're not careful - because his language goes down the lines that the Suarezians want to take.  Even Giorio Pini read him this way.  It's not the way other texts clearly go; also, it's not the way the Thomist school went.)

Still, it's perplexing to me, and I'm a little bit on the fence.  Later on, you get the weird division of Minor and Major Logic.  This is just a pedagogical splitting though.  It usually divides along the lines of the old formal and material logic.  (There are other more odd things in the 19th and 20th century because of "Criteriology " and "Critique".  Nothing to be said here about those phenomena. Critique is valid as a defensive office of metaphysics.)

The general line is this.  Allow me to ramble in what basically is two sentences with one very long paragraph.  As always, I write in haste, so it's a bit rambling....!

De interpretatione and Prior Analytics deal with the formal structure of the syllogistic: the formal structures of the parts of syllogisms (propositions) and those of syllogisms themselves (considered in their figures and the immediate properties of those figures).  Beyond that valid structure, you have questions of truth and certitude (with the latter comes the basic question of scientific knowability and certitude - they coined scibilitas in distinction from cognoscibilitas; hence, the Posterior Analytics concern with discussing not syllogistic-figure-related issues but with the conditions for science: e.g., per se nota propositions, and definition / division as regards the middle term of demonstration [book 2]; one then sticks the concerns of the Categories in here to this latter bit, but this seems a bit fabricated to me because there is a formal structure in defining [superiority, inferiority, etc.; the issue is, though, and here the tradition is mostly on to something that very quickly the predicables come up, and when you have to deal with accidental vs. proper definitions vs. essential definitions, you are dealing with a "material" issue]).

Thus, the general analogy (and it's only that) is:

f. logic : m. logic :: conditions of validity : conditions of soundness


Except, material logic is more than the posterior analytics.  It includes the Topics (the bastard child of the Organon, but very important; I am going to be doing some work on this eventually) and the Sophistical Refutations (think of it like "crap matter").  For Aquinas and generally for the school, one wants to put Rhetorics in here with the Poetics.  I think it is actually the correct position.  But, this is just in need of some more development.  Remember, this represents a huge battle in the Aristotelian world; Deborah Black's monograph will give you some thoughts here.

Now, a quick few other bits:

For the Thomists, 2nd intentions are those relations made in things as known and ordered by the natural process of the 3 acts of the intellect.  Remember, each act has its own unique character:

1st. Defining: This is a unique work, not syllogistic.  The predicables fall here for example.  Genus, species, etc.  But also "extension" and "intention" etc.  Nous trying to get clear on a idea.  That's how to think of it.  (I can get you an excellent remark by Garrigou on this.)

2nd. Proposition formation.  Remember, propositions bear on complexes (Man-being-risible); they aren't merely the semi-simple definition by property "political animal" (=first act of intellect). Thus, you can even say: "The political animal is a being ordered to a common good materially defined by a legitimate authority."   In any case, the 2nd act of the intellect forms its own relations in these complexes.  (Subject-predicate; etc.)  There are various properties here regarding opposition, equipolence, etc.  Remember, I stress this as a Thomist: the 2nd act of the intellect forms its own verbum.  Not completely clear in Aquinas, but it's there enough that the school picks up on it.


3rd. Syllogizing: Here you deal with all the other sorts of higher level relations so familiar to those focusing on the Prior and Posterior Analytics.  No new verbum; perhaps qualitatively altered (because to know a proposition as a conclusion adds a characteristic to that sort of knowledge).

Again, these are relations in things insofar as they objectively / intentionally exist.    This differentiates them from real relations.  They are reflexively known.

There is some disagreement late in the school, and I can't put my finger on it, that says that logic must be divided according to the formal character of its object.  If its object is divided according to the 3 acts, which uniquely create different kinds of relations, then one should divide logic this way instead.  (Now, perhaps there would be formal and material sub-branches; I don't know.  It's not that easy; just trust me.  The various acts interact a bit.  For example, suppositio only befalls terms because they are in enunciations; and enunciations only are called propositions if they are in syllogizing; etc.)

Explicative Syllogisms

Some scholastic goodies for those who care to see it.  Dense stuff—but important distinctions regarding what is and what is not a syllogistic inference.  Used this to explain something in a footnote to a forthcoming translation of Fr. Garrigou-Lagrange's Le principe de finalité.

Austin Woodbury, Logic, The John N. Deely and Anthony Russell Collection, St. Vincent College, Latrobe, PA, p.239-241 (n.299-300).

"In every syllogism properly so-called, from one truth is inferred ANOTHER TRUTH.  Therefore, whenever by a syllogism there is not inferred a NEW TRUTH, this is a syllogism improperly so-called.  The syllogism improperly so-called is twofold, to wit: the expository syllogism and the explicative syllogism…  From the expository syllogism must be distinguished the explicative syllogism; whereof, this is an example: ‘Man is mortal.  But a rational animal is a man.  Therefore, a rational animal is mortal.’"

"Here, [the middle term] is universal, and therefore there is a true illation.  Nevertheless, it is not a syllogism properly so-called, because it does NOT infer in the conclusion another truth, i.e. a judgment other than in the premises.  For here, the conclusion expresses the same truth but explicates it BY OTHER CONCEPTS.  For these two propositions, ‘man is mortal,’ and, ‘rational animal is mortal,’ express the same truth, but the latter expresses it by more distinct concepts than the former.  Wherefore, to this is rightly given the name of EXPLICATIVE syllogism."

"In the explicative syllogism, the conclusion is IDENTICAL AS REGARDS ITSELF (quoad se) with the major but NOT AS REGARDS US (non quoad nos); and therefore, there is a formal illation, but not an objective illation.  [He cites here R.-M. Schultes, Introductio ad historiam dogmatum (Paris: Lethielleux, 1922).]"

"OBSERVE that the major [premise] and the conclusion of an explicative syllogism are in THE SAME MODE OF SAYING ‘PER SE’; otherwise, there would be had, not an explicative syllogism but a syllogism PROPERLY SO-CALLED.  In the example given above, both these propositions are IN THE SECOND MODE of saying ‘per se.’  But the case is otherwise with this syllogism: ‘A rational animal is capable of science.  But man is a rational animal.  Therefore man is capable of science.’  Here, the major [premise] is in the FOURTH mode of saying ‘per se’; otherwise, the syllogism would be employed to no purpose.  But the conclusion is in the SECOND manner of saying ‘per se.’  Wherefore this is a syllogism properly so-called."


Logical and Metaphysical Universal

This selection is taken from the schematic found on Austin M. Woodbury, Logic, The John N. Deely and Anthony F. Russel Collection, St. Vincent College Library, Latrobe, PA, 63.

More to come later, for I will likely be reworking some of these texts:

"The Universal [sic] is something REAL or the NATURE OF THE THING, which if it be considered . . .  as ABSTRACTED from real existence . . . but not from mental existence, is universal and can be considered either in itself AS REGARDS THE THING CONCEIVED, [in which case] it is the METAPHYSICAL UNIVERSAL, or relatively to inferiors (OR, AS REGARDS MODE [sic] OF CONCEIVING), whose property is PREDICABILITY, which is aptitude for predication, [in which case] it is the LOGICAL UNIVERSAL"

Modes of Knowing

This selection is adapted from Austin M. Woodbury, Logic, The John N. Deely and Anthony F. Russel Collection, St. Vincent College Library, Latrobe, PA, 120-121.

The general issue to be considered here are the instruments that logic furnishes for the the manifestation of truth, enabling us to proceed from a vague knowledge to a distinct knowledge.  We should note here the pivotal role played in this by means definitions and divisions.  These are often ignored even though they are what bring about the perfection of the first operation of the intellect.  Nous has its own instruments or "procedures" for bringing clarity out of the nebulous cloud from which insight first emerges.

Notion of "Mode of Knowing"

First, we must consider what we mean by a "mode of knowing."  At first, the human intellect knows nothing perfectly but, instead, has knowledges that are obscure, confused, or doubtful.  To perfect its knowledge, the intellect uses logical instruments that we call "modes of knowing."  For this reason, a mode of knowing is defined as, "A discourse that is manifestive of something that is unknown"—oratio alicuius ignoti manifestiva.  Here, we do not mean by "unknown" that something is utterly unknown.  Instead, we take "unknown" for obscure, confused, or doubtful.

Division of the Modes of Knowing

Now, we must consider the division of modes of knowing accepted by the Thomistic school.  There are two sorts of unknowns that we may need to make manifest, namely something that is incomplex (simple) or something that is a complex truth.  Now, with regard to incomplex things (which are the simple essence of a thing), manifestation occurs either (1) with regard to its constitution or (2) with regard to its parts.  Its constitution is manifested by means of definitions, while it is manifested with regard to its parts by means of divisions.  However, as regards a complex truth, i.e. the logical truth found only in judgments (which are logically complex), manifestation occurs by means of proof or argumentation

Thus, there are are three modes of knowing, namely:

  1. Definition
  2. Division
  3. Argumentation

However, it is important to note that a term is not, of itself, a logical instrument (i.e. a mode of knowing), except in a remote manner.  This is so because we do not bring our knowledge to perfection by means of terms by themselves.  They only play a role in such perfecting of knowledge when they are conjoined to one another in some special way—i.e. inasmuch as definitions, divisions, or argumentations are formed from termsInasmuch as these latter three are the "modes of knowing" that we are discussing here (namely, with regard to the perfecting of human knowledge), they are the modes of knowing that we are concerned with here.

Also, we should note that sense experience, by which we know the truth of a fact is not a mode of knowing, for the truth of a fact known by sense experience does not need a medium whereby it is manifested.

Likewise, faith, by which something is believed on the testimony of a witness, is not a mode of knowledge because it does not manifest the thing itself but, instead, leave it obscure.

Finally, we can concede that logic itself is indeed a mode of knowing.  However, it is only such ain a universal manner (given that it provides the universal instrument for directing human knowledge), but not in a specific manner.