Aristotle on singular terms

According to Fred Sommers (The Logic of Natural Language, chapter 3) in traditional formal logic (TFL) as opposed to modern predicate logic (MPL), indefinite noun phrases do refer. “The distinctions crucial to MPL between subject expressions like ‘Socrates’ and ‘denoting phrases’ like ‘a senator’ are not crucial in TFL” (p.51).

Where he gets this idea I don’t know. The scholastic logicians followed Aristotle, and Aristotle says (Peri hermenias 17a38) ‘λέγω δὲ καθόλου μὲν ὃ ἐπὶ πλειόνων πέφυκε κατηγορεῖσθαι, καθ’ ἕκαστον δὲ ὃ μή’. ‘By universal I mean what is by nature disposed (πέφυκε) to be predicated of many, by singular what is not [thus disposed]’. He gives the example of ‘man’ as universal, and the proper name ‘Callias’ as singular. The Greek terms καθόλου and ἕκαστον were translated by the Latins as universale and singulare respectively, from which we get the corresponding Latin-English terms. Note the ‘by nature disposed’ bit – Greek πέφυκε, Latin natum est. I.e. it’s in the very nature of a common term like ‘man’ to be predicable of more than one individual. But this is not true of a genuinely singular term, i.e. its nature is such as to be predicable only of one.

Aristotle also says (Metaphysics 1040a28) that we cannot define singular terms, and that we should not be deceived by the fact that some individual objects have attributes that are unique, like ‘going round the earth’ (= the sun according to his geocentric theory). He points out that more than one thing could go round the earth, or none, so the definite description doesn’t really define ‘sun’ (ἥλιος). ‘But the sun was supposed to be an individual (ἕκαστα), like Cleon or Socrates’. So the ‘nature’ of a genuinely singular term is not just to be predicable of one thing alone, like a uniquely applying description, but to be predicable of that thing in virtue of its very meaning. Is Aristotle anticipating Kripke’s doctrine of the rigidity of reference?

Geach has a challenging objection to this. Suppose I say, referring to a meeting I attended ‘a man was shouting’. And suppose the indefinite noun phrase ‘a man’ refers to, i.e. picks out or identifies some man in the crowd, say Frank, or aims to do so. But suppose Frank wasn’t shouting, but Richard was. Then ‘a man was shouting’ is true, because Richard was shouting. Yet I meant to refer to Frank. I meant to say something which is actually false, but which is true because some other person than I meant satisfied the predicate.

The whole point of indefinite noun phrases is not to refer, at least if to refer means to identify or pick out, to tell you which individual I have in mind. In that sense, ‘a man was shouting’ doesn’t tell you which person you have in mind. It is true just so long as at least one man – it absolutely doesn’t matter which – was shouting. This contrasts with definite terms, which are true only when the person identified satisfies the predication.

I hold that all singular ‘reference’, i.e. telling the audience which individual is said to satisfy the predicate, is intralinguistic, and that there are chains of back-reference which originate in some indefinite noun phrase, e.g. ‘a certain young man’. This originating phrase does not refer in the sense that it ‘tells us which’. Clearly it can be satisfied, i.e. true of some man. But it doesn’t tell us which man it was. For example, some have thought that the man in Mark 14:51 was Mark himself, i.e. the author of the gospel. After all, all the other disciples had fled, so who knew about the man in the linen cloth, apart from the author himself? On the other hand, there were other witnesses present, and the story might have been passed around until Mark heard it, who put it in his account.

Points and indivisibles

Following my post yesterday, William has updated his post. He writes

So if you're A[ristotle], then given a line segment between two points, you can keep cutting it and keep finding points, none of with (of course) touch. And in your mind, therefore, you have a series of line segments separated by points. What you can't do is consider all possible cuts, because that kind of realised infinity is foreign to his way of thinking.

In which case, the final step is to go back and say, given that definition / idea, is his original proof valid? I think that, given that, his original result is valid, but vacuously so: he refuses to consider completed infinities, and a line, to be made of points, needs an infinite number of points, which he has ruled out, therefore a line isn't made of an infinite number of points. But only because of his artifical restriction on the meaning of infinity.

I think the idea of points 'appearing' when you divide the continuous is foreign to Aristotle's intention (at least at Physics 231a21). Rather, you divide the continuous and you get more continuous, period. You don't 'find' any points after a finite number of division, for the 'points' could only appear when the process of division is complete, which (for Aristotle) can never happen.

Remember that Aristotle doesn't talk about 'points'. He talks about the 'indivisible'. You start with the idea of a continuous thing as something which when divided gives two continuous things. It follows logically from this that the continuous is not indivisible, since it is part of of its definition that it can always be divided. It also follows that no finite process of division will yield anything that cannot be divided further.

If we then define 'composed of' as the relation between the continuous and any set of parts that result from any process of division, it follows that the continuous is composed solely of parts which are continuous when the process is finite. I.e. no points, no 'indivisibles' at all. Just many bits of continuous. Now add the assumption, which Aristotle thinks is impossible, that the process of division can be completed, and by definition (a) the process cannot be finite, from our original definition (b) what is left over will be indivisible, otherwise the process would not be complete and (c) the original continuous thing will be 'composed' of these indivisible thingies, from our definition of 'composed'.

That is, it’s not that the points start appearing as soon as you start splitting the marble. Rather, you only get more bits of marble. But if you keep bashing away hard enough so as to get millions of tiny grains of marble, a heap of fine sand, you can visualise where the process is heading – do this infinitely many times and those little grainy atoms as it were turn into real atom which cannot be further subdivided. Then, and only then, do the points appear. For points are indivisible.

On William's claim that Aristotle has an 'artifical restriction on the meaning of infinity' that's completely wrong. Aristotle understands the same as we do: an infinite process is one that cannot be completed in a finite number of steps. But he also holds that such a process cannot be completed at all, because it is infinite.

Connolley on the continuum

Bill Connolley has post at Stoat about Aristotle and the continuum, and I think I finally see what his problem is.  (and it's also my problem). Is Aristotle's notion of the continuum roughly congruous with the modern notion, and did Aristotle simply get it wrong? In which case, how on earth could he have got it so wrong?

.. the problem I'm having now is to see how his argument can ever have been believed, by him or by anyone else

Or was Aristotle's notion something quite different, such that his view that 'it' is not composed of indivisibles is perfectly consistent. In which case,  what on earth was his notion?

I think I see a way out (noting carefully that I am not a mathematician, and this is just my two cents).  Connolley starts with the idea that the continuum is just the real numbers between two points (say 0 and 1).  If that's what the continuum is, i.e. if it is just those numbers, then it's surreal to ask whether it is composed solely of indivisibles, i.e. composed of numbers. If that's how you define it, it's an absurd question. And even more absurd to argue that is isn't composed of numbers at all. That would be like concluding that bachelors are married men.

But we don't have to start with that idea at all. Suppose we characterise what-is-continuous as that which is divisible into parts, and which after any finite number of such divisions leaves parts which are continuous themselves.  Then it is an open question whether such divisibility could be completed or not.  Clearly there would have to be an infinite number of such divisions, since by definition any finite division leaves continuous parts which can be further subdivided. And if that were possible, i.e. if it were possible to complete the process, then by definition of 'complete', what was left over would be indivisible.

So perhaps it is coherent to hold that  Aristotle agrees with the moderns in a defining characteristic of the continuum (i.e. infinite divisibility into parts), but disagrees over the accidental property of whether the process of divisibility can be completed.  And disagrees, of course, that it is an accidental property at all, for he holds that the impossibility of completion can be proved by logical means, and is thus an essential property.

Aristotle against the continuum - reply

Our earlier discussion of Aristotle's argument that the continuum is not composed solely of points ('indivisibles') neatly illustrated an important philosophical principle: that the only adequate reply to a philosophical argument is to show what is wrong with it. It is no good simply saying that the conclusion is false. Nor claiming that some respected authority says it is false. Nor even stating an arguments against it (which simply shows that there are two arguments with conflicting conclusions). No: the only suitable way is to show what is wrong with the argument. And there are only two ways of doing that: either show that the argument is not valid, i.e. that the premisses can be true with the conclusion false. Or show that the argument is not sound, i.e. one or more of the premisses is false.

Now Aristotle's argument is this.

(1) If a continuum is composed solely of points, these points must be either continuous with one another, or touch, or be in succession.

(2) The points are not continuous

(3) They do not touch

(4) They are not in succession

(5) Therefore the continuum is not composed solely of points.

Clearly the argument is valid. If the four premises are true, the conclusion cannot be false. For the consequent of the implication in (1) is a disjunction. A disjunction is false when all of the disjuncts are false. Premisses (2)-(4) assert the falsity of each of the disjuncts, so if they are true, the consequent is false. If the consequent is false (and if the implication is good) the antecedent is false – consequens falsum ergo antecedens. And if the antecedent is false, the conclusion is true, for the conclusion is the opposite of the antecedent. Therefore the argument is valid.

Is the argument sound? I don't see anything wrong with premises (2)-(4), given the definitions that Aristotle supplies in the text, i.e. the definitions of continuity, contact, succession etc. (A common problem with replies to philosophical arguments is that they ignore careful definitions given in the preliminaries, and focus on something else). So the culprit is clearly (1), as is obvious after a little thought. Take any two points on the continuum you like. Then it does not have to be true that they are either 'in contact', or 'continuous' or 'in succession'. Of any two different points, it can – and indeed always is - true that there are further points in between them.

Why is the argument convincing at all? Probably because it has the appearance of rigour, and because it starts with the covert and natural assumption that each point has a successor. If it has a successor, then there can't be a point in between them (otherwise the point between would be the successor). But there must be something else in between, something that is not a point, and therefore the continuum can't consist wholly of points. But only if there is a successor, which is not necessarily true.

So Aristotle's argument is flawed. But not because Cantor was right, nor because modern mathematics is better, or clearer, or because mathematics is different from the real world (whatever the real world is). It is flawed because it has a flaw, a flaw which we can clearly demonstrate. That is where we philosophers are coming from.

Aristotle against the continuum

Belette ponders how we could show how Aristotle's argument that the continuum can't be composed of indivisibles is wrong. For reference, the argument is in Physics book 6 at 231 a2. Thomas Aquinas' discussion of it is in his lectures on Physics 6, lecture 1 n2.

Aristotle says that two thing are 'continuous' if their extremities are one, 'in contact' if the extremities are together, and 'in succession' if there is nothing of their own kind in between them. An 'indivisible' is that which has no parts.

Thus a continuum cannot be composed of indivisibles. For such indivisibles are either continuous, or in contact, or in succession. Not continuous, for no point can have separate extremities. Not in contact, for one thing can be in contact with another only if whole is in contact with whole or part with part or part with whole. But since indivisibles have no parts, they must be in contact with one another as whole with whole. And if they are in contact with one another as whole with whole, they will not be continuous: for what is continuous has distinct parts: and these parts into which it is divisible are spatially separate. Not in succession, for things are in succession if there is nothing of their own kind intermediate between them. But there is always a line between two points. And (supplementing his argument) a line is either composed of points, in which case the points are not in succession, by definition, or it is not, in which case the continuum is not composed of indivisibles alone.

What is wrong with the argument?

How often does the moon rotate around the earth?

Connolley makes a curious objection here to my claim that the moon rotates around the earth once a day. What is wrong with that? Doesn’t it? From the beach on holiday this effect was clearly visible. I concede that it does not do this exactly once a day. But simplification is a virtue, as Connolley himself shows when he refers to ‘two tides a day’ (actually there are two tides every 24h and 50 minutes).  So what, broadly speaking, is wrong with my claim?

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.

Reply to Freeman

Charles Freeman has commented on my last post in a way that misunderstands my point so fundamentally that it probably needs stating again, more clearly. It was as follows.

1. Many of Aristotle's scientific explanations are obviously wrong.

2. On the assumption that Greek science ended in the 4th century, Greek science had about 700 years to correct these obvious errors. But it didn't (in the sense that it did not arrive at a consensus of where Aristotle was wrong).

The first point is not simply that Aristotle was wrong. It was that he was obviously wrong. For example, he states in De Caelo (tr. Guthrie, Cambridge 1960 pp. 49-51) that if a weight falls a certain distance in a given time, a greater weight will move faster, with a speed proportional to its weight. This is obviously wrong: obvious in a way that his statement about why glass is transparent is not obviously wrong. To refute his theory about glass requires instrumentation and a complex atomic theory, neither of which was available to Aristotle. So while his transparency theory is wrong, it was not obviously wrong. But to refute his theory about falling bodies requires only a few simple experiments. In the 6th century A.D., loannes Philoponus challenged this as follows.

But this [i.e. Aristotle's theory] is completely erroneous, and our view may be
corroborated by actual observation more effectively than by any sort of verbal
argument. For if you let fall from the same height two weights of which one is
many times as heavy as the other, you will see that the ratio of the times
required for the motion does not depend on the ratio of the weights, but that
the difference in time is a very small one." [M. R. Cohen and I. E. Drabkin, "A
Source Book in Greek Science" (McGraw Hill. N.Y.) 220 (1948) - my emphasis].

So my first point stands: some of Aristotle's scientific observations are obviously wrong, in a way that the technology and understanding of the time could easily have shown. On my second point, that Greek science did not correct these obvious mistakes, the history shows that clearly enough. You may object that Philoponus was Greek, and that he spotted at least one obvious error. I reply: Philoponus' observation does not amount to a scientific consensus. We make progress in science when we arrive at a view that is not necessarily correct, but which is accepted by a majority, or a significant majority, of the scientific community. This was not properly achieved until Galileo. And note also that Philoponus was writing somewhat later than Freeman's 'cutoff point' of 381 AD. Moreover, he was a Christian thinker.

The problem of Aristotle

I have just noticed The Closing of the Western Mind by Charles Freeman. The thesis is that after Constantine declared Christianity the state religion in 312, the church successfully quashed any challenges to its religious and political authority, in particular any challenges arising from the tradition of Greek rationalism and (in effect) held up human development for a thousand years until the Renaissance.

The difficulty with any such view is that it must face up to the 'problem of Aristotle'. If there really was a 'spirit of Greek rationalism', why did Greek science and philosophy apparently not advance much beyond Aristotle, writing in the fourth century BC, and Constantine in 312 (that's about 700 years)? And if Christian dogma was really that stifling, how was it that Western science developed from the rediscovery of Aristotle's work at the end of the 12th century to the scientific revolution in the 17th century (that's about 500 years)?

It is particularly difficult to explain given that (as I noted here, and as everyone knows) Aristotelian science is so spectularly wrong. Nearly all his scientific views are false, indeed spectacularly and obviously false, and in a way that the simplest experiment would confirm. How did the Greeks did not notice this? As Hannam notes (God's Philosophers chapter 11), simple observation of the trajectory of an arrow or of a ball thrown through the air, noted by Albert of Saxony as early as the 14th century, would have refuted a considerable part of Aristotle's physics.

Why and how was it that the medieval West eventually progressed well beyond Aristotle's science, when Greek culture did not? Constantine's state religion seems completely irrelevant.

Why light passes through glass

The Longeway book arrived very quickly (2 days) and is a credit to Amazon . Compare this with Waterstone's, who had no copy in any of their London shops, and who said that ordering may take weeks or months, or with the university libraries in London (only UCL library had a copy, but this horribly-designed and uncomfortable building is to be visited only as a last resort).

There is much to say about the book. The introduction is long and as interesting as the reviews suggest. One example, illustrating Longeway's attention to detail, is the way he notices the interesting passage by Aristotle at 88a11. This is in some ways more interesting than the later and better known passage about the lunar eclipse beginning at 89b26. In the case of the eclipse it is theoretically possible for us directly to observe to cause of the eclipse (namely, as he says at 90a24, if we were living on the moon). In the case the transparency of glass, by contrast, it is theoretically impossible for us to observe directly the passage of light through the 'pores' in glass. The passage is also interesting for the insight that some ancient Greek scientists thought that the transparency of glass could be explained through some atomic or molecular theory.

On why glass actually is transparent, see this elementary explanation. It is intended for children, although I didn't follow it that well. It says the reason is that the molecules in liquids are disorganised and random, and so light can pass through them. It cannot pass through solids, because the arrangement of molecules is ordered (I didn't follow this reasoning). Light passes through all liquids, glass is a liquid, therefore light can pass through glass (I did follow this, however).

Note we can express the second reasoning in both Aristotelian propter quid and quia forms, as follows.

Propter quid
Light passes through liquids
Glass is a liquid
Therefore, light passes through glass

Quia
Light only passes through liquids
Light passes through glass
Therefore glass is a liquid

My earlier observations apply here as well. Both syllogisms are essentially trivial and hardly count as 'reasoning' at all. The real reasoning involves how we arrive at the (superficially implausible) premiss that glass is a liquid.

A priori and propter quid

In chapter 17 of Book III part 2 of Summa Logicae, Ockham gives a neat explanation of the terms propter quid and quia that shows how they are close, or even equivalent to the terms a priori and a posteriori respectively. I discussed this earlier. The translation is mine. (Sadly, I failed to get John Longeway's translation from our local Waterstone's, or indeed any Waterstones in the country, and had to resort to Amazon).

Separately, I am working on a translation of Buridans Questions on the Posterior Analytics. The translation of 'scire' is tricky, as both Ockham and Buridan use it with 'notare'. Both mean a sort of knowing. As they use it (and define it) 'scire' means a sort of reasoned knowing, the thing you get from understanding a demonstration, or 'syllogism that produces knowing'. Thus scientia, from which we get the English word 'science'. The modern and the medieval Latin meaning are closely connected. Understanding how they are different is a difficult matter that needs teasing out.

Latin	English
Propter quod oportet scire quod quaedam est demonstratio cuius praemissae sunt simpliciter priores conclusione, et illa vocatur demonstratio a priori sive propter quid.	On account of this we must know [scire] that one sort of demonstration whose premisses are absolutely prior to the conclusion, and this is called demonstration a priori or propter quid.
Quaedam est demonstratio cuius praemissae non sunt simpliciter priores conclusione, sunt tamen notiores sic syllogizanti, per quas devenit sic syllogizans in notitiam conclusionis, et talis demonstratio vocatur demonstratio quia sive a posteriori.	Another sort is demonstration whose premisses are not absolutely prior to the conclusion, and which are nevertheless better known to the syllogiser in this way, through which the syllogiser thus arrives at knowledge of the conclusion. And such demonstration is called demonstration quia or a posteriori.

Logic and scientific reasoning

This is a follow-on from my earlier post about whether Aristotle's account of scientific reasoning truly captures what scientific reasoning is. He describes two forms: propter quid where we reason from cause to effect, and quia, where we reason from effect to cause.

Propter quid
Being an A is the cause of anything being a B
This X is an A
This X is a B

Quia
Being an A is the only cause of anything being a B
This X is a B
This X is an A

Neither of these captures the process of geniune scientific reasoning or discovery. In propter quid, the major premiss cannot be known unless the causal connection 'A causes B' has already been established. Since proof of the causal connection is the end-product of scientific reasoning and methodology, rather than the beginning, Aristotle's syllogism captures nothing useful. The same objection applies to the quia form, with the additional objection that the 'only' qualification cannot be established with any certainty at all. Scientific reasoning involves constructing a model of reality that explains the observed effects. It is difficult to establish that such a model is the only one. Ptolemy's model of the solar system (where the earth is at the centre) explained the observations available to ancient scientists. Copernicus' model (sun at the centre, circular orbits) explains the same observations, but in a different way. Kepler's model (sun at the centre, elliptical orbits) is different again. Further changes and refinements to this model continued into the twentieth century. It is difficult to prove that any model is the only explanation of the observed effects.

And in any case, how could such a simple syllogism as Aristotle's capture the essence of what is essentially a complex reasoning process that could take many forms?

See also Thomas Reid on the utility of logic.

"The art of syllogism produced numberless disputes, and numberless sects who
fought against each other with much animosity, without gaining or losing ground,
but did nothing considerable for the benefit of human life. The art of
induction, first delineated by Lord Bacon, produced numberless laboratories and
observatories, in which nature has been put to the question by thousands of
experiments, and forced to confess many of her secrets that before were hid from
mortals: and, by these, arts have been improved, and human knowledge wonderfully
increased.

"In reasoning by syllogism from general principles, we descend to
a conclusion virtually contained in them. The process of induction is more
arduous, being an ascent from particular premises to a general conclusion. The
evidence of such general conclusions is probable only, not demonstrative: but
when the induction is sufficiently copious and carried on according to the rules
of art, it forces conviction no less than demonstration itself does."

On whether 'induction' is any improvement on Aristotelian 'deduction', more later.

Scientific reasoning

At the end of Posterior Analytics, book I, Aristotle gives some examples of scientific reasoning.

Quick wit is a faculty of hitting upon the middle term instantaneously. It would
be exemplified by a man who saw that the moon has her bright side always turned
towards the sun, and quickly grasped the cause of this, namely that she borrows
her light from him; or observed somebody in conversation with a man of wealth
and divined that he was borrowing money, or that the friendship of these people
sprang from a common enmity. In all these instances he has seen the major and
minor terms and then grasped the causes, the middle terms. Let A represent
‘bright side turned sunward’, B ‘lighted from the sun’, C the moon. Then B,
‘lighted from the sun’ is predicable of C, the moon, and A, ‘having her bright
side towards the source of her light’, is predicable of B. So A is predicable of
C through B. (Posterior Analytics I.34 89b 10)

The syllogism that Aristotle gives right at the end is demonstration propter quid, reasoning from cause to effect.

The moon is lit by the sun
Things lit by the sun have their bright side turned towards the sun
The moon has her bright side turned towards the sun

But the reasoning process he describes is demonstration 'quia', reasoning from effect to cause. The man sees that the the moon has her bright side always turned towards the sun, and reasons from this effect to the cause of it, namely sunlight.

The moon has her bright side turned towards the sun
Things that have their bright side turned towards the sun are lit by the sun
The moon is lit by the sun

Are either of these illustrative of scientific reasoning itself? Surely not. Whoever has grasped the truth of the minor premiss or 'middle' has already grasped why the effect follows from the cause. The 'reasoning' described by Aristotle does not describe the thought-process that solves the scientific puzzle. What is the thought process that leads to the discovery of the middle? Aristotle merely says it is 'quick wit'.

There are some examples of scientific reasoning here. Unfortunately these do not describe how individuals such as Archimedes or Galileo or Newton actually hit upon the ideas that led to their discoveries. In this paper the nineteenth century epidemiologist John Snow argues, using the case of a water pump Broad Street, Soho in 1854, that cholera must be transmitted by drinking water. He reasons that there was no particular outbreak or increase of cholera except among the people who were in the habit of drinking the water from the pump. Nearly all the deaths were within a close distance of the pump. People who lived close to the pump but did not use it (such as the employees of a local brewery who only drank ale). But the paper is a reasoning process intended to convince others - it does not necessarily represent the thought process that Snow went through in arriving at his discovery. There is an important distinction between proving something to yourself, and proving it to others.

Is there any common thought process that underlies scientific reasoning and scientific discovery?

Longeway on Ockham on science

There's a neat review here of John Longeway's translation of book III-II of Ockham's Summa Logicae*. I can't vouch for it, as I haven't got hold of the book itself (it is on the reading list), but it seems coherent and well-written (my first line of defence against nonsense on the Internet).

The book is an English translation of Ockham's commentary on Aristotle's Posterior Analytics, and includes an extensive commentary and a history of the intellectual background to Ockham's work. Longeway argues for Ockham's importance as the founder of empiricism in the West. According to the review:

... he avoided that error of Early Modern empiricism that now seems most
objectionable: the attempt to construct our public world from purely subjective
experience. Ockham is a direct realist, relying on the causal relation between
concept and object to establish the concept's reference. In his view, what makes
belief cognition is the right causal relation between the knower and what is
known, not the possession of a sufficient justification for one's belief.

Definitely worth acquiring. Unfortunately (and surprisingly) not yet in the Warburg Library, so we shall see if Waterstones can deliver.

* Demonstration and Scientific Knowledge in William of Ockham: A Translation of Summa Logicae III-II: De Syllogismo Demonstrativo, and Selections from the Prologue to the Ordinatio.

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

Andronicus of Rhodes

A remark by Boethius about Andronicus of Rhodes took me on a search for the man. As usual, Wikipedia came up. I was struck again, as so many times before, by Wikipedia's reliance on old out-of-copyright material mostly from the late nineteenth and early twentieth century, and by the ironic contrast between the advanced technology which led to the birth of the "Web 2.0" project, and the sort of material that ends in it - informative and interesting but essentially obsolete scholarship from more than a hundred years ago.

I have compiled a table below showing how the Wikipedia article on Andronicus was entirely plagiarised from two sources. Most of it is from William Smith's Dictionary of Greek and Roman Biography and Mythology, with the exception of two short passages taken verbatim from the 1911 Encyclopedia Britannica article about him (in bold). The only difference is the part at the end which was omitted from Wikipedia (presumably because too dull or serious).

There is now much better scholarship available about Andronicus. The Stanford Encyclopedia of Philosophy article is a good start. But the SEP project involves professional philosophers who are rewarded for their contribution by having their name against the article, and by the guarantee of protection against vandalism of the 'anyone can edit' sort. Interesting as the project is, I don't think we will ever see anything of real value from Wikipedia.

If Wikipedia is around in 100 years time, will the historical information in it still be 100 years out of date? But then which encyclopedias will it use? This was supposed to be the project that made traditional encyclopedias obsolete.

Smith	Wikipedia
ANDRONICUS of RHODES, a Peripatetic philosopher, who is reckoned as the tenth of Aristotle's successors,	Andronicus of Rhodes (fl c 60 BC) was a Greek philosopher from Rhodes who was also the eleventh scholarch of the Peripatetic school[Ammonius, In de Int 524]
was at the head of the Peripatetic school at Rome, about B C 53, and was the teacher of Boethus of Sidon, with whom Strabo studied (Strabxivpp 655,757; Ammon, in Aristot Categ P8, , a, ed Ald)	He was at the head of the Peripatetic school at Rome, about 58 BC, and was the teacher of Boethus of Sidon, with whom Strabo studied[ Strabo, xiv; Ammonius, in Aristot Categ]
We know little more of the life of Andronicus, but he is of special interest in the history of philosophy, from the statement of Plutarch (Sull, c 26), that he published a new edition of the works of Aristotle and Theophrastus, which formerly belonged to the library of Apellicon, and were brought to Rome by Sulla with the rest of Apellicon’s library in BC 84	We know little more of the life of Andronicus, but he is of special interest in the history of philosophy, from the statement of Plutarch,[ Plutarch, Sulla c 26] that he published a new edition of the works of Aristotle and Theophrastus, which formerly belonged to the library of Apellicon, and were brought to Rome by Sulla with the rest of Apellicon's library in 84 BC
Tyrannio commenced this task, but apparently did not do much towards it, (Comp Porphyry vit Plotin C24; Boethius ad Aristot de Interpret 292 ed Basil 1570) The arrangement which Andronicus made of Aristotle's writings seems to be the one which forms the basis of our present editions and we are probably indebted to him for the preservation of a large number of Aristotle's works	Tyrannion commenced this task, but apparently did not do much towards it [Comp Porphyry, Vit Plotin c 24; Boethius, ad Aristot de Interpret] The arrangement which Andronicus made of Aristotle's writings seems to be the one which forms the basis of our present editions and we are probably indebted to him for the preservation of a large number of Aristotle's works
Andronicus wrote a work upon Aristotle, the fifth book of which contained a complete list of the philosopher's writings, and he also wrote commentaries upon the Physics, Ethics, and Categories	Andronicus wrote a work upon Aristotle, the fifth book of which contained a complete list of the philosopher's writings, and he also wrote commentaries upon the Physics, Ethics, and Categories
None of these works is extant, for the paraphrase of the Nicomachean Ethics, which is ascribed to Andronicus of Rhodes, was written by someone else, and may have been the work of Andronicus Callistus of Thessalonica	None of these works is extant Two treatises are sometimes erroneously attributed to him, one On Emotions, the other a commentary on Aristotle's Ethics (really by Constantine Palaeocapa in the 16th century, or by John Callistus of Thessalonica)
, who was professor at Rome, Bologna, Florence, and Paris, in the latter half of the fifteenth century Andronicus Callistus was the author of the work Peri Pathon, which was also ascribed to Andronicus of Rhodes, The Peri Pathon was first published by Hoschel, Aug Vi del 1594, and the Paraphrase by Heinsius as an anonymous work, Lugd, Bat 1607, and afterwards by Heinsius as the work of Andronicus of Rhodes Lugd Bat 1617, with the Peri Pathon attached to it The two works were printed at Cantab 167? and Oxon 1809 (Stahr, Aristotelia, ii p129)

Bat's eye view

Thomas' commentary on Book II of Aristotle's Metaphysics ("Alpha the lesser") is here. On reading it again, I was struck by Aristotle's comment here as well as by Thomas' lengthy comment on it from n7 to n14. Aristotle says (Ross's translation)

Perhaps, too, as difficulties are of two kinds, the cause of the present
difficulty is not in the facts but in us. For as the eyes of bats are to the
blaze of day, so is the reason in our soul to the things which are by nature
most evident of all.

Aristotle and Thomas are commenting on how reaching the truth is both difficult and easy. It is easy (according to Aristotle) in the sense that the sun is the most obvious and visible object in the world. It is so obvious, in fact, that the eyes of a bat are blinded by it, and cannot see it (Thomas mentions owls, and other translations have moles, I think). Thus, the truth is right before us, and in an obvious way. Yet we are blinded by it, and cannot grasp it.

Is that right? How is this idea related to the distinction between a posteriori and a priori that I discussed here? A priori reasoning is from what is logically prior to what is derivable from it. The exemplar is geometric and mathematical reasoning, and in that sense the truth must be easy, for we begin with self-evident truths, and move from them to other truths which are less evident, but logically deducible. A posteriori reasoning is from effect - typically observed effect - to cause. The exemplar being the truth attained by the natural sciences, which is clearly difficult to get hold of, as I suggested earlier.

But is that what Aristotle has in mind? Probably not. The difficulty of a posteriori investigation - from effect to cause - is precisely because the cause is not visible to us. This is clearly not like the case of the sun. Thomas interprets him as follows:

Obviously, then, the difficulty experienced in knowing the truth is due
principally to some weakness on the part of our intellect. From this it follows
that our soul’s intellectual power is related to those immaterial beings, which
are by nature the most knowable of all, as the eyes of owls are to the light of
day, which they cannot see because their power of vision is weak, although they
do see dimly lighted things.

The analogy is between the weakness of an owl's eye (or a bat's eye, or a mole's eye) and the weakness of our intellect. The difficulty is not a matter to be resolved by scientific investigation, i.e. natural scientific investigation. The problem (according to Thomas) is that the human mind cannot be elevated to the level of knowing the essences (quidditates) of immaterial substances because they are not on the same level as sensible substances. The difficulty is not in things but in us.

And here you have the fundamental problem of understanding the Metaphysics, indeed the problem of understanding the project of all Western philosophy. Is it a fundamentally rational project? But as Hugh Lawson-Tancred says in his excellent introduction to and commentary on the book, "it seems excessively implausible that mere rumination on some of the more elementary features of our quotidian experience could lead to a profound revision of our conception of the universe". Or is it essentially mystical, as the popular meaning of the word metaphysics suggests? More later.