Absence of Evidence

In the comments thread to a post on another blog, a commenter gave the following quotation:

'The simplest explanation for the total absence of evidence for gods is a total absence of gods'.

I've increasingly over the past couple of years come across claims of this sort (the commenter seems to be quoting someone, but I don't know who), and I find it interesting because the underlying idea seems to be pretty clearly wrong, for all its superficial plausibility, even when we ignore the obvious hyperbole of 'total absence of evidence'. (Obviously there's evidence -- religious experiences, etc.; the question is just whether it's adequate to establish the conclusion. It is very rare to find cases of actual disputes where one side literally has no evidence at all, inconvenient as that fact may be. Even believers in house elves have strange occurrences to call to witness. What we usually mean is that the evidence is weak, which is very different from being nonexistent. The rhetorical advantages of conflating weak evidence with no evidence are, of course, obvious; but we should not treat a rhetorical figure as literal speech.) What we mean by "total absence of evidence" is at most a total absence of evidence available to be used in reasoning (otherwise the only way to establish total absence of evidence for X is to prove that X can't possibly exist -- if we aren't talking about evidence available to us, we'd have to take into consideration all evidence available to everyone at every time, including the future, and therefore we would need to establish a guarantee that no real evidence could possibly turn up in the future). And because of this, if all other things are equal, the simplest explanation for absence of evidence is that you've probably just overlooked it or not come across it. It is simplest in at least three different ways:

(1) It involves the weakest supposition about the world. If I commit to the claim that some evidence of X probably exists, I'm not by that committed to any claim for or against the existence of X, just to the existence of something that someone could reasonably classify as evidence for the existence of X, whatever that evidence might be. This is clearly a weaker supposition, with fewer commitments, than the supposition that there is no X.

(2) It is the simplest in that, unlike a categorical rejection or affirmation of something's existence, it allows for the subsumption of the case under an already well-established generalization, that is, the straight psychological fact that people often overlook or fail to come across evidence for things.

(3) It is the simplest in that it provides the least impediment to future inquiry: it closes down the fewest options for further research.

Part of the problem, I think, is that phrases like 'total absence of evidence for the existence of X', despite the literal meaning, actually convey in practical, colloquial speech the idea that there is, overwhelmingly, evidence against the existence of X, and it is indeed true that the simplest explanation for overwhelming evidence against the existence of X is X's nonexistence. And perhaps a failure to recognize that we do not, in actual practice usually judge absence of evidence absolutely but relative to what is accessible to us (the distinction I mentioned above) contributes to this confusion. But what is actually happening is that an entire range of suppositions is being elided. And there's a reason why people often say that absence of evidence is not evidence of absence: it's precisely that actual absence of the thing/event/whatever is not the simplest explanation for absence of evidence, considered on its own.

There are actual cases where an absence of evidence would be evidence of absence, of course; the cases, that is, where all other things are not equal. In practice, all of these are cases where we actually have pre-existing preponderant reason (either through preponderance of evidence or through actual proof) that X's existence is inconsistent with the lack of evidence in question, or else made definitely unlikely by it, and that it is either impossible or unlikely that the reason the evidence is lacking is your fault. But these cases, of course, don't salvage the general principle.

Chrysorrhoas

Today is the Feast of St. John of Damascus. John was a Syrian Christian; his name at birth may have been Mansur ibn Sarjun al-Taghlibi -- our records are not wholly clear, and if I understand correctly it is possible that this was really the name of his father. The family of Mansur was a family of fair local importance in a time of great change: John's grandfather was in charge of taxes under the Byzantine Empire, and then, when the region was conquered by the Umayyad caliphate, the family continued in the civil service, working for the caliph (which was common among the civil servants of the time). Indeed, John's father, Sarjun, was put in charge of building the Arab fleet for the purpose of attacking Constantinople. John himself served in the court of the caliph for some time, before going to the Mar Saba monastery. It was there, at Mar Saba, that he took the name John as his monastic name. He wrote quite a few important works, the most important of which is the one usually known in the west as the Exposition of the Orthodox Faith. Because he's primarily a synthesizer of doctrine, his creativity is often overlooked; as with most synthesizing geniuses, the creative ingenuity he constantly displays is not flashy and obvious but often very subtle. He is sometimes called Chrysorrhoas, which means, "streaming with gold."

Tolstoy's cousin, Count Alexei Tolstoy, wrote a poem about John of Damascus that became the core of a famous cantata by Taneyev, Ioann Damaskin, also sometimes called A Russian Requiem. It is Russian music at its finest, and streaming with gold itself. The following is but an excerpt (the third movement).

Make Plain My Pathway Still

O Thou Essential Word
by Catherine Winkworth

O Thou essential Word,
Who wast from the beginning
With God, for Thou wast God;
Thou hope of all the sinning,
Chosen to save our race,
Welcome indeed Thou art,
Redeemer, Fount of grace,
To this my longing heart.

Come, self-existent Word,
And speak Thou in my spirit!
The soul where Thou art heard
Doth endless peace inherit.
Thou Light that lightenest all,
Abide through faith in me,
Nor let me from Thee fall,
And seek no guide but Thee.

Ah! what hath stirred Thy heart,
What cry hath mounted thither,
And reached Thy heavenly throne,
And drawn Thee, Savior, hither?
It was Thy wondrous love,
And my most utter need,
Made Thy compassions move,
Stronger than death indeed.

Then let me give my heart
To Him who loved me, wholly;
And live, while here I dwell,
To show His praises solely;
Yes, Jesus, form anew
This stony heart of mine,
Make it till death still true
To Thee, for ever Thine.

Let nought be left within
But what Thy hand hath planted;
Root out the weeds of sin,
And quell the foe who haunted
My soul, and set the tares;
From Thee comes nothing ill,
O save me from his snares,
Make plain my pathway still.

Thou art the Life, O Lord,
And Thou its Light art only!
Let not Thy blessèd rays
Still leave me dark and lonely.
Star of the East, arise!
Drive all my clouds away,
Till earth’s dim twilight dies
Into the perfect day!

Winkworth, one of the very small handful of hymn-translators to rival John Mason Neale in importance and quality, is here translating a German hymn by Laurentius Laurenti.

Cogito Ergo Sum XII

Descartes, Second Replies (CSM II, 104):

Now some of these perceptions [of the intellect] are so transparently clear and at the same time so simple that we cannot ever think of them without believing them to be true. The fact that I exist so long as I am thinking, or that what is done cannot be undone, are examples of truths in respect of which we manifestly possess this kind of certainty. For we cannot doubt them unless we think of them; but we cannot think of them without at the same time believing they are true, as was supposed. Hence we cannot doubt them without at the same time believing they are true; that is, we can never doubt them.

Cogito Ergo Sum XI

Descartes, Second Replies (CSM II, 140):

When someone says 'I am thinking, therefore I am, or I exist', he does not deduce existence from thought by means of a syllogism, but recognizes it as something self-evident by a simple intuition of the mind. This is clear from the fact that if he were deducing it by means of a syllogism, he would have to have had previous knowledge of the major premiss 'Everything which thinks is, or exists'; yet in fact he learns it from experiencing in his own case that it is impossible that he should think without existing.

Philosophical Folklore

As some long-term readers know, I have an interest in philosophical folklore; much of this folklore is found in discussions of critical thinking and informal logic, which is a pretty fruitful hunting ground for it: almost everything that goes by the name 'critical thinking', and much in the field of informal logic, is philosophical folklore, bits and pieces that have filtered down and become common legend. Some of these bits and pieces, used wisely, do good work; others are, as we might say, mere superstition -- things that were once held by only a few for very specific and very controvertible reasons, or things that have long since become too crudely simplified to do the work they are supposed to do, or things that once made good sense but are now consistently understood a completely different way due to the accidents of linguistic change.

But one finds philosophical folklore elsewhere, especially when it comes to history of philosophy. I've mentioned, for instance, the irony that what is often called Leibniz's Law is not found in Leibniz; you can find superficially similar claims, but on closer claim they turn out not to have anything to do with identity in the proper sense, or else to be obviously different in logical character from what goes by the name. For instance, Leibniz explicitly tells us that his claim in Discourse on Metaphysics, section 9, which is often said to be the source, is paradoxical, in the company of claims like "You can't divide substances in half" or "Every substance mirrors the entire world." It's also based purely on Leibniz's very peculiar account of what an individual substance is. Nothing like this is even remotely in view when people talk about "Leibniz's Law". In this case what seems to have happened is that some claims made by Leibniz were put into a very different logical form than Leibniz himself would or could have put them, and by people making assumptions Leibniz himself wouldn't or couldn't have made, with the result that things were changed significantly in the translation.

Another example is that what is usually called Pascal's Wager actually does not derive directly from Pascal, although it was influenced by him. It really derives from Arnauld and Nicole's Port-Royal Logic and you can recognize it by the fact that it gives a role in the Wager to hell -- i.e., very bad consequences play an important role in the argument. This is not the way Pascal sets up his own Wager, in any of the fragments we have. What happened there is that Port-Royal Logic was published long before anything directly from Pascal (we only have Pascal's version in fragmentary notes published posthumously), and therefore it had a chance to become very widespread, although, since it clearly is influenced by Pascal, it gets Pascal's name.

Another example, about which I've been meaning to write a post (but it's a complicated issue and so I need to have a good stretch of time to do it), has to do with the phrase "Knowledge is Power". It's usually attributed to Francis Bacon. It is indeed a very Baconian sentiment, and Bacon does have the Latin phrase scientia est potentia in his writings. But there he's talking about divine simplicity, and the claim he is making is that knowledge is (the same as) power for God, as opposed to us. One occasionally also finds it attributed to Thomas Hobbes, and indeed, Thomas Hobbes also says that knowledge is power; and the meaning is much more like what we usually mean by it. But he adds sed parva, roughly, "but only a little", and that's a pretty important qualification.

The list could be extended at considerable length. Not all bits of philosophical folklore are wrong, it should be said, although explaining the ones that are wrong is often a more interesting task than explaining the ones that are right. And even those that are wrong if taken straight may nonetheless show some real insight -- "knowledge is power" is indeed a pretty good summary of Baconian philosophy, even if Bacon never thought to summarize it exactly that way, and it would be virtually impossible to come up with a three-word summary that does better -- or be based on conflations or errors that even very reasonable people may make.

What sets me in mind of all this is this discussion of a bit of philosophical folklore, by T. H. Irwin. One occasionally encounters the claim that Augustine argued that the virtues of pagans were merely 'splendid vices', splendida peccata. As with most such philosophical folklore, one can make some Augustinian sense of the claim (although, as Irwin notes in the paper, how much Augustinian sense is a tricky matter to determine, with lots of room for controversy); but Augustine himself seems never actually to say this. This is a particularly interesting case because it has been a massively influential bit of philosophical folklore. Because philosophical folklore is popular and widely accepted, it does tend to have some real influence, which is why it's very worthwhile for historians of philosophy like myself to study it (and a real shame that we don't do it more often). But the degree of influence of this particular tidbit through history has been quite extraordinary; there are probably only a relatively small handful of folkloric tidbits (like Ockham's Razor) that have been more influential.

Cogito Ergo Sum X

Descartes, Meditations on First Philosophy, Meditation Two:

But how do I know that there is not something different altogether from the objects I have now enumerated, of which it is impossible to entertain the slightest doubt? Is there not a God, or some being, by whatever name I may designate him, who causes these thoughts to arise in my mind? But why suppose such a being, for it may be I myself am capable of producing them? Am I, then, at least not something? But I before denied that I possessed senses or a body; I hesitate, however, for what follows from that? Am I so dependent on the body and the senses that without these I cannot exist? But I had the persuasion that there was absolutely nothing in the world, that there was no sky and no earth, neither minds nor bodies; was I not, therefore, at the same time, persuaded that I did not exist? Far from it; I assuredly existed, since I was persuaded. But there is I know not what being, who is possessed at once of the highest power and the deepest cunning, who is constantly employing all his ingenuity in deceiving me. Doubtless, then, I exist, since I am deceived; and, let him deceive me as he may, he can never bring it about that I am nothing, so long as I shall be conscious that I am something. So that it must, in fine, be maintained, all things being maturely and carefully considered, that this proposition I am, I exist, is necessarily true each time it is expressed by me, or conceived in my mind.

Cogito Ergo Sum IX

Descartes, Discourse on Method, Part IV:

Accordingly, seeing that our senses sometimes deceive us, I was willing to suppose that there existed nothing really such as they presented to us; and because some men err in reasoning, and fall into paralogisms, even on the simplest matters of geometry, I, convinced that I was as open to error as any other, rejected as false all the reasonings I had hitherto taken for demonstrations; and finally, when I considered that the very same thoughts (presentations) which we experience when awake may also be experienced when we are asleep, while there is at that time not one of them true, I supposed that all the objects (presentations) that had ever entered into my mind when awake, had in them no more truth than the illusions of my dreams. But immediately upon this I observed that, whilst I thus wished to think that all was false, it was absolutely necessary that I, who thus thought, should be somewhat; and as I observed that this truth, I think, therefore I am, was so certain and of such evidence that no ground of doubt, however extravagant, could be alleged by the sceptics capable of shaking it, I concluded that I might, without scruple, accept it as the first principle of the philosophy of which I was in search

In the next place, I attentively examined what I was and as I observed that I could suppose that I had no body, and that there was no world nor any place in which I might be; but that I could not therefore suppose that I was not; and that, on the contrary, from the very circumstance that I thought to doubt of the truth of other things, it most clearly and certainly followed that I was; while, on the other hand, if I had only ceased to think, although all the other objects which I had ever imagined had been in reality existent, I would have had no reason to believe that I existed; I thence concluded that I was a substance whose whole essence or nature consists only in thinking, and which, that it may exist, has need of no place, nor is dependent on any material thing; so that " I," that is to say, the mind by which I am what I am, is wholly distinct from the body, and is even more easily known than the latter, and is such, that although the latter were not, it would still continue to be all that it is.

Cogito Ergo Sum VIII

Avicenna, Al-Shifa: Soul, I.1 (Hackett Reader 178-9):

So we say that it has to be imagined as though one of us were created whole in an instant but his sight is veiled from directly observing the things of the external world. He is created as though floating in air or in a void but without the air supporting him in such a way that he would have to feel it, and the limbs of his body are stretched out and away from one another, so they do not come into contact or touch. Then he considers whether we can assert the existence of his self. He has no doubts about asserting his self as something that exists without also asserting the existence of any of his exterior or interior parts, his heart, his brain, or anything external. He will, in fact, be asserting the existence of his self without asserting that it has length, breadth, or depth, and, if it were even possible for him in such a state to imagine a hand or some other extremity, he would not imagine it as a part of his self or as a necessary condition of his self - and you know that what can be asserted as existing is not the same as what cannot be so asserted and that what is stipulated is not the same as what is not stipulated. Thus, the self whose existence he asserted is his unique characteristic, in the sense that it is he himself, not his body and its parts, which he did not so assert. Thus, what one has been alerted to is a way to be made alert to the existence of the soul as something that is not the body - nor in fact any body - to recognise it and be aware of it, if it is in fact the case that he has been disregarding it and needed to be hit over the head with it.

Two Poem Drafts

Unrung Change

Our churches have no bells;
the harridans of hell
have come and cut them down.
To every chapel-town
they came and took our voice.

In cheer and fear the bells
across the plains and hills
spoke words of hope and faith;
they now are merely wraiths;
they now have lost all voice.

Our churches have no bells;
their songs will never swell
with clamor born of joy;
their bronze is now destroyed
and we have lost our voice.

Casting Correspondences on the Old Man's Tortoise Shell

Patternable pattern: unstable pattern.
Nameable name: unstable name.

Nameless: therefore root of sky and land.
Named: therefore mother of ten myriad things.

Therefore:
Never yearning: seeing the profound.
Ever yearning: seeing the surface.
Both these things: the same result.
Opposing names: the same meaning.

Therefore:
One obscure: both obscure.

Much that is profound: therefore a way through.

Cogito Ergo Sum VII

Augustine, On the Trinity, Book XV, Chapter 12:

In regard to this, indeed, we are absolutely without any fear lest perchance we are being deceived by some resemblance of the truth; since it is certain, that he who is deceived, yet lives. And this again is not reckoned among those objects of sight that are presented from without, so that the eye may be deceived in it; in such way as it is when an oar in the water looks bent, and towers seem to move as you sail past them, and a thousand other things that are otherwise than they seem to be: for this is not a thing that is discerned by the eye of the flesh. The knowledge by which we know that we live is the most inward of all knowledge, of which even the Academic cannot insinuate: Perhaps you are asleep, and do not know it, and you see things in your sleep. For who does not know that what people see in dreams is precisely like what they see when awake? But he who is certain of the knowledge of his own life, does not therein say, I know I am awake, but, I know I am alive; therefore, whether he be asleep or awake, he is alive. Nor can he be deceived in that knowledge by dreams; since it belongs to a living man both to sleep and to see in sleep. Nor can the Academic again say, in confutation of this knowledge: Perhaps you are mad, and do not know it: for what madmen see is precisely like what they also see who are sane; but he who is mad is alive. Nor does he answer the Academic by saying, I know I am not mad, but, I know I am alive. Therefore he who says he knows he is alive, can neither be deceived nor lie. Let a thousand kinds, then, of deceitful objects of sight be presented to him who says, I know I am alive; yet he will fear none of them, for he who is deceived yet is alive. But if such things alone pertain to human knowledge, they are very few indeed; unless that they can be so multiplied in each kind, as not only not to be few, but to reach in the result to infinity. For he who says, I know I am alive, says that he knows one single thing. Further, if he says, I know that I know I am alive, now there are two; but that he knows these two is a third thing to know. And so he can add a fourth and a fifth, and innumerable others, if he holds out. But since he cannot either comprehend an innumerable number by additions of units, or say a thing innumerable times, he comprehends this at least, and with perfect certainty, viz. that this is both true and so innumerable that he cannot truly comprehend and say its infinite number. This same thing may be noticed also in the case of a will that is certain. For it would be an impudent answer to make to any one who should say, I will to be happy, that perhaps you are deceived. And if he should say, I know that I will this, and I know that I know it, he can add yet a third to these two, viz. that he knows these two; and a fourth, that he knows that he knows these two; and so on ad infinitum. Likewise, if any one were to say, I will not to be mistaken; will it not be true, whether he is mistaken or whether he is not, that nevertheless he does will not to be mistaken? Would it not be most impudent to say to him, Perhaps you are deceived? When beyond doubt, whereinsoever he may be deceived, he is nevertheless not deceived in thinking that he wills not to be deceived. And if he says he knows this, he adds any number he chooses of things known, and perceives that number to be infinite. For he who says, I will not to be deceived, and I know that I will not to be so, and I know that I know it, is able now to set forth an infinite number here also, however awkward may be the expression of it. And other things too are to be found capable of refuting the Academics, who contend that man can know nothing.

Thinking Links for Linking Thinkers

* Sean Carroll has a very interesting discussion of Szilárd's Engine, which is about the relation between (accessible) information and energy.

* Taylor Marshall on what 1 Clement tells us about the early Pauline canon.

* I'm sure I've linked to it before, but the Logic Museum has Thorburn's "The Myth of Ockham's Razor" up.

* Sam Crane considers whether Confucianism can function as a stand-alone political philosophy.

* It's not the sort of snark I usually like, but I did find this Lama-or-Pope bit mildly amusing. People just don't really appreciate the fact that Buddhists take seriously the idea of eliminating craving.


* Eight songs by Matteo Ricci. (ht)

* A discussion of marbled paper. (ht) One of the more unusual uses of marbled paper is the marbled page of Tristram Shandy: usually marbled paper is used for fly-leaf and the like, but Sterne simply inserts it as an ordinary page. I discussed it briefly a long while back, along with the black page (which is no longer rendering properly in the post) and the blank page.

* Chris Gabbard describes how he changed his views on mental disability. Very much worth reading. (ht)

* Russia is building an orbital space pod to clean up space debris. China is planning to build an orbital interceptor to protect earth from asteroids and such. Of course, there's probably more here than pure altruism: both projects have the convenient feature of being people-friendly projects that can easily be adapted to military use if necessary (the U.S. was at one point the world's Grandmaster in designing such projects, but we seem to have lost our touch recently).

Cogito Ergo Sum VI

Augustine, On the Trinity, Book X, chapter 10:

But since we treat of the nature of the mind, let us remove from our consideration all knowledge which is received from without, through the senses of the body; and attend more carefully to the position which we have laid down, that all minds know and are certain concerning themselves. For men certainly have doubted whether the power of living, of remembering, of understanding, of willing, of thinking, of knowing, of judging, be of air, or of fire, or of the brain, or of the blood, or of atoms, or besides the usual four elements of a fifth kind of body, I know not what; or,whether the combining or tempering together of this our flesh itself has power to accomplish these things. And one has attempted to establish this, and another to establish that. Yet who ever doubts that he himself lives, and remembers, and understands, and wills, and thinks, and knows, and judges? Seeing that even if he doubts, he lives; if he doubts, he remembers why he doubts; if he doubts, he understands that he doubts; if he doubts, he wishes to be certain; if he doubts, he thinks; if he doubts, he knows that he does not know; if he doubts, he judges that he ought not to assent rashly. Whosoever therefore doubts about anything else, ought not to doubt of all these things; which if they were not, he would not be able to doubt of anything.

Cogito Ergo Sum V

Augustine, Enchiridion, Chapter 20:

But I am not sure whether one ought to argue with men who not only do not know that there is an eternal life before them, but do not know whether they are living at the present moment; nay, say that they do not know what it is impossible they can be ignorant of. For it is impossible that any one should be ignorant that he is alive, seeing that if he be not alive it is impossible for him to be ignorant; for not knowledge merely, but ignorance too, can be an attribute only of the living. But, forsooth, they think that by not acknowledging that they are alive they avoid error, when even their very error proves that they are alive, since one who is not alive cannot err. As, then, it is not only true, but certain, that we are alive, so there are many other things both true and certain; and God forbid that it should ever be called wisdom, and not the height of folly, to refuse assent to these.

Cogito Ergo Sum IV

Augustine, City of God, Book XI, Chapter 26:

For we both are, and know that we are, and delight in our being, and our knowledge of it. Moreover, in these three things no true-seeming illusion disturbs us; for we do not come into contact with these by some bodily sense, as we perceive the things outside of us—colors, e.g., by seeing, sounds by hearing, smells by smelling, tastes by tasting, hard and soft objects by touching—of all which sensible objects it is the images resembling them, but not themselves which we perceive in the mind and hold in the memory, and which excite us to desire the objects. But, without any delusive representation of images or phantasms, I am most certain that I am, and that I know and delight in this. In respect of these truths, I am not at all afraid of the arguments of the Academicians, who say, What if you are deceived? For if I am deceived, I am. For he who is not, cannot be deceived; and if I am deceived, by this same token I am. And since I am if I am deceived, how am I deceived in believing that I am? For it is certain that I am if I am deceived. Since, therefore, I, the person deceived, should be, even if I were deceived, certainly I am not deceived in this knowledge that I am. And, consequently, neither am I deceived in knowing that I know. For, as I know that I am, so I know this also, that I know. And when I love these two things, I add to them a certain third thing, namely, my love, which is of equal moment. For neither am I deceived in this, that I love, since in those things which I love I am not deceived; though even if these were false, it would still be true that I loved false things. For how could I justly be blamed and prohibited from loving false things, if it were false that I loved them? But, since they are true and real, who doubts that when they are loved, the love of them is itself true and real? Further, as there is no one who does not wish to be happy, so there is no one who does not wish to be. For how can he be happy, if he is nothing?

Rough Jottings on Zeno's Argument and Paradoxes Generally

Graham Priest has an article on dialetheism and paraconsistency at the NYT's "Stone" blog. I was struck by what he says about Zeno's paradox:

Here we can’t just accept the conclusion: we know that the car can get to point B. So something must be wrong with the argument. In fact, there is now a general consensus about what is wrong with it (based on other developments in 19th-century mathematics concerning infinite series). You can do an infinite number of things in a finite time — at least provided that these things can be done faster and faster.

The consensus, which is sometimes called the Standard Solution, can only get "You can do an infinite number of things in a finite time - at least provided that these things can be done faster and faster," if it provides a solution to the paradox, not vice versa. And it's not so clear that the Standard Solution does everything that would be required to resolve/solve/dissolve the Paradox. And, indeed, when you look at elaborations of how the Standard Solution is supposed to solve the paradoxes, such as the IEP article on the subject, all the responses very clearly end up being, "Wherever there's a problem, we assume that you can do what Zeno denies can be done, and make a distinction based on that assumption." Which is fine, but one should be quite clear that this is not what solving a paradox is: to make this response work you need not only to show that you avoid the paradox and have provided a consistent answer; you need also to show that there is independent good reason to reject the assumptions of the paradox you are rejecting. People have given the conclusion Priest gives for literally ages -- Aristotle explicitly mentions it in response to the Dichotomy. What has always been in question is what can support this conclusion without begging the question. This is why Aristotle makes his famous distinction between actual and potential infinites here: actuality and potentiality are more fundamental concepts than anything in the Paradox itself, and are presupposed by the Paradox itself, and so can be used simultaneously to argue that its assumptions are wrong and that an alternative is right. Whether one agrees with Aristotle as to the actual answer or not, this is the way to dissolve a paradox. The Standard Solution doesn't do this, and the usefulness of the mathematics that yield it is neither here nor there: it always remains open to accept both the Standard Solution and the Paradox by being an anti-realist about the former and a realist about the latter. This is a regular problem with mathematical solutions to non-mathematical problems: we know for a fact that extremely useful mathematical solutions can fail to correspond to reality, and therefore it's always an option to be anti-realist about any of them. The Standard Solution at most shows you that, if certain things are true about change, then a consistent system can be had in which Zeno's Paradox can't be formulated. It doesn't show that those things are true about change, but at most that if we at least pretend that they are we get right answers without having to worry about the Paradox. The Paradox is evaded for practical purposes, which is good, and the evasion is shown not to be inconsistent with itself, which is very good, but if you leave it at that, the Paradox has not been resolved. Indeed, if you leave it at that, you clearly show that you have no idea what resolving/solving/dissolving a paradox is. And showing that every feature of the (extraordinarily complex) Standard Solution has real, independently establishable, physical counterparts is a massive challenge that no one has ever undertaken.

It reminds me a little, actually, of common responses to the Preface Paradox, which was talked about at length in the blogosphere some time back. The usual response was to posit as true whatever was required to make there no longer be a paradox. This is an evasion of the paradox, and a perfectly reasonable thing to do for practical purposes, but it doesn't deal with the paradox at all: what you need to do is prove that what you are positing really is true and doesn't just save the appearances. And when you set out to do that you find that independent proof of the assumptions they make is extraordinarily difficult (and that many of the proposals for handling the paradox that are taken by their proponents as just obvious are inconsistent with each other).

It's also not really correct to say that the Standard Solution is a general consensus: there is no general consensus. The Standard Solution is easily the dominant single position, but it has quite a few robust rivals, and when you take those into account it's not even always clear that the Standard Solution is accepted by a majority of people. Lots of people still prefer Aristotelian approaches of various kinds, at most thinking that they need to be refined; lots of people are constructivists; lots of people prefer appeal to infinitesimals; and so forth. No one of these groups is even close to being as dominant as the Standard Solution group, but all together make a very sizable bunch. What we have is a dominant proposal; this is very different from a general consensus.

Further, Zeno's Paradox wasn't an argument that there could be no consistent mathematical system without the Paradox; it was an argument that actual motion through actual space and time was something opponents of Parmenides and Zeno (it is not, and never has been, clear whether Zeno was attempting to defend Parmenides or merely to criticize the arguments proposed against Parmenides, because we don't know how closely Zeno himself actually followed Parmenides) could not coherently account for. This is as certainly known as anything else about Zeno's Paradox; it's one of the few things that is agreed on by the three major interpretations of the Paradox (that Zeno was defending Parmenidean monism against common-sense pluralism; that Zeno was a nihilist attacking both monism and pluralism; that Zeno was not defending any particular position but only raising problems). The genuinely important question is not, "Is there some set of assumptions that, if true, would dissolve the paradox?" because the answer to that is "Of course," regardless of the paradox. The question, "What proves these dissolving assumptions actually true?" is more important, but is still not the most important question. The most important question is: "What are the common features of the accounts of motion Zeno's Paradox on its own makes it impossible to accept?" That is, people often look at paradoxes upside down: they focus on finding things that at least evade the paradox. There are always a great many of those, and sometimes the answer that dissolves the paradox is actually not interesting, beyond dissolving the paradox. What is really and consistently valuable in a paradox -- and it always remains even when the paradox is dissolved -- is what it tells us about what we can't accept.

Cogito Ergo Sum III

Augustine, On Free Choice of Will, Book II, chapter III:

Augustine: So, to start off with what is clearest, I ask first whether you yourself exist. Are you perhaps afraid that you might be deceived in this line of questioning? Surely if you did not exist you could not be deceived at all.
Evodius: Go on.
Augustine: Therefore, since it is clear that you exist, and it would not be clear to you unless you were alive, this too is clear: You are alive. Do you understand that these two points are absolutely true?
Evodius: Yes indeed.
Augustine: Then this third point is also clear, namely: You understand.
Evodius: Clearly.

Brief Points on the Contraception Furor

Jimmy Akin has argued for some time, quite plausibly, that the most authoritative censures of contraception by the Catholic Church are explicitly directed toward Christian married couples, and that the misconception that it is broader than this is due in part to bad information and in part to bad translation. He discusses one part of that argument here. There is in fact good reason to think that some of the reasons for rejecting the use of contraception in Christian marriage would also support the conclusion that at least much use of contraception outside of it would be rejected as well; but the extent of this has never been officially pronounced, and, indeed, has barely even been discussed.

As I've said before, Humanae Vitae is not on the subject of contraception but explicitly on the subject of how to have a marriage-friendly modern society, with contraception and other technological quesions being some of the major issues that come up as part of that problem. The conclusions about contraception there do not build on any simple argument, but on several complex strands: (1) the theology of marriage as a sacrament; (2) a single species-level point of natural law (which I've talked about here) along with natural-law precepts relevant to sex in a broader or more indirect way; (3) respect for the whole natural functioning of the human organism, which might be called the integrity of the rational animal; (4) a virtue-theoretical account of familial love, both between spouses and between parents and children, as part of human civilization; and (5) the function of marriage as a source of natural growth for the Church. It is not, in fact, difficult to find all of these points all over various pronouncements on the subject; but, except for very garbled versions of (2), one rarely finds any of it in summaries. It's very much a case of "What Everyone Knows" drowning out what is demonstrably the case. Catholics themselves have been major contributors to the confusion, including, unfortunately, Catholic priests of the kind who like to open their mouths before they use their minds (and reading skills!), although they are hardly the only ones to blame for it.

Actually, this sort of furor has been pretty common for quite some time now. The Church had almost exactly the same problems with the moral theology of truth-telling in the nineteenth century that it began to have with the moral theology of marital sex in the twentieth century; and while it surely says something about our society that the Victorian and Edwardian British were in this sort of furor over candour and we are in it over condoms, one still sees the same breakdowns of communication, the same kinds of deliberate misrepresentation in polemic, and the same steady attempt to oversimplify and drop all qualifications. And that was when the Church could build on Alphonsus Liguori, a far better expositor of natural law and virtue than any Catholics pontificating on the subject today. Modern moral theology is really in shambles; its expositors are in general simply not intellectually up to the task, and the relative few who are cannot do everything on their own. But even if they were, the problems would not go away; all the problems would arise because they result not from any particular content or failing but from the structure of Catholic controversy itself, and Catholic controversy we've had in one form or another for a very long time. (The Suburban Banshee gives a handful of other examples, for those who are interested.)

Cogito Ergo Sum II

Augustine, Soliloquies, Book II, Chapter 1:

Reason: Thou who wilt know yourself, do you know that you are?
Augustin: I know.
Reason: Whence do you know?
Augustine: I know not.
Reason: Feelest you yourself to be simple, or manifold?
Augustine: I know not.
Reason: Knowest you yourself to be moved?
Augustine: I know not.
Reason: Knowest you yourself to think?
Augustine: I know.
Reason: Therefore it is true that you think.
Augustine: True.

Cogito Ergo Sum I

Aristotle, Nicomachean Ethics (1170 / Book IX):

But if life itself is good and pleasant (which it seems to be, from the very fact that all men desire it, and particularly those who are good and supremely happy; for to such men life is most desirable, and their existence is the most supremely happy) and if he who sees perceives that he sees, and he who hears, that he hears, and he who walks, that he walks, and in the case of all other activities similarly there is something which perceives that we are active, so that if we perceive, we perceive that we perceive, and if we think, that we think; and if to perceive that we perceive or think is to perceive that we exist (for existence was defined as perceiving or thinking); and if perceiving that one lives is in itself one of the things that are pleasant (for life is by nature good, and to perceive what is good present in oneself is pleasant); and if life is desirable, and particularly so for good men, because to them existence is good and pleasant for they are pleased at the consciousness of the presence in them of what is in itself good); and if as the virtuous man is to himself, he is to his friend also (for his friend is another self):--if all this be true, as his own being is desirable for each man, so, or almost so, is that of his friend.