Metalogic Resolution of "Barbara" to "Celarent"

Aristotle offers arguments that resolve the valid syllogisms to various first figure syllogisms (Prior Analytics I.7). He further argues that the particular first figure forms, both negative and affirmative (i.e. "Darii" and "Ferio") can be resolved to the universal negative of the first figure ("Celarent") by contradiction and reductio. Thus, of the fourteen valid forms, ten resolve directly or indirectly to "Celarent" and two resolve to "Barbara" (they are both negative: "Baroco" and "Bocardo"). However, there seems to be no resolution of "Celarent" to "Barbara." However, one can offer the following arguments that the "perfection" of these figures, that the mind can immediately grasp the necessity of the conclusion, by resolving them to the principle of contradiction. Furthermore, perhaps, we have a from these arguments an argument that the negative does resolve to the affirmative universal figure.

The necessity of the conclusion from the "Celarent" form is per se notum because "Celarent" is a form of speech that sets down the negation (not-being) of a predicate whole from a subject whole, which is in turn the predicate whole of a subject part, but such a form appeals to the negative side of the principle of contradiction, which is per se notum. "Celarent" also appeals to the principle that the whole is greater than the part.

The necessity of the conclusion from the "Barbara" form is per se notum because "Barbara" is a form of speech that sets down the affirmation (being) of a predicate whole of a subject whole, which subject whole is predicate to a subject part, but such a form appeals to the positive side of the principle of contradiction, which is per se notum. Likewise, this form utilizes the first principle that the whole is greater than or contains the part.

However, being is prior to non-being in notion, and therefore affirmation (saying of something that it is) is prior to negation (saying of something that it is not) in notion. Thus the necessity of "Celarent" depends upon that of "Barbara."

I apologize for the dirty word in the title. These arguments are actually attempting to be a part of metaphysics.

S. Thoma Aquinatis, Doctor Communis atque Expositor

Plato, philosopher and teacher of Aristotle, once taught that, "There is a real distinction between existence and essence." Note that, of the two predications in the preceding statement, the truth of each is evaluated by two different disciplines. An individual man could conceivably argue to falsity of the main clause, and the truth of the quotation, but he would require two different sciences, history and philosophy respectively, each with differing degrees of certitude as to their judgments.

Consider this sentence: St. Thomas held that "A demonstration of the existence of an immaterial, first, and unmoved mover is required to differentiate the science of physics and the science of metaphysics as to their subjects." It succumbs to an identical analysis as the statement concerning Plato. As a further consequence, the student of philosophy ought to invest his time secondarily seeking the answer to the historical question, and primarily the philosophical one. However, when it comes to knowing and defending the authority of one's teachers, and whom one's teacher indicates as teachers, the answer to the former question takes on more importance.

The disciples of St. Thomas take a broad spectrum of positions concerning the Angelic Doctor as the Expositor of Aristotle, the Philosopher. At one extreme, everything St. Thomas writes concerning Aristotle's philosophy in the commentaries is to be taken as (permit me the use of a dirty word) "Thomistic philosophy" (e.g., Weisheipl), unless St. Thomas explicity states otherwise in the same or parallel contexts. The other extreme holds that St. Thomas was only a theologian, and no such Thomistic philosophy can be found (Gilson). A more moderate position states that "When the views [Thomas] presents in more independent writings agree with those he exposes in a particular commentary on Aristotle, we may assume that he accepts the latter as his own position as well. When there is disagreement between the two discussions, we should be very hesitant in assigning such a position from one of his commentaries to Thomas himself, unless there is also some evidence pointing to change or development in his thinking on that point." [1] This view leans to the Gilsonian extreme, stating that St. Thomas agrees with what he says in commentaries on Aristotle only where explicitly stated elsewhere. Otherwise, the Expositor is merely expositing what Aristotle thought was philosophy, and isn't making any "truth-value judgments."

However, one could bend the stick towards the "River Forest" extreme and take what is (too strongly) named "The McInerny Identity Thesis": that St. Thomas agrees with what he says concerning what Aristotle said, unless he explicitly states otherwise (in any place). That this seems to be the case can be evidenced from the following place.

Concerning the disagreement over the distinction of the subject of physics from metaphysics, Wippel's position concerning the texts from Metaphysics IV, VI, and XI as St. Thomas treats of it in his commentary is that: "In these cases we have Thomas's explanation of Aristotle's text, but not Thomas's personal position concerning the conditions of possibility for separation and hence for the discovery of the subject of metaphysics." [2] Metaphysics VI.1 states:

...if there is no substance other than those which are formed by nature, natural science will be the first science; but if there is an immovable substance, the science of this must be prior and must be first philosophy, and universal in this way, because it is first. [1026a27]

St. Thomas, in his commentary, does "little more than repeat the Stagirite's text." [3] Now, without going into the intricacies of this issue philosophically, one can argue from the opponent's own grounds that St. Thomas in fact holds Aristotle's position. For, if there is another text (an independent text) where St. Thomas sustains this view, then it can be attributed to his own philosophical teaching.

In Summa Contra Gentiles, I.12, St. Thomas argues against those who hold that the existence of God can only be held by faith, and cannot be demonstrated by reason. Three arguments for fideism are brought up, and before they are answered in order, St. Thomas presents the four following arguments for the truth of the matter:

Huius autem sententiae falsitas nobis ostenditur, tum ex demonstrationis arte, quae ex effectibus causas concludere docet. Tum ex ipso scientiarum ordine. Nam, si non sit aliqua scibilis substantia supra substantiam sensibilem, non erit aliqua scientia supra naturalem, ut dicitur in IV Metaph. Tum ex philosophorum studio, qui Deum esse demonstrare conati sunt. Tum etiam apostolica veritate asserente, Rom. 1-20: invisibilia Dei per ea quae facta sunt intellecta conspiciuntur.

These arguments seem to be arranged in descending order of philosophical force: 1) from the teachings of logic, causes are to be concluded to from their effects; 2) from the order of the sciences, which argument will be considered in a moment; 3) from the desire or zeal of the philosophers; 4) from the authority of Scripture.

In the third argument, St. Thomas argues that the order of the sciences shows that fideism is false: "For if there are not any knowable substances above sensible substances, there would be no science higher than natural [science], as is said in Metaphysics IV." But, modus tollens, there is a science of metaphysics. Therefore there are knowable separate substances, hence fideism does not hold.

Note that St. Thomas quotes Metaphysics IV, whereas the passage he paraphrases clearly occurs in Metaphysics VI. The passage cited by the Pegis translation of the Summa Contra Gentiles is from Metaphysics IV.3, 1005a18ff, a passage Wippel includes in his dismissal. This misquotation I cannot explain. Concerning this misquoted text, in his commentary (written after SCG) St. Thomas also mentions the same difficulty: the reason for why the naturalists sought to treat of first principles: because they thought that there were no separate substances.

For our purposes, this text shows that St. Thomas must agree with what he states in his commentary on Aristotle concerning the texts in question (Metaphysics IV.3 and VI.1). The force of the argument in SCG depends upon an order of the sciences considered from the rank of their objects. By paraphrasing Aristotle, St. Thomas appeals contextually to the difficulty of distinguishing the subject of physics from metaphysics as part of that order. If they can be distinguished, fideism fails. If they cannot be distinguished, fideism holds. However, the solution to the difficulty (as St. Thomas indicates himself in his commentary, following Aristotle) is that the argument from Physics VIII for an immaterial prime mover establishes the subject of metaphysics.

If St. Thomas did in fact disagree with the Philosopher concerning this point, it is very misleading for him to paraphrase a well-known passage of Aristotle, importing its contextual solutions, in refutation of an error concerning the Catholic faith.

There are at least two replies that could be offered: 1) St. Thomas is appealing only to the order of learning, and 2) St. Thomas is using Aristotle's authority in a merely dialectical fashion: St. Thomas could still hold a "personal solution" to the problem of differentiating the subjects of physics and metaphysics.

Contra 1.: St. Thomas cannot be relying solely on the order of learning for this difficulty: in order to refute fideism, the existence of a science posterior to physics must hold (the order of teaching such a science in relation to physics would be posterior to such a consideration: nobody cares about the order you teach non-existent sciences).

Contra 2.: St. Thomas cannot offer merely dialectical responses to fideism. Philosophy as handmaiden must (in its defensive mode) show this to be (paradoxically) an error pernicious to the faith. Now, the argument from the "desire of the philosophers" is dialectical: "Surely all these men are not hunting in vain." The argument from logic is (in a like fashion, though stronger) dialectical, for while it teaches that effects prove the existence of causes, logic as a science cannot demonstrate the existence of those causes. The way to demonstratively refute fideism is to show the science itself. Now, if St. Thomas is quoting Aristotle as his authority for this, but disagrees with the Stagirite's solution (which solution must be clear, for St. Thomas indicates it in his commentary), all the while making no mention of it, his argument fails his hearers. It is greatly irresponsible for a teacher to introduce a difficulty in the presence of his students which he himself cannot solve.

Now, none of these arguments are demonstrative, and such arguments never will be. However, in the interest of clinging to St. Thomas a the Expositor, it seems that they lend support to following him as he follows the Philosopher.

[1] John F. Wippel, Metaphysical Thought of Thomas Aquinas, p.xx
[2] ibid., p.59
[3] ibid., p.57

Consistency of Truth

Aristotle teaches (Prior Anal., I.32) that the truth is consistent with itself. Perhaps a modern symbolic logician would express this fact in such a manner: for any given premise set, the set is consistent if there are no formal contradictions that can be formed through conjunction, of the general form p•~p. A better way to say this is that truth, or being as known, cannot be false, for truth in the fullest sense is knowledge through causes, and for truth to be inconsistent with itself would be for an ordered and ultimately divine sequence of causality to cause being and non-being with respect to the same. Hence, Garrigou-Lagrange can state truthfully (God, vol. 1, xiii) that to accept the principle of non-contradiction is to accept implicitly the existence of a God who is simple and identical with Himself, a First Cause who is not only true and the cause of truth, but, being these things, is Truth itself.

Blindness of Soul

"The submission of a servant is necessary in seeking God. In outward things light helps to prevent one from falling; but in the things of God just the opposite is true: It is better for the soul not to see if it is to be more secure." (St. John of the Cross, Sayings of Light and Love, III, n.133)

This blindness of soul (contrasted to the possession of light to see our way down physical paths) is necessary because the way to God is beyond our comprehension. God Himself must lead us. Thus, we can only follow. True following involves a sort of ignorance because the principle of reaching the goal (the leader, God), is other than the led, the follower. The best sort of creature must be the truest follower.

Commentary on the Golden Plate From Hipponion

The pagan gold prescribes:
Speak, oh Son of Earth and Starry Sky,
Being of the border world, describe
Your plight: it is "parched with thirst and am dying."

The heathen gold counsels:
Ask for water from Mnemosyne's mere,
For the Muses' Mother's draught
Is cold and quick and bracing.

The idol gold prophesies the turn:
Pity of dead princes will reach you
They will mediate Memory's lake.
Alas, it cannot quench your parched and deadly spirit.

The pagan gold can give no guidance:
'You are setting out on' a thronged road,
Your companions famous, you among the 'initiates.'
Yet their merely human strength will fail,
Your pagan potation proves nothing.

"Cum venerit, quod perfectum est,
Evacuabitur, quod ex parte est." (1)

1: See I Cor. 13

On Teaching

CF: St. Thomas, De Veritate, Q. 11, (the 'De Magistro'), a. 1

1. St. Thomas points out that a man acquires science because of the certain seeds of knowledge that are in him. These are the first concepts and first principles. These seeds contain in their power all other actual and more particular knowledges. Whence from this potency, knowledge is led into act in a man.

2. However, St. Thomas compares this acquisition of knowledge to a doctor and health. In this comparison, the acquisition of knowledge, or learning, happens in two ways.

2.a. First, the way that health is regained naturally by the body, i.e. by it "healing itself." This St. Thomas compares the way of teaching oneself or the inventio of knowledge.

2.b. Second, the way that a doctor using the medical arts assists the body in healing itself. This is the way a man teaches another man, by reducing the potential knowledge in him to act by leading the learner along the way of inventio in the best route possible. This way is called disciplina.

3. Whence, it seems to me, given that "teaching" most properly said is in the second way (2.b), that the reduction of potential knowledge to actual knowledge in the learner is what all other analogous, metaphorical, and corrupt uses of the term "teach" are ordered towards this meaning.

3.b. Thus teaching has this respect to truth, that it leads a mind from potency to act with respect to the intellect's object of truth.

4. Two corollaries can be drawn regarding the "ethical realm" of teaching and learning. The first corollary uses this proper sense of teaching with respect to the ethics of disciplina; the second uses this proper sense with respect to inventio.

5. First corollary. Premise: to know propositional truth is the proper (natural) operation,proper good, and hence perfection, of the human intellect. Whence anything opposed to this is unnatural, bad, and an imperfection. A teacher, when using his authority in his office as teaching with respect to a student, in proposing something for them to learn, must pay attention to this standard. This is especially true when he, in his pedagogical method, invokes the authority of another, e.g., "As Aristotle says," or even the strongest example of quotation, claiming that someone is actually "teaching" and hence claiming a true reduction of potential knowledge to actual knowledge, and so a teacher might say "As 'so-and-so' teaches." In this way a teacher is to be compared to a doctor, who (as Mr. Berquist teaches often in Junior philosophy) makes the best murderer, because he knows the human body insofar as it is a composite and corruptible whole, and hence knows best how to decompose it and reduce it to perfect corruption. Just as a doctor would abuse his art and commit an evil by harming or killing his patient, so a teacher commits an evil (to varying degrees) if he harms the intellects of his learners by ignorance or falsity. "Teaching" must be measured against its proper sense, and if it fails this standard, the proposed disciplina is somewhere between folly and ignorance (the use of authority in place of true knowledge, or lack of knowledge and recourse to a sort of boasting) and dogmatism or pernicious lies. This is the gamut between sophistry and ideological tyranny, the organon of the dictator.

6. Second corollary. Same premise. Whence, in the way of inventio, a man must evaluate all sources of 'disciplina' professing to lead him on the way of learning or the way of discovery against this standard. This allows for an ordering of the uses of "teaching" when attributed to someone by way of authority, i.e., it indicates degrees among the proper use of "teach" while respecting the fact that (again, as Mr. Berquist is fond of pointing out) it is very hard to be all wrong. Whence, "As Descartes teaches," or "As Kant teaches," or "As Plato teaches," or "As Aristotle teaches," or "As St. Thomas teaches," or "As Jesus teaching in the Gospels," are all statements that require a certain order and judgment (taken in the sense of the second act of the intellect, with the mutatis mutandis for the Faith and grace). This evaluation takes the form of, in one's own via inventionis, of finding and following a master from whom to accept a via disciplinae.

A Reflection Upon Intellectual Perfection and Method

"In the older systems both the kind of man the teachers wished to produce and their motives for producing him were prescribed by the Tao---a norm to which the teachers themselves were subject and from which they claimed no liberty to depart. They did not cut men to some patter nthey had chosen. They handed on what they had received: they initiated the young neophyte into the mastery of humanity which over-arched him and them alike. It was but old birds teaching young birds to fly." (1)

Here is encapsulated the essence of teaching and learning according to true intellectual perfections. What it is to be a master and what it is to be a learner, in the sense that men, in so doing, act according to their own natures, and conform to that very nature according to their proper activity as intellectual beings, is found in this exchange, this gift and reception according to an order that is itself given to our knowledge. In stark contrast, however, stands this passage:

"...the whole tradition of the disciplines presents us with a series of masters and pupils, not a succession of discoverers and disciples who make notable improvements to the discoveries." (2)

The proposal of the modern method, taken here as found in seminal form in the New Organon, clashes with a resounding and cacophonous racket against the conception of learning and intellectual perfection found in the earlier period, the "older system." Indeed, while Bacon claimed that the modern age was really the old age of the world, when men had arrived at full intellectual maturity and were ready to take on the challenges of adult scientific life, the situation of the ancients is portrayed as one of childhood and fruitless and infertile adolescence. The basic accusation here is that the old system will produce nothing but more birds who can fly in the same old fashion. Indeed, what happens if this chain of knowledge should be lost? If the entire intellectual endeavor is ordered around imitation and emulation of a master, without a drive to make better upon one's predecessors in the same spirit they possessed, that is in making new and more productive discoveries, is not the ancient way in the predicament of the followers of Socrates on the day of his death?

"[SOC:]...do you think everybody can give an account of the things we were mentioning just now? [SIMMIAS:] I wish they could, but I'm afraid it is much more likely that by this time tomorrow there will be no one left who can do so adequately." (3)

Does not a method which promotes attainment of an already measured-out perfection run the risk of destroying itself? If there is no man who can measure up to the achievements of the master, of what good is the science?

Now as perverse as such an objection might seem, this seems nevertheless to be the modern rant of science against the systems and wisdoms of old. These hoary heads have been mocked and beaten about the pate as crazy fools, and useless mystics. While the old craved perfection according to a measure set forth by nature, the new seeks a perfection that it claims will ever be bettered, a vast sum and history of particulars ruled by laws continually improved upon, and only measure by nature per accidens, in the sense that eventually the techne can eliminate this chain of phusis, which it truly is, a chain, and no measure.

From this it seems that the modern and post-modern effort has pointed out (perhaps unwittingly) the key difference. Is it not that the perfection of the new scientific method is extensive, whereas the perfection of the old wisdom is intensive? The new science bases itself upon the massive historical categorization of particulars according to laws, assisted with the powerful tools of imagination and mathematics, and is in itself a sort of snowball, which gathers speed and appears to be making great progress, but at the same time separates the various parts from the others and makes a fragmentary whole. This kind of expansive, or extensive, or more material perfection evidences itself in the mode of training: it is discoverer and disciple, who in turn surpasses the previous discoverer as merely another link in the chain.

On the other hand, the old science bases itself upon an approach to what is formal and intensive, which requires an intellectual discipline that makes it appear as mysticism, for the approach from what is magis nota quoad nos to what is better known by nature is fraught with many difficulties, and requires certain sacrifices, virtues, and material conditions (e.g. leisure). Furthermore, this penetration into the universal, the intellectual, and the realm of the fundamentally real, cannot produce "results" in the material sense because it is more noble and indeed prior to such an endeavor. This old science is the wondering after the causes, about which man can truly do nothing, and realizes he can do nothing, almost as a fuzzily conceived prerequisite to entering upon such speculation. As this method prescinds from the material and humanly changeable (insofar as its perfection is concerned), it cannot be transmitted easily, or simplified, or improved upon by later "discoverers" of shortcuts. Hence this kind of intensive and "occult" knowledge requires a mode of training that likens the student to the one who has already mirrored in his intellect the order of reality.

Now, granted, in both kinds of learning, the student will pass from a state of ignorance to a state of knowledge. Furthermore, in both "kinds" of science improvements have been made by later thinkers upon their predecessors. Nevertheless, it seems consistent that the old science improves itself by becoming clearer, whereas the new science improves itself by expansion and becoming more powerful. Finally, I would submit that anytime the new science is improved by becoming clearer, it is actually participating in the old.

How then can we relate the two branches? Do they grow from the same tree? Is the elder a demented sot inebriated with his soured vintage, or is the younger a frightful bastard monster that should have been exposed?

Perhaps they can be brought into harmony:

"If by philosophy of nature is understood a science in a quite rigorous sense, that defined in Posterior Analytics I.1, and if by experimental sciences we mean those branches of the knowledge of natural things which remain in a condition of dialectical movement because they cannot sufficiently detach themselves from the singular and whose generalizations will thus always be tentative and provisory, it is understood that the two are quite distinct. Nevertheless, they bear on the same subject, their principles have a common origin, sensible matter; their term is the same, knowledge of natural things as much as possible in their proper principles. In this respect, the experimental sciences are only a continuation of the properly demonstrative science of nature. But this continuation requires the use of another method, not only in the search for principles, but for the choice and positing of the principles themselves [cites Topics I.16]" (4)

In this, then, seems to be the burden: to effect a reconciliation between the fragmented parts that constitute modern science, care must be taken to see what is prior and what is posterior, and then one can recognize that a true unity is to be found.



(1) C. S. Lewis, The Abolition of Man, HarperCollins, New York, 2001; pp. 60-61
(2) Francis Bacon, Novum Organum, Cambridge, 2000; p. 7, "Preface to the Great Renewal"
(3) Phaedo, 76c
(4) Charles DeKoninck, "Are the Experimental Science Distinct from the Philosophy of Nature?", from The Writings of Charles DeKoninck, transl. and comp. by Ralph McInerny, Notre Dame, 2008, p. 453