More about non-men

Anthony has asked for some more about indefinite (or 'infinite') negation.  Well he will have to wait for our book to come out (working title: Time and Existence: Duns Scotus' Questions on the Perihermenias) if he wants much more. Opus II Book I Q4 ("Does an Indefinite Name Posit Something") and Opus II Book II Q2 (Does ‘This Is Not Just; Therefore, This Is Non-Just’ Follow?) refer. Until that happy day, here is Thomas Aquinas on the same subject, in his commmentary on the Perihermenias, Book II lecture 2:

Latin	English*
Sicut ipse dicit,enunciatio aliqua virtute se habet ad illud, de quo totum id quod in enunciatione significatur vere praedicari potest: sicut haec enunciatio, homo est iustus, se habet ad omnia illa, de quorum quolibet vere potest dici quod est homo iustus; et similiter haec enunciatio, homo non est iustus, se habet ad omnia illa, de quorum quolibet vere dici potest quod non est homo iustus.	It must be noted that, as Aristotle himself says, the enunciation, by some power, is related to that of which the whole of what is signified in the enunciation can be truly predicated. The enunciation, "Man is just,” for example, is related to all those of which in any way "is a just man” can be truly said.So, too, the enunciation "Man is not just” is related to all those of which in any way "is not a just man” can be truly said.
Secundum ergo hunc modum loquendi, manifestum est quod simplex negativa in plus est quam affirmativa infinita, quae ei correspondet. Nam, quod sit homo non iustus, vere potest dici de quolibet homine, qui non habet habitum iustitiae; sed quod non sit homo iustus, potest dici non solum de homine non habente habitum iustitiae, sed etiam de eo qui penitus non est homo: haec enim est vera, lignum non est homo iustus; tamen haec est falsa, lignum est homo non iustus.	According to this mode of speaking it is evident, then, that the simple negative is wider than the infinite affirmative which corresponds to it. Thus, "is a non-just man” can truly be said of any man who does not have the habit of justice; but "is not a just man” can be said not only of a man not having the habit of justice, but also of what is not a man at all. For example, it is true to say "Wood is not a just man,” but false to say, "Wood is a non-just man.”
Et ita negativa simplex est in plus quam affirmativa infinita; sicut etiam animal est in plus quam homo, quia de pluribus verificatur. Simili etiam ratione, negativa simplex est in plus quam affirmativa privativa: quia de eo quod non est homo non potest dici quod sit homo iniustus. Sed affirmativa infinita est in plus quam affirmativa privativa: potest enim dici de puero et de quocumque homine nondum habente habitum virtutis aut vitii quod sit homo non iustus, non tamen de aliquo eorum vere dici potest quod sit homo iniustus.	The simple negative, then, is wider than the infinite affirmative-just as animal is wider than man, since it is verified of more. For a similar reason the simple negative is wider than the privative affirmative, for "is an unjust man” cannot be said of what is not man. But the infinite affirmative is wider than the private affirmative, for "is a non-just man” can be truly said of a boy or of any man not yet having a habit of virtue or vice, but "is an unjust man” cannot.
Affirmativa vero simplex in minus est quam negativa infinita: quia quod non sit homo non iustus potest dici non solum de homine iusto, sed etiam de eo quod penitus non est homo. Similiter etiam negativa privativa in plus est quam negativa infinita. Nam, quod non sit homo iniustus, potest dici non solum de homine habente habitum iustitiae, sed de eo quod penitus non est homo, de quorum quolibet potest dici quod non sit homo non iustus: sed ulterius potest dici de omnibus hominibus, qui nec habent habitum iustitiae neque habent habitum iniustitiae.	And the simple affirmative is narrower than the infinite negative, for "is not a non-just man” can be said not only of a just man, but also of what is not man at all. Similarly, the privative negative is wider than the infinite negative. For "is not an unjust man” can be said not only of a man having the habit of justice and of what is not man at all—of which "is not a non-just man” can be said—but over and beyond this can be said about all men who neither have the habit of justice nor the habit of injustice.

Note that 'man is just' etc is better translated as 'a [or the] man is just'.  According to Aristotle and the scholastics, the apparently negative 'is non-just' is really something positive or affirmative said about anyone who has a determinate nature such as a man or an animal.  Thus is not as wide as definite negation, because not being a just man can apply to anything you like, so long as it is not just, or is not a man.

That's not to say the matter is any clearer, really.

*Translated by Jean T. Oesterle Milwaukee: Marquette University Press, 1962

De re and de dicto

Tristan Haze recommended this 1977 paper by Kripke which I am working through. He mentions the de re / de dicto distinction on page 258, and once again I am struck by the way that so much of our terminology and ideas are inherited from medieval Latin philosophy and logic.  I discussed this before with respect to a priori.

The de re / de dicto distinction is mentioned in a passage here from Thomas's Summa Theologiae, which I quote here using the Dominican translation.

Latin

English

Unde et haec propositio, omne scitum a Deo necessarium est esse, consuevit distingui. Quia potest esse de re, vel de dicto. Si intelligatur de re, est divisa et falsa, et est sensus, omnis res quam Deus scit, est necessaria. Vel potest intelligi de dicto, et sic est composita et vera; et est sensus, hoc dictum, scitum a Deo esse, est necessarium.

Hence also this proposition, "Everything known by God must necessarily be," is usually distinguished; for this may refer to the thing, or to the saying. If it refers to the thing, it is divided and false; for the sense is, "Everything which God knows is necessary." If understood of the saying, it is composite and true; for the sense is, "This proposition, 'that which is known by God is' is necessary."

I am not sure about the translation. 'De re' is rendered as 'about the thing', and 'de dicto' as 'about the saying.  Correct-ish, but we have the difficulty of translating a Latin term which is probably being used in a technical sense.   He uses the verb consuevit which means 'is usually' or 'is customarily', which suggests that the terminology was established when he was writing in the 1270s.  It certainly was - the distinction is mentioned at the end of this very technical discussion probably written in Paris around the same time (Aquinas taught in Paris in the 1260s).  Even Abelard, writing in the 12th century, mentions it. A dictum - literally 'what is said' - of a proposition is what is said or asserted by the proposition.  In Latin it is expressed by the accusative-infinitive form, e.g.. Socratem currere which means 'that Socrates runs' or 'Socrates's running'.  A de dicto proposition is thus one which has a dictum as subject.  For example, in Socratem currere est verum (it is true that Socrates is running) the subject is Socratem currere, which is the dictum (or refers to it, medieval texts frequently conflate use and mention), and the predicate is verum.  See Catarina's interesting paper here.

When Thomas talks about the composite and divided sense, he almost certainly means what Ockham is talking about here.  (Not yet available with English translation, however).  Ockham's point throughout the Summa is that the dici de omni pretty much always applies to propositions understood de re, and so Frege's puzzle does not apply in such a sense.  In propositions understood de dicto, there are nearly always problems with substitution.  His ideas about this are mostly in Part III-1 of the Summa, none of which is available in English online, and indeed very little of which is available offline. It is a philosophical scandal that the works of one of England's greatest philosophers are not available in the language of his own country. (For much of his life William would have spoken as well as written in Latin, but the language of ordinary people was a form of middle English similar to the English of Chaucer which would still be intelligible to us modern folks).

Book VII of the Metaphysics

The big one: Thomas' commentary on Book VII of Aristotle's Metaphysics. As with all the commentaries here, it is closely linked to Aristotle's text. In this case, William of Moerbeck's Latin translation from the Greek, in parallel with Ross's English translation from the Greek. The text also includes links to Averroes' commentary on the Metaphysics, in the Latin that translated from the Arabic (from an edition published in Venice in 1562), also links to a 14th century manuscript of William's translation.

Book VII is at the heart of the Metaphysics. It is very difficult to understand. Thomas's commentary is usually very clear, and helps a bit.

Aristotle's Physics (Logic Museum)

Just out. A version of Aristotle' Physics in the Logic Museum. Fully indexed with Bekker numbers and other references so that (unlike other versions on the web) you can take a reference from some other source and locate it exactly. Accompanying it is Thomas Aquinas' commentary, fully linked to Aristotle's text.

The Physics includes many of Aristotle's most famous claims, some of them now discredited, such as that

• the void (Latin: vacuum) does not exist.
• motion in a void is impossible.
• there are four types of cause.
• nature has a purpose.
• there is no actual infinite.
• the world has existed from eternity.
• the continued motion of projectiles is caused by the surrounding medium.
• a body in moving in a void would continue moving if externally unimpeded.
• bodies of different weights fall at different speeds.

Aquinas on Aristotle's Posterior Analytics

Just out in the Logic Museum. Thomas's very accessible and highly recommended commentary on Aristotle's Posterior Analytics.

Aquinas on the Metaphysics - books V and VI

Book V and Book VI of Thomas's commentary on the Metaphysics just out in the Logic Museum. Let me remind you again of the hyperlinkish wonder of the Web. I have nearly completed a translation of one of Burley's questions on the Perihermenias (which will itself shortly end up in the Museum). He says (though I don't claim fully to understand this)

[...] certain persons say that being is not the essence of a thing, but
nonetheless proceeds from the essential principles of a thing of which it is the
being, and is in the same genus by reduction with the thing of which it is the
being, just as motion is of the same genus by reduction with a finishing point.
Therefore the being of a substance is a single actuality in the genus of
substance by reduction, and is neither substance nor accident. And Thomas and
Giles hold this opinion.

The footnote in Stephen Brown's edition, (Fran. Stud. 34 (1974) 200-295) refers us to Thomas commentary on book IV, IV, lect. 2 n. 558. In the old days you would have to look for some old book, probably in some university library. Now you can just follow the link. And it doesn't end there, because the commentary is linked right back to Aristotle's text.

What Thomas says is as follows. As I said, I don't claim to understand it fully.

Latin

English

Sed in primo quidem non videtur dixisse recte. Esse enim rei quamvis sit aliud ab eius essentia, non tamen est intelligendum quod sit aliquod superadditum ad modum accidentis, sed quasi constituitur per principia essentiae. Et ideo hoc nomen ens quod imponitur ab ipso esse, significat idem cum nomine quod imponitur ab ipsa essentia.

558. But in regard to the first point he does not seem to be right; for even though a thing’s existence is other than its essence, it should not be understood to be something added to its essence after the manner of an accident, but something established, as it were, by the principles of the essence. Hence the term being, which is applied to a thing by reason of its very existence, designates the same thing as the term which is applied to it by reason of its essence.

Faith, understanding and apostasy

The second of the second part of Summa Theologiae now available in the Logic Museum. Questions 1-7 on the object of faith; the virtue of faith; the cause and effects of faith; questions 8 and 9 on understanding and knowledge, and questions on unbelief, heresy, apostasy and blasphemy.

Aquinas on the Perihermenias

Just out, Thomas Aquinas' commentary on Aristotle's Perihermenias (also known as De Intepretatione). the commentary was probably written between 1269 and 1271, following his other 'Aristotelian' commentaries such as on the Posterior Analytics and on the Metaphysics. There are some notes on the Perihermenias, together with links to other commentaries (including this one) here.

I see Charles Freeman has just commented on an earlier post - welcome Charles. There were dozens, if not hundreds of medieval commentaries on this logical work by Aristotle. Many of them were written before the thirteenth century - Abelard's being the most notable of those.

Demonstration of the reason why

This month I am struggling with Aristotle's Posterior Analytics. It gives Aristotle's account of demonstration, especially scientific demonstration. There is a nice illustration in Book I chapter 13 of the difference between what the scholastics called propter quid and quia demonstration. Demonstration propter quid (which Muir translates as 'demonstration of the reasoned fact' is when syllogistic reasoning shows us the reason why something happens. For example (ignoring Aristotle's actual science* for sake of argument).

Propter quid
Near things do not twinkle
Planets are near
Planets do not twinkle

The reasoning is from cause (nearness) to effect (not twinkling). With demonstration quia, on the other and, we reason from effect to cause, as follows.

Quia
Things that do not twinkle are near
Planets do not twinkle
Planets are near

Here, you have demonstrated a fact by reasoning from effect to cause. Of course pretty much all demonstration in the natural sciences is of this sort. The medieval Aristotelians were perfectly aware of this.

Sometimes that which is more known in reference to us is not more known
absolutely, as happens in natural sciences where the essences and powers of
things are hidden, because they are in matter, but are disclosed to us through
the things which appear outwardly. Hence in these sciences the demonstrations
are for the most part made through effects which are better known in reference
to us but not absolutely. (Lectures on the Posterior Analytics, Book I lecture
5).

* On the actual science, I found this helpful. If this is correct, the propter quid syllogism should be as follows:

Objects sufficiently large that they have non-zero apparent diameter when viewed from the Earth do not twinkle
Planets [or nebulas] have non-zero apparent diameter when viewed from the Earth
Planets [or nebulas] do not twinkle

Aristotle on the history of philosophy

New in the Logic Museum: the commentary on the first boook of Aristotle's Metaphysics. It includes a comprehensive set of links to Ross's (English) text of the same book here. Aquinas' commentary is always clear and is still a good introduction to Aristotle, whose writing is terse and obscure. Once Google has the text indexed, you will also be able to search it using the Museum's Latin site searcher.

By coincidence, there was a Horizon programme on British television last night: What Happened Before the Big Bang? I was struck by the resemble to Aristotle, in many ways. They say "They are the biggest questions that science can possibly ask: where did everything in our universe come from? How did it all begin?" Aristotle says "For it is owing to their wonder that men both now begin and at first began to philosophize; they wondered originally at the obvious difficulties, then advanced little by little and stated difficulties about the greater matters, e.g. about the phenomena of the moon and those of the sun and of the stars, and about the genesis of the universe. " The scientists in the program presented a bewildering variety of theories about what may have happened before the Big Bang. Aristotle refers to a bewildering variety of theories proposed by different pre-Socratic philosophers about the origin and fundamental causes of the universe. The scientists were divided between material accounts of the universe, and purely mathematical-theoretical ones. The pre-Socratics included those who thought matter was the fundamental principle of being, as well as those (the Pythagoreans) who thought that number explained everything. Many of the modern scientific ideas were pretty strange (the scientists interviewed included Roger Penrose, author of the idiotic The Emperors New Mind). Practically all the ancient Greek ideas were equally daft. Thales thought the world was made of water. Hesiod thought the basic principles were love and strife.

So nothing has changed. In particular, no one seems to have an answer, which is depressing, but then still we have that sense of wonder, which is good. More on Book I later.

Aquinas in the Logic Museum: IIa 49-70

10 October 2010. Questions 49-70 of the first part of the second book of Summa Theologiae. Concerning habits in general, their causes and effects; the virtues - intellectual, moral, cardinal and theological; the gifts, beatitudes and blessings of the Holy Ghost.

Aquinas on the passions

Now available in the Logic Museum. Thomas explores and analyses the phenomena of love and hatred, concupiscience and delight, pain and sorrow, fear and daring, and anger.

What did Aquinas know about Islam?

An interesting page here. What did Thomas know about Islam? There are two specific references in his works. One at the beginning of Summa contra gentiles, written for Dominicans who were going to preach in Muslim territories, the other, De rationibus fidei contra Saracenos, Graecos et Armenos ad Cantorem Antiochenum*, where Thomas considers the main objections which Muslims make to the Catholic Faith, such as the possibility of the Trinity and of the Incarnation, the wisdom of the Crucifixion and human liberty before divine predestination.

There are some interesting summaries of which Islamic philosophers and which of their works are mentioned by Thomas, and which of their works he appears not to have known.

See also Joseph Kenny's website here. Many translations of Aquinas.

*Now in parallel Latin-English at the Logic Museum.

Aquinas in the Logic Museum

29 September 2010. Questions 1-21 of the first part of the second book of Summa Theologiae. Index page here. This is part of a continuing project to take the whole work (three books) into a parallel Latin-English version (the only one on the web). There is now full indexing on the questions for Book II. For example, if you want to link to q. 19 a. 8 arg. 1, use the link as follows: authors/aquinas/summa/Summa-IIa-18-21.htm#q19a8arg1. More to come.