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.
Tuesday, November 30, 2010
Cogito Ergo Sum V
Augustine, Enchiridion, Chapter 20:
Monday, November 29, 2010
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:
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.
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.
Sunday, November 28, 2010
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.)
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.
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