Saturday, May 13, 2006

Moral Dread

His mind was destitute of that dread which has been erroneously decried as if it were nothing higher than a man's animal care for his own skin: that awe of Divine Nemesis which was felt by religious pagans, and, though it took a more positive form under Christianity, is still felt by the mass of mankind simply as a vague fear at anything which is called wrong-doing. Such terror of the unseen is so far above mere sensual cowardice that it will annihilated that cowardice: it is the initial recognition of a moral law restraining desire, and checks the hard bold scrutiny of imperfect thought into obligations which can never be proved to have any sanctity in the absence of feeling. "It is good," sing the old Eumenides, in Aeschylus, "that fear should sit as the guardian of the soul, forcing it into wisdom--good that men should carry a threatening shadow in their hearts under th full sunshine; else, how shall they learn to revere the right?" That guardianship may become needless; but only when all outward law has become needless--only when duty and love have united in one stream and made a common force.

This is from my favorite George Eliot novel: Romola, Chapter XI. The reference is to Aeschylus's Eumenides.

Friday, May 12, 2006

The Imaginative Charge of Words

But even among the synonyms of our own tongue we cannot ignore the imaginative charge of words without being monstrous. You might, for example, be excused for declining an invitation to dinner when the menu that was offered was dead calf with fungus in heated dough, scorched ground tubers, and cabbage stalks, all swilled down with rotten German grape juice, and topped off with the dust of burnt berries in scalding water diluted with the oozings from the udders of a cow. You might well decline such a bill of fare, but you would miss an excellent meal of veal and mushroom pie, roast potatoes and spring greens,chased by a bottle of hock, and finished with a steaming cup of coffee and cream. What's in a name? Just about everything.

--Paul Roche, "Translator's Preface," Euripides: Ten Plays (Signet, 1998) xvii.


Comments on a post that I found in the most recent Teaching Carnival have started me thinking about the love poetry of Robert Herrick, which is an interesting set of poems to read. Some of the poems are quite striking:

The Rainbow, Or Curious Covenant

Mine eyes, like clouds, were drizzling rain ;
And as they thus did entertain
The gentle beams from Julia's sight
To mine eyes levell'd opposite,
O thing admir'd ! there did appear
A curious rainbow smiling there ;
Which was the covenant that she
No more would drown mine eyes or me.

Others strike the ear as odd, not because they are bad poetry, but because we moderns have no real sense of imagery:

Her Legs

Fain would I kiss my Julia's dainty leg,
Which is as white and hairless as an egg.

Which, it must be admitted, is a nice attribute for a leg to have; but it reminds one of the Song of Songs, where the woman has teeth like a herd of wet sheep. The imagery is perfect, as far as it goes; but we just don't have any real sense for it, so it sounds hilarious.

Some of the poems, of course, are just a tad silly, and probably deliberately so:

Upon Julia's Breasts

Display thy breasts, my Julia—there let me
Behold that circummortal purity,
Between whose glories there my lips I'll lay,
Ravish'd in that fair via lactea.

That could scarcely be said with straight face unless it were said as at least half a joke. There are several poems like this; more like cleverly expressed bawdy jokes than anything else. Others are more sensual:

Upon Julia's Breath

Breathe, Julia, breathe, and I'll protest,
Nay more, I'll deeply swear,
That all the spices of the east
Are circumfused there.

And still others mix the sensual and the bawdy:

The Vine

I dream'd this mortal part of mine
Was Metamorphoz'd to a Vine;
Which crawling one and every way,
Enthrall'd my dainty Lucia.
Me thought, her long small legs & thighs
I with my Tendrils did surprize;
Her Belly, Buttocks, and her Waste
By my soft Nerv'lits were embrac'd:
About her head I writhing hung,
And with rich clusters (hid among
The leaves) her temples I behung:
So that my Lucia seem'd to me
Young Bacchus ravished by his tree.
My curles about her neck did craule,
And armes and hands they did enthrall:
So that she could not freely stir,
(All parts there made one prisoner.)
But when I crept with leaves to hide
Those parts, which maids keep unespy'd,
Such fleeting pleasures there I took,
That with the fancie I awook;
And found (Ah me!) this flesh of mine
More like a Stock then like a Vine.

But others are sweeter and gentler:

Another Upon Her Weeping

She by the river sat, and sitting there,
She wept, and made it deeper by a tear.

Definitions and Descriptions

Julian Baggini has an unfortunately confused little musing on sin in The Guardian (HT: Butterflies and Wheels). In it he says:

Sin is as alien to the contemporary mind as fetching water from a well, darning your own socks or finding Demis Roussos sexy. According to the Catholic Catechism, sin is "humanity's rejection of God and opposition to him", which of course means that the godless (a bracket into which a large number of generation Y will fall) find the whole notion irrelevant, senseless or both. This is precisely what Christians who accept the idea of sin find deeply disturbing: a culture that doesn't even care about sin has truly cut itself off from God's grace and is therefore sinful in the most profound sense.

Well, I don't find it disturbing, since it's exactly what one would expect. But what I want to focus on is not that but the confusion. Baggini confusedly takes a description for a definition in his appeal to the Catholic catechism. From a Christian perspective, every sin will be a rejection of and opposition to God, but it doesn't follow from this that that's what the term 'sin' means. Claiming that every sin is properly described as a rejection of and opposition to God is not the same as claiming that that's what the term 'sin' means. One might as well say that, because a credit card can be described from a certain perspective as a convenient form of payment, the term 'credit card' means 'a convenient form of payment'. To distinguish descriptions from definitions takes serious analysis. It is also one of the oldest and most venerable parts of philosophy as we know it, since the distinction of mere descriptions from definitions was the whole point of Socratic investigation. I refer you to Plato's dialogues if you need a refresher on the subject.

Sin is a morally bad act; it is to action what vice is disposition. Had Baggini taken a more technical definition, such as Aquinas's (deriving from Augustine), which in one form or another is very popular, he wouldn't be so quick to assume that 'sin' always means 'contrary to God's will' when Christians talk about it. For 'sin' in that sense is a word, deed, or desire contrary to eternal law -- and so human sin is word, deed, or desire contrary to our little bit of eternal law, namely, the authoritative moral dictates of practical reason. And, last I heard, most atheists hadn't foresworn practical reason or the authority thereof. So it's unfortunate that Baggini has chosen to dabble in equivocal word play rather than serious analysis or substantive argument; people have a right to expect more from philosophers in public view, and, as it is a purely regressive contribution to the discussion, it doesn't do anyone any good.

UPDATE: Here is the section from the Catechism to which Baggini refers (386):

Sin is present in human history; any attempt to ignore it or to give this dark reality other names would be futile. To try to understand what sin is, one must first recognize the profound relation of man to God, for only in this relationship is the evil of sin unmasked in its true identity as humanity's rejection of God and opposition to him, even as it continues to weigh heavy on human life and history.

Notice that there is no claim here of defining sin; rather, the claim is that no one fully understands the evil of sin until they recognize that all sin is humanity's rejection of God and opposition to him. This is confirmed by the very next section:

Only the light of divine Revelation clarifies the reality of sin and particularly of the sin committed at mankind's origins. Without the knowledge Revelation gives of God we cannot recognize sin clearly and are tempted to explain it as merely a developmental flaw, a psychological weakness, a mistake, or the necessary consequence of an inadequate social structure, etc. Only in the knowledge of God's plan for man can we grasp that sin is an abuse of the freedom that God gives to created persons so that they are capable of loving him and loving one another

Notice that the point is clarification and clear recognition of sin, of avoiding mistakes in explaining sin; there is no attempt here to define sin. In other words, the intended idea is that we are here dealing with a true description; it isn't put forward as a definition. When the Catechism actually sets out an informal definition of sin (1849), it adapts and quotes Aquinas's.

Sor Juana Rebukes a Rose

Here's a slight reworking of an old translation I made of Sor Juana's "En que da moral censura a una rosa, y en ella a sus semejantes". You can see the Spanish and the earlier draft here. It still needs work.

In which she rebukes a rose, and in it those like it

Divine rose, you are grown in grace,
with all your fragrant subtleness,
teacher with scarlet beauty blessed,
snowy lesson in a lovely face,

twin of human frame and doom,
example of a gentility vain,
in whom are unified these twain:
the happy cradle, the grieving tomb.

Such haughtiness in your pomp, such pride,
such presumption; you disdain mortal fate;
later you are dismayed and hide

as dying you show a withered state
of which, by learnéd death and foolish life,
alive you lied, but dying demonstrate!

UPDATE: Thinking about the matter more, I think 'snowy lesson in a lovely face' might be better as 'a winter lesson in a lovely face', because 'snowy' sounds like it's the color of the rose (which jars with the previous line), whereas the point is that it's the situation of the rose -- the rose is in an early winter snow. One thing that's in the original that doesn't show up well in the translation are the cognates; this could perhaps be improved slightly by using 'graciousness' rather than 'gentility' in the second stanza.

Thursday, May 11, 2006

Which Musical Instrument Would the Mind Be?

According to Hume, it would be a string instrument, at least with regard to the passions:

Now if we consider the human mind, we shall find, that with regard to the passions, 'tis not of the nature of a wind-instrument of music, which in running over all the notes immediately loses the sound after the breath ceases; but rather resembles a string-instrument, where after each stroke the vibrations still retain some sound, which gradually and insensibly decays. The imagination is extremely quick and agile,; but the passions are slow and restive: For which reason, when any object is presented, that affords a variety of views to the one, and emotions to the other; tho' the fancy may change its views with great celerity; each stroke will not produce a clear and distinct note of passion, but the one passion will always be mixt and confounded with the other.

Media Points

The new trailer for Shyamalan's Lady in the Water (uses QuickTime). I confess myself intrigued.

If you haven't seen Season One of Cherub: The Vampire with Bunny Slippers, you should. There will, of course, be a second season beginning in June.

Wintergreen's "When I Wake Up" video tells the story of the Atari E.T. video game, perhaps the biggest flop in the history of the genre -- so bad that most of the cartridges had to be taken to the landfill as unsellable. We had that game -- still do, unless it got lost in one of our many moves. (Both song and video are pretty cool.)

You can play some classic '80s games online. Asteroids is as addictive as ever.

UPDATE: Also, check out some of the papers from the Bloggership conference on blogging and scholarship.

Tuesday, May 09, 2006

On Teaching People to Reason Well

Richard has an interesting 'problems with non-philosophers' post up. I think most people who are philosophically trained can sympathize with all the points listed; and, as he says, they really do touch on things that every schoolchild should be learning. (There's another side, of course, as Richard notes; I cannot count on my two hands the number of people I've met with philosophical background who largely use what they've learned to bully others, or to make themselves feel smarter than they are, or to nurse other despicable habits. But the existence of such people should not take away from the fact that these 'problems with non-philosophers' are serious problems.) If nothing else it should be considered a fundamental civic responsibility: a deliberative democracy depends crucially on having a large pool of people, from all represented walks of life, who can follow serious reasoning and engage in critical thought. There's no requirement that anyone be perfect at it; there's just the fundamental necessity that a deliberative democracy is, by its very nature, based on reasoning. If people are not taught to reason well, the society is not being given a solid foundation.

So the question is, what should citizens be learning? Starting with Richard's list, I think we can identify several things that are often lacking; these make natural starting points. They are:

(a) an ethos of inquiry;
(b) a familiarity with the way arguments work;
(c) good judgment about relevance;
(d) skill at avoiding fallacies.

(Of the annoyances Richard lists, the ones I'm setting aside are his #2, #5, and #7. I can see how these would be annoying in particular cases, but I don't think they can be considered general problems from the perspective that I'm taking here -- i.e., of what people should be taught as a minimum for healthy participation in civic life. Considering civic life in a deliberative democracy alone, there needs to be a healthy respect for received wisdom, a tendency to look at all the factors that are relevant, and an inclination to stick close to the factual and the likely. In particular cases these will often be problematic, but overall they are useful to the reasoning of society, as long as they are balanced by a-d.)

As Richard said over a year ago in the post he links to on the subject of philosophical education, education should primarily be a matter of skills rather than facts. Part of one's skill set should be things like inquiry into facts, evaluation of their relevance, etc., and learning most skills requires learning facts, so facts have a serious place; but they are not the point of education. They are the means. One way to say it is that good teaching will mostly be a teaching of facts but will never primarily be a teaching of facts; primarily it is a teaching of skills relevant to facts.

Naturally, however, the big question is how one would go about teaching a-d. I don't have any foolproof plans and programs, but I do have a few thoughts.

(a) An ethos of inquiry. In a sense I don't have much to say about this. Any teacher worth her salt is trying to cultivate this. I do think that we strain our schools a bit by giving them two distinct goals, which sometimes are in tension. By this I mean that we use our schools both to educate and to certify; it's possible to do both, but it's very easy for certification to overwhelm education. Everyone has dealt with this in one way or another: students who are more interested in what will be on the test than on what they can take away from their courses, teachers who expect you simply to regurgitate what they have said, administrators whose criteria of accountability have more to do with making the school look good on paper than with building thriving teacher-student-community relationships. There's nothing wrong with certification, but if too much emphasis is placed on it, it will inevitably result in people who have managed to pass a few tests but are not educated.

One of the aspects of an ethos of inquiry that I think we are completely failing to cultivate is conversibility, by which I mean an ability to treat arguments not merely as arguments-for-conclusions but elements of discussion. (In all fairness to non-philosophers it isn't hard to find people with Ph.D.'s in philosophy who are horrible at this.) After all, that is one of the primary points of formulating arguments explicitly: to be able to provide reasons to another person. To this end I think we need to do more to incorporate Socratic method into our teaching -- by which I mean not 'Socratic method' in the sense used in law, which is only loosely Socratic, but the sort of Socratic method one finds in Socrates, e.g., in the Gorgias. (I mention the Gorgias because it's a great way to see the Socratic approach in action. Not only is it, obviously, a Socratic dialogue, but Socrates also explicitly formulates elements of his approach as he goes along. It's a great text for becoming acquainted with Socratic midwivery.)

(b) Familiarity with the way arguments work. There is no way to get around this: the fact that most schools do not teach logic as a regular thing is genuinely scandalous. Every student who has reached high school, at the latest, should be able to distinguish validity and soundness. The approach should not emphasize (as I think logic courses usually do) invalidity. The fact that an argument is not valid is not actually very useful, given enthymemes, inductive arguments, analogical arguments, and the like. But there are few things more useful in all the world than being able to tell when an argument is valid, or to tell what premises could be added to an argument to make it valid. And the ability not to confuse validity with soundness -- a sound argument being a valid argument from true premises -- is crucial. I think many times the kinds of annoyances in Richard's list spring from an inability to appreciate the validity of an argument even when you have reason to think it unsound. Even more important than this, we need to teach informal logic -- and we need a better way to teach it than we currently seem to have. More on this below.

(c) Good judgment about relevance. This is the hardest thing on the list, and I think the one that teachers can do least about. However, we could still perhaps do better than we do by focusing more particularly and explicitly on what early modern Scottish philosophers called good taste. Good taste in a topic involves three things:

1) Broad familiarity with the facts and cases involved in a topic;
2) Skills useful for discerning features and making comparisons and contrasts;
3) Self-critical examination of one's own biases.

It's clear that we often try to teach, or at least encourage, these things; but we are so very piecemeal about it, despite the fact that there is probably nothing more important to a good education than the development of good taste over a large range of topics. Good taste is what good reasoners use whenever they are reasoning non-demonstratively; it is the very essence of critical thought. If you want to make good, rational judgments about (say) Shakespearean tragedy, you need a good sense of what goes into tragedies, what sort of tragedies there are, what features they have, what differences there are among them, what similarities they have, what biases might interfere with good judgment. You need experience with tragedies, skills of reasoning and perception relevant to texts and plays and the like, and the ability to know your own limitations. It is not enough to read Shakespearean tragedy, you must learn to read it well, at least to the extent that you can. Not everyone is capable of the same degree of good taste on any given topic; but everyone is capable of good taste on a lot of topics. Good teachers already go some way toward cultivating these things; but I think we would all benefit if we were more explicit about it and all in agreement on it.

(d) Skill at avoiding fallacies. This is a matter of logic -- chiefly informal logic -- but one thing that certainly does not work is giving student lists of fallacies or maxims or taxonomies or any number of other things we tend to use to introduce students to informal logic. For one thing, the maxims and taxonomies are often wrong; for another, if you give students a list of fallacies you aren't teaching them to avoid fallacies, you are teaching them how to label others -- for what students do is simply try to place (forcibly, and without good reason) arguments they don't like under the label of some fallacy.

What we need is what the medievals called dialectic: we need what they would call a topics (see also here). To put it in other terms, we need to teach students what types of inferences are based on (the seats or places -- topoi or loci -- of inferences); we need to give students not lists of fallacies, but guide them through arguments while pointing out potentially misleading features. The only way anyone ever really becomes good at avoiding fallacies is by coming to understand -- really understand -- aspects of reasoning itself. This is so both for reasoning in general (general topics) and discipline-specific inferences (specific topics). To do this we need a much more inspired logic pedagogy than we currently seem to have.

So those are a few ideas. I'm sure that other people have other ideas. How about you?

Science-versus-X Syndrome

Something I recently read -- I forget exactly what, but it was somewhere in the blogosphere -- has set me to thinking about a serious flaw in the way we (as a public or society) tend to talk about science; namely, the tendency to try talk about it opposing various things: science versus astrology, science versus creationism, or whatever. My thoughts on this are still inchoate and patchy, but here's what I have so far.

The problem with this way of talking is not that it's wholly off-base, but that it's just never a fruitful way of thinking about the matter. The goal of scientific work is truth or (if you are more inclined to qualify it) useful theory; scientific work and practice, taken generally, isn't really set in opposition to anything -- it's just some things turn out not to have a place in the work; some of those cases (ethical reasoning of the standard sort, for instance) can have a serious rational foundation, others (e.g., astrology), it would appear, cannot; and that's the end of the story. The sense in which scientific work and practice is in opposition to something is always very indirect -- in the course of refining its approximations to truth or (if you are more inclined to qualify it) its useful theories, some things get eliminated as not tenable, others begin to have difficulty with new evidences that are brought to light, and so forth. There's nothing personal about it; there's nothing political about; 'science', however one thinks of it, is not 'out to get' anything. Not only is it not monolithic enough to do anything like this, there's nothing about scientific work and practice, as such, that puts it in opposition to anything. What's really happening is that people doing scientific work are uncovering more and more of the world or (if you are more inclined to qualify it) finding better and better models of the world, and some ideas -- sometimes even good ideas -- fall by the wayside in the process. Some things just don't fit with the world as better understood or (if you are more inclined to qualify it) modeled; that's the only opposition. Scientific work and practice, as such, is not in opposition to anything. Given experiments or theories might put things into question, and some things might be put into utter doubt, but it's rather misleading to treat this as an opposition -- it's just a failure of some things to make the cut.

If this sounds like a trivial point, a mere matter of rhetorical preference, I invite you to take a moment to consider how people on the supposed other side -- fundamentalists, defenders of astrology, etc. -- sometimes think in these terms and how much it enables them to obscure the discourse. Once you concede the Science-versus-X mode of talking, you have ipso facto conceded a way of talking that makes it sound like scientific processes and practices are biased from the beginning against whatever is put in the X place. But the serious scientific problems with claims of ESP (to give just one example) were largely found out by people doing work that originally had nothing to do with the question one way or another -- electricity and gravity and fundamental forces and the like.

If you accept the science-versus-X discourse, you are also conceding a way of talking that reifies science, and thus often has the effect of apparently minimizing the problems with various positions. The problem with a given claim is never 'science' but such-and-such discoveries, such-and-such theoretical work, such-and-such experiments, etc. -- in other words, a potential panoply of evidences and reasonings, all of which may cause problems for the claim. Contrast that to just saying that 'science' problematizes the claim -- it sounds to the ear like a much weaker claim. What's involved in it? A handful of evidences? General relativity? Everything we currently know about biology? It just gets piled together, so, for all it tells us, it could just be one bit of evidence or a hundred thousand independent bits of evidence. And this is a situation that inevitably favors the X.

This is actually a general point; it's true of every truth-seeking endeavor. 'Opposition' is really a figure of speech, and should be recognized as being no more than that. It is remarkable, though, how easily we tend to slip into this antagonistic, and very misleading, mode of discourse. We seem to find it easier to think in terms of a battle -- even when it's clear there's no battle going on -- than to think in terms of a complicated tangle of developments that, in its ordinary processes of growth, pushes some candidates out of the running and forces others to adjust.

ADDED LATER: It might not need to be said, but I'll say it anyway: I'm not criticizing the specific forms 'science-vs.-X' or 'Science opposes X', but the whole battery of similar claims. If you tell people that 'Biology shows that X is false', for instance, you are not telling them anything -- biology is not an evidence or reason, it is a discipline. What shows X wrong, if anything does, are facts, well-founded theories, etc., that biologists have found. And so it is with every scientific discipline, and every X, and every alleged antagonism between them.

Links of Note

* A lovely post on Euripides' play, Iphigenia among the Taurians at "Seoul Hero". Actually, I think it's the other Iphigenia play by Euripides, Iphigenia at Aulis, that makes for the most interesting comparisons and contrasts with the Akedah or Binding of Isaac, but I can see the point with this one.

* Speaking of the Akedah, the poem On Abraham and Isaac, usually attributed to St. Ephrem the Syrian, is an interesting rendition, which reads the Binding of Isaac Christologically.

* Allen Wood has a lovely paper on the subject of Kant on Conscience (PDF).

* Eric Schwitzgobel muses on The Problem of the Ethics Professors at "The Splintered Mind" (HT: Matthew Mullins)

* Fr. Tucker's sermon for the Fourth Sunday of Easter at "Dappled Things" is worth reading.

* Miriam Burstein has a great list of links on Gustave Doré.

* I missed the Feast of St. Catherine of Siena (April 29), and by quite a bit, since it slipped my mind entirely. But Catherine's letters are worth reading.

* I was at Lake Brownwood this weekend, where there was a big storm; and it has put me in mind of St. Columban's Boat Song.

* Mark Steyn has a biting -- and very Canadian -- critique of certain forms of Canadian anti-Americanism at

* The BBC has an informal poll of people's 'intuitions' about ethical thought experiments. I'm not a big fan of this sort of thing -- polls about ethical thought experiments are useful, I think, primarily for seeing how morally stunted people's moral 'intuitions' are -- but it certainly makes interesting reading. There's some discussion of it at TAR, particularly about how the particular ways the open-ended word problems (which is a more accurate name for these so-called 'thought experiments') are phrased might be affecting answers. I agree with Mike Almeida that it's unfortunate that they don't ask the questions for Judith Jarvis Thompson's violinist that Thompson herself asked; one of the strengths of the word problem is that it admits of a lot of variation.

* The ever-likable Rex Murphy reflects on rock icon Keith Richards. (HT: Magic Statistics)

* UPDATE: Was John Home a better playwright than William Shakespeare? David Hume thought so. Of course, Home was Hume's cousin -- le bon David changed the spelling in an effort to get the English to pronounce it correctly, and he and Home often had friendly arguments about who was spelling it correctly. One suspects there may have been a little familial bias in Hume's comment to Smith. It's perhaps worth noting, by the way, that Home's tragedy, Douglas, sparked a major battle between the Moderate Party and the Evangelical Party of the Church of Scotland: Home was a churchman of the Moderate Party, and Evangelicals like Witherspoon didn't think it was appropriate for good Christians, and especially not appropriate for ministers, to go around indulging in the immorality of the theater. Witherspoon wrote a tract on the evils of stageplays. Through the comic sensibilities of providence, Witherspoon (who went on to become president of Princeton and to sign the Declaration of Independence) is the direct ancestor of Reese Witherspoon.

Monday, May 08, 2006

Online Philosophy Conference

The second week is up, and there are several interesting papers worth reading. Thomas Hurka discusses whether friendship is a problem for consequentialism, and Benj Hellie has a very good paper that should interest those with a taste for the history of analytic philosophy. The exchange that I think is best, though, is Fischer vs. Vihvelin on Frankfurt examples, in which Vihvelin argues (convincingly, I think) that even from a compatibilist perspective Frankfurt examples are a bad argumentative strategy.


I don't usually comment much elsewhere, but as it's a facet of my blogging that doesn't show up much here, I thought I would just note some of the discussions I've had elsewhere in the recent past (past few weeks).

At "Philosophy, etc." I've been discussing God and possible worlds;

at "Alanyzer" whether an infinite past is possible;

Kant's Antinomies at "What is is like to be a blog?";

at "Assimilatio Dei" whether Newman was an empiricist;

and the Star Trek franchise at "Parableman".

Aristotle on Infinite Divisibility of Time

Hence Zeno's argument makes a false assumption in asserting that it is impossible for a thing to pass over or severally to come in contact with infinite things in a finite time. For there are two senses in which length and time and generally anything continuous are called 'infinite': they are called so either in respect of divisibility or in respect of their extremities. So while a thing in a finite time cannot come in contact with things quantitatively infinite, it can come in contact with things infinite in respect of divisibility: for in this sense the time itself is also infinite: and so we find that the time occupied by the passage over the infinite is not a finite but an infinite time, and the contact with the infinites is made by means of moments not finite but infinite in number.

Aristotle, Physics VI