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.