December 26, 2006 § Leave a comment
Consider the statement “Given logic L and factual premeses F, there exists a deductive proof P[i] for every true theorem D[i].”
This is not a claim of consistency. It is a claim of completeness. In fact it is probably a claim of inconsistency in disguise.
If logic L has the machinery to represent ordinary arithmetic, for example, this completeness claim asserts that either the given facts F are mutually inconsistent or that logic L is itself inconsistent.
When someone makes a claim of this form thinking that what he is insisting on is consistency, what he is in fact probably insisting on is inconsistency.
December 26, 2006 § 38 Comments
An Examined Life has up another post on the development of doctrine. I made the following comment in the combox there:
My only objection – and it is important to understand how narrow an objection it is – is to this claim:
Ultimately, however, anything that is accepted as de fide will have some deductive proof following from other irreformable doctrines and the theorems that can be derived from them.
I object to this claim precisely because it is in the same class of claims as David Hilbert’s postulate (disproven by Godel) about mathematics: that every mathematical truth must admit of a deductive proof from primordial axioms. (In our logic we substitute “is de fide” for “is true” in the metalanguage, and the game is immediately over**). (I am leaving out what would be a nontrivial discussion of the implications of ruling out abstract reasoning capable of performing Peano arithmetic here, but this is after all just a combox).
Specifically, I do not object to this claim:
My second assumption is that whatever the Church teaches, at any time in history, will be logically compatible with everything else the Church has ever taught, or ever will teach, at any point in her history.
There is a difference between a relatively weak assertion of logical compatiblity (inductive inferences are not ruled out by a requirement for logical compatibility) and the strong assertion of the existence of a deductive proof for every theorem (where inductive inferences, and indeed all inferences which are not a matter of mechanical application of the [some] rules of logic, are ruled out).
And interestingly, both of our “stakes in the game” here are the same: we are both attempting to understand DD in a way which avoids logical contradiction. If my understanding is correct, insisting on the existence of a deductive (solely deductive) proof for every theorem results in a logical contradiction.
** I didn’t say this in the comment at AEL, but this can be expressed unambiguously at the formal level by making every statement take the form “It is de fide that X”.
December 22, 2006 § 8 Comments
Scott Carson at An Examined Life makes the argument (assuming I understand it correctly) that doctrine develops only by applying deductive reasoning to a body of formally revealed facts and principles which were finalized at the time of the Apostles. I’ll call this position sola deduction. Mike Liccione at Sacramentum Vitae makes the case that there is more to the development of doctrine than just logical deduction from preestablished premeses.
It probably doesn’t surprise any of my legions of regular readers that I come down firmly on the side of Sacramentum Vitae and against sola deduction. The reason I come down against it is that sola deduction is a specific case of a much more general error; a general error which some may have noticed is a personal bugaboo of mine, the windmill of my personal Don Quixote. That windmill is positivism.
If all valid doctrines follow from turning the formal crank of deductive reasoning on the raw material of facts and principles established at the time of the Apostles, and doctrines so established are not underdetermined by that deductive reasoning, then the Magisterium can be replaced by a computer.
But the situation for sola deduction is even worse than is made clear by Mike’s argument, though Mike’s argument is in my opinion sufficient for his purposes. If we accept sola deduction on its own terms as a thought experiment, we ultimately (though not trivially) end up with a logical contradiction. An assertion of logic alone is itself quite literally illogical.
UPDATE: Scott Carson fires back, finding my comments not merely unhelpful but singularly so. The most critical thing I should clarify is that when I characterize Scott’s argument as saying that doctrine only develops deductively, I don’t mean that the actual discovery of doctrines by actual particular persons proceeds only deductively as an historical matter. That would be a manifestly silly thing to claim. What I mean is that (as I understand the criteria) once discovered, genuine doctrines must be derivable without underdetermination by deductive reasoning alone from some original fixed set of doctrines (oral or written) existant at the time of the Apostles. The “without underdetermination” bit means that this deductive proof or theorem for a given developed doctrine, which though not necessarily explicit must at least exist in principle, settles the matter over and against any competing claims to doctrinal truth which are inconsistent with it.
If that is what he means, my criticism stands as written. And if that isn’t what he means by his claim that legitimate development of doctrine must proceed solely by deduction (as far as I can tell he uses the term “non-ampliative” to mean “solely by deduction” in the sense I just clarified) to “establish the truth of any particular inference to the [logical] exclusion of all competing, non-consistent inferences”, well, then I really have no idea what he does mean.
Oh, and everyone have a blessed Christmas!
December 15, 2006 § Leave a comment
New posts from both Paul Cella (“For the patriot is a lover; and thus cosmopolitanism is adultery”) and Jim Kalb (“The Muslims still seem rather ham-handed manipulating public views. Maybe they should consult the gays?”)
UPDATE: And Lawrence Gage too: “…contracept[ion is] … degrading to women (insofar it severs a woman’s connection to the ineffable mystery of bringing forth new human life, and opens her to being seen as only a pleasure machine to satisfy men)…”
December 10, 2006 § 53 Comments
A little rule of thumb may be helpful.
If the thing we are talking about is actually done by someone else, it isn’t the object of your act.
Recent discussions have led me to conclude that the difference between the moral object of an act and formal cooperation with the acts of others has become confused in the minds of many.
Suppose I order Lieutenant Shaeffer to slaughter those civilians lined up over there. The object of my act is not to slaughter the civilians, and my act is not intrinsically evil: that is, my act is not evil because of the inherent nature of its object.
This is, I think, fairly straightforward to demonstrate.
Suppose for example that the Lieutenant and I have prearranged a code. When I tell him to slaughter civilians, what I am really preparing him to do is take down the wicked colonal who is telling me to give the order. Because of intentions and circumstances it is not evil for me to use my body to utter “Go slaughter those civilians”.
Demonstrably, then, there isn’t anything intrinsically evil in my act.
Now, if I intend for Lt. Shaeffer to actually slaughter those civilians and he does so, I have still done something terribly evil: evil because of my intentions, which include formal cooperation in Lt. Shaeffer’s intrinsically evil act. My act isn’t any less evil for not being intrinsically evil. But my specific choice to utter that specific order is not intrinsically evil.
Well, OK smart guy, but what about certain acts where it takes two to tango? What about adultery, for example?
The answer seems to me to be equally straightforward. I can’t commit adultery without choosing to perform the act of adultery – my necessary part in it – myself. If I order Lieutenant Shaeffer to commit adultery, intend for him to actually do so, and he does, my own act is not intrinsically evil. It is still evil – formal cooperation with evil, in fact – and may even be more gravely so than the Lieutentant’s act. But it isn’t intrinsically evil, and if the circumstances or my intentions were different it might not be evil at all.
If the thing being specified is not something you actually did, then the thing being specified is not the object of your act. It is probably the object of someone else’s act, and it may well be that your act is an act of formal cooperation with that other person’s act. But somebody else’s act isn’t your act, and the object of somebody else’s act isn’t the object of your act.
December 9, 2006 § 1 Comment
Broken clocks can be right now and then, but don’t let anyone convince you that modern environmentalism isn’t a pagan religion.
December 8, 2006 § 1 Comment
No, that isn’t one of her titles, as far as I know. But it should be. When you dig all the way to the bottom of sin, what you find is a lie. We tell lies to ourselves and that enables us to do things we shouldn’t. Mostly we do this – I know I do this – not because we don’t see the truth out of the corner of our eye, but because we are not brave enough to face the truth head-on. When we see that flicker in the corner of our eye we turn away. If we turn away often enough and strenuously enough we can even sometimes make that flicker go away. We are (I am) incapable, due to a fear of putting complete trust in God, of a simple unequivocal fiat.
But not Our Lady. By God’s grace through Christ she was conceived without sin: without the built in cowardice that leads to sin. She is the bravest of all of us: our light, our sweetness, our hope.
And we love you so, Mother.
December 7, 2006 § 23 Comments
Part of what my previous post was getting to is that there is a difference between choosing for there to be less of a particular evil and choosing one evil (considered to be the smaller one) over a distinct evil considered to be larger. It is never licit to choose evil, period**. It can however be licit to choose for there to be less of a particular evil; and indeed we should always be choosing to decrease the gravity of those particular evils we cannot eliminate entirely.
In a nutshell, it is licit to choose for there to be less of a particular evil, but it is not licit to choose the “lesser” of two or more evils.
** It can of course be licit to engage in remote material cooperation with evil. But it is never licit to choose evil.
December 6, 2006 § 26 Comments
A commenter at CAEI suggests that the non-partisan credibility of Catholic Answers would soar if torture was added to the list of non-negotiables in the CA Voter’s Guide. That is true, and I think it would be a good thing in general for the non-partisan credibility of CA to soar.
But that isn’t a good reason to add torture as a sixth non-negotiable. The only good reason to propogate the notion of six non-negotiables is if it is in fact true that there are six non-negotiables; specifically the six being propogated.
And note what it would not imply: it would not imply that it is OK to vote for a Democrat whose express policies include one or more of the non-negotiables over a Republican whose express policies include one or more (presumably different) non-negotiables. It would imply that if any candidate’s express policy is one of the non-negotiables, you may not vote for that candidate, period, even if that means staying home.**
And this is where it starts to get interesting. If there are in fact non-negotiables – and I think there probably are, though what makes voting for a candidate and his policy non-negotiably wrong is not yet clearly established – then voting in a way which chooses one non-negotiable over a different one is inherently proportionalist. What that implies is that modern democracy is a kind of lex orandi (or behavioral training ground) for the lex credendi of proportionalism.
In fact, perhaps even more interestingly, this last point is true even if, as an objective matter, there is no such thing as a non-negotiable in the act of voting. If people believe themselves to be choosing a lesser of two evils they are training themselves to choose the lesser of two evils. And training ourselves to choose the lesser of two evils is, itself, an evil thing to do.
** Unless and only unless all other available options are also identically wrong on each and every one of the non-negotiables. This is a pathological (in the mathematical sense) situation which occurs so rarely that it can be discounted as nonexistent, unless it happens to be the case that the number of non-negotiables is very small and the number of races and candidates is also very small. At some point I may develop another post to show quantitatively that as the number of non-negotiables, races, and candidates go up the number of races it is licit to vote in at all (at least for a major party candidate***) becomes a very small percentage of the total number of races.
*** This qualifier sidesteps the argument that voting in protest for a third-party candidate you do not expect to win is a different kind of act from voting for a major-party candidate you intend to actually win.
December 5, 2006 § 1 Comment
In a comment on Jimmy Akin’s blog explaining my understanding of torture and why I think it may be more accurate than a few other proposed definitions (reasonable definitions to which I do not take exception as inherently proportionalist) I wrote:
So the composition of the choice “make him suffer” and it’s moral quality “as a thing not a person” is what makes the object evil, thus making the act intrinsically evil.
The object of the act is your specific choice of behavior (which JPII states “cannot be separated from its bodily aspect”), independent of why you choose to do it. It is, indeed, the very place where free will meets reality and has its immediate effect on reality. Given the difficulties in defining free will discursively – philosophers have tried to do so for millennia and failed – it isn’t surprising that people struggle with putting this into words. Assuming that it can be put into a “definition” with “criteria” is, if not understood correctly, already to make an error.
If you don’t believe me, try to make a specific definition of “greenness” as experienced by a conscious person.
Because it is nevertheless, like “greenness”, something we all experience quite directly. So talking about it indirectly is all we can do on the one hand, but on the other hand it is a part of all of our universal experience.
Despite the obscurities – obscurities driven in part by our modern positivist and scientistic tendencies (and thus obscurities which would not necessarily have been thought of as such in the classical tradition) – we still can get a pretty good understanding discursively. Words are powerful things for communicating meaning, even though (or perhaps because) positivism is dead. So it is possible to talk about these things and even specify them in a sense, but not in a positivist sense.
An act is intrinsically evil when it is, in its chosen object, opposed to the truth about Man. The object is the acting subject’s immediate choice of behavior. “Inflict suffering” isn’t an object at all in itself: it raises and does not answer the question “inflict suffering on what?”
For example, we might inflict suffering on a dog, or a beetle, or a man. And it is wrong to do so, always and everywhere, whenever there is a lie built into the object: whenever the object is by its very nature opposed to the truth about Man and God. When a perpetrator chooses to torture a man, the thing he is choosing to make suffer is not a man in his understanding as he makes that choice: that is, if he is treating that man as nothing but raw materials for producing a fungible commodity, there is a lie built into the object of the act.
Now we’ve already established (or at least claimed) that it isn’t possible to determine the object of an act solely by reference to direct external observation. And it isn’t: as JPII says, in order to grasp the object of the act it is necessary to place onesself in the perspective of the acting subject, in addition to taking into account its physical dimension. But for the sake of positive law we can indirectly ask questions which can tell us if the “as a thing not a man” quality is present in the act: not to a point of logically deductive discursive certainty, but to a point where we can make and enforce external rules (which are different in kind from the natural and divine law, since these rules we are making are only formal third-party rules). So we can make and enforce a law which says that failing to stop at a red light results in a ticket, even though it is literally impossible to discursively define “redness” and it is impossible to directly observe whether or not the acting subject chose to ignore the truth of that redness. And we can make a law which says that making a captive suffer just to get something you need from him, external to due process and legitimate punishment, is itself punishable by court martial; we can do this even though we can’t discursively define “treating-a-person-as-an-objectness”.
In fact we have made and ratified such laws. Some of them are generally referred to as “The Geneva Conventions”.