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Category: Philosophy

The philosophy of science, empiricism, a priori reasoning, epistemology, and so on.

October 16, 2018 | 4 Comments

Gödel And The Limits of Rationality

From the conclusion of “Cantor’s Diagonalization Method” by Alexander Kharazishvili (and I’ll assume the reader has some familiarity with Gödel’s famous theorems):

Tarski’s theorem leads to Gödel’s first incompleteness theorem. Let Pr denote the set of natural numbers corresponding to the provable sentences in formal arithmetic. Pr is recursively enumerable. Since any recursively enumerable set of integers is arithmetical, Pr cannot coincide with Tr [“the set of all natural numbers that correspond to those sentences true in the standard model of formal arithmetic”]. It can only be a proper subset of Tr. Truth and provability are not the same. That this discovery was revolutionary hardly does justice to its significance. Thus, there is a sentence S that is true, but not provable, in the standard model of formal arithmetic. Neither S, nor its negation, ¬S, is provable and formal arithmetic is incomplete. A similar argument is applicable to any recursive mathematical theory that is stronger than formal arithmetic (e.g., ZFC set theory).

We’ve talked about this many times: the idea that reason and rationality are enough, or are the ultimate (as in best) form of thought, are obviously false ideas. They are useful and necessary, but alone they are insufficient.

Reason, in the way I am thinking about it, is almost mechanistic. It takes a pile of thoughts, processes them by known rules, and spits out ideas. The processing is like a machine, which can be souped up or in poor repair. However complex it is, it isn’t anything more than brute mental force.

The ore at the base of the pile of thoughts must be supplied from outside. Reason needs fuel it can’t provide itself. Reason operating only itself is like a perpetual motion machine, an impossibility.

It is not reason that concludes Reason is reasonable. It is not Reason that proves truths that cannot be proved by Reason. “Truth and provability are not the same.” Provability by Reason, that is. Proof by other mechanisms is still possible; indeed, necessary.

All mathematics proceeds from two things: (1) unproveable-by-Reason propositions (axioms) and (2) unproveable-by-Reason belief Reason will work to generate new true propositions. This sequence does not apply to mathematics alone, but all thought.

Therefore there must be something beyond Reason providing our deepest and most consequential truths.

October 14, 2018 | 5 Comments

Summary Against Modern Thought: You Need God To See God

Previous post.

You can’t do everything on your own: be sure to first review last week for an understanding of what that means.

THAT NO CREATED SUBSTANCE CAN, BY ITS OWN NATURAL POWER, ATTAIN THE VISION OF GOD IN HIS ESSENCE

1 However, it is not possible for any created substance, by its own power, to be able to attain this manner of divine vision.

2 Indeed, a lower nature cannot acquire that which is proper to a higher nature except through the action of the higher nature to which the property belongs. For instance, water cannot be hot except through the action of fire. Now, to see God through His divine essence is proper to the divine nature, for it is the special prerogative of any agent to perform its operation through its own form. So, no intellectual substance can see God through His divine essence unless God is the agent of this operation.

Notes Hence, “if you seek Him you have already found him.”

3 Again, the form proper to any being does not come to be in another being unless the first being is the agent of this event, for an agent makes something like itself by communicating its form to another thing. Now, it is impossible to see the substance of God unless the divine essence itself is the form whereby the intellect understands, as we have proved. Therefore, it is not possible for a created substance to attain this vision, except through divine action.

4 Besides, if any two factors are to be mutually united, so that one of them is formal and the other material, their union must be completed through action coming from the side of the formal factor, and not through the action of the one that is material. In fact, form is the principle of action, while matter is the principle of passion. For the created intellect to see God’s substance, then, the divine essence itself must be joined as an intelligible form to the intellect, as we have proved. Therefore, it is not possible for the attainment of this vision to be accomplished by a created intellect except through divine action.

Notes This ties to what we have been saying about the highest forms of knowledge, i.e. that which comes directly from God, as insight or (sometimes) intuition. I.e. induction, of a sort.

5 Furthermore, “that which is of itself is the cause of that which is through another being.” But the divine intellect sees the divine substance through itself, for the divine intellect is the divine essence itself whereby the substance of God is seen, as was proved in Book One [45]. However, the created intellect sees the divine substance through the essence of God, as through something other than itself. Therefore, this vision cannot come to the created intellect except through God’s action.

6 Moreover, whatever exceeds the limitations of a nature cannot accrue to it except through the action of another being. For instance, water does not tend upward unless it is moved by something else. Now, seeing God’s substance transcends the limitations of every created nature; indeed, it is proper for each created intellectual nature to understand according to the manner of its own substance. But divine substance cannot be understood in this way, as we showed above. Therefore, the attainment by a created intellect to the vision of divine substance is not possible except through the action of God, Who transcends all creatures.

7 Thus, it is said: “The grace of God is life everlasting” (Rom. 6:23). In fact, we have shown that man’s happiness, which is called life everlasting, consists in this divine vision, and we are said to attain it by God’s grace alone, because such a vision exceeds all the capacity of a creature and it is not possible to reach it without divine assistance. Now, when such things happen to a creature, they are attributed to God’s grace. And the Lord says: “I will manifest Myself to him” (John 14:21).

October 9, 2018 | 11 Comments

“Doctors” Suggest Hacking Up Live Patients For Their Organs, Then Killing Them

The paper in the oh-so-prestigious New England Journal of Medicine is “Voluntary Euthanasia — Implications for Organ Donation” by Ian M. Ball, Robert Sibbald, and Robert D. Truog, a couple of docs and somebody else. We shall see that this paper at least proves knowing the knee bone is connected to the thalamus, or whatever, does not train one especially well to make ethics decisions.

Now doctors don’t kill patients, except by accident or neglect. Executioners kill people by design, on purpose, and with no legal culpability. When a person who was formally a doctor on purpose or by design kills somebody (and is not in the military engaged in war and such like), he is no longer a doctor but an executioner. You can never again have the same trust you had in this individual that he has your best interest in mind when you suspect he might be smiling at you because he likes the shape of your liver.

Doctors, as I know by many, many years association with them, really do think well of themselves. Because they are, mostly, engaged in enhancing and saving lives, this excess ego can be forgiven them. Unless it causes them to start believing their own press.

We can look to doctors regarding the ethics and morality of organ donation in the same way we look to physicists about the capabilities of nuclear weapons. The physicist can tell us what will happen, and of the nature of the effects, but the physicist is in no way especially competent to say when and under what circumstance such weapons should be used. Physicists are not moralists. Neither physicians, though they do gain some practical experience in the area.

This means we cannot leave physicians to themselves to decide what is best and what worst and what is anathema about killing somebody to take their organs. For the least proof of this we see that few or no doctors yet (to my knowledge) have embraced the term executioner, even as they advocate the active killing of patients.

Secondly, they never say killing and always employ a euphemism. Euphemism, except for comedic effect, always indicate somebody is hiding something. The euphemism (in this paper and elsewhere) “voluntary euthanasia” is interesting. Why the “voluntary”? Why its emphasis? (These are rhetorical questions.)

If you’re in the market for used spleens, you can’t be thrilled when a spleen holder dies at home, far from a hospital and its facilities for spleen removal. Bodies left to linger for even small amounts of time are like fish left in the sun. First thing you can do, then, if your hunger for used spleens is to encourage people to come to (warm, quiet) hospitals to die. Dying, it seems, requires expertise (just like births). The authors of this paper do not say “Do not die at home”, but the bias for a hospital death is there.

The dead donor rule — a traditional ethical principle guiding organ procurement — states that vital organs may not be retrieved before the patient’s death and that the procurement of organs may not cause the patient’s death. This principle assures patients and the public that physicians will be bound to the interests of their patients before the interests of potential organ recipients.

The dead donor rule doesn’t do that for me, because of the suspicion a doctor turned executioner will hasten the patient’s death. Assisted suicide is the euphemism. Our authors aren’t keen on the rule, either, because of the possibility of spoilage (my emphasis) done by the killing method.

Although some patients may want to be sure that organ procurement won’t begin before they are declared dead, others may want not only a rapid, peaceful, and painless death, but also the option of donating as many organs as possible and in the best condition possible. Following the dead donor rule could interfere with the ability of these patients to achieve their goals. In such cases, it may be ethically preferable to procure the patient’s organs in the same way that organs are procured from brain-dead patients (with the use of general anesthesia to ensure the patient’s comfort).

Whose goals? Drug ’em up and start cuttin’. What can’t be used is easily disposed of.

Patients who want a rapid, painless, and peaceful death while optimizing the number of organs they can donate are best cared for in an operative setting, where they can be fully anesthetized and where optimal organ procurement is supported.

There’s the death-in-hospital preference, even for patients the doctors kill.

The authors also recognize the idea of “non-therapeutic practices” has to be jettisoned. Pumping chemicals into a body you’re about to go shopping in is not by definition therapeutic.

Well, once you’ve given up on the idea physicians should do no harm, abandoning the rest of traditional medical ethics is far less painful.

October 8, 2018 | 15 Comments

Proof Cause Is In The Mind And Not In The Data

Pick something that happened. Doesn’t matter what it is, as long as it happened. Something caused this thing to happen; which is to say, something actual turned the potential (of the thing to happen) to actuality.

Now suppose you want to design a clever algorithm, as clever as you like, to discover the cause of this thing (in all four aspects of cause, or even just the efficient cause). You’re too busy to do it yourself, so you farm out the duty to a computer.

I will take, as my example, the death of Napoleon. One afternoon he was spry, sipping his Grand cru, and planning his momentous second comeback, and the next morning he was smelling like week-old brie. You are free to substitute this event for one of your liking.

Plug into the computer, or a diagram in the computer, or whatever you like, THE EVENT.

Now press “GO” or “ACTIVATE” or whatever it is that launches the electronic beastie into action.

What will be the result?

If you said nothing, you have said much. For you have said your “artificial intelligence” algorithm cannot discern cause. Which is saying a bunch. Indeed, more than a bunch, because you have proven lifeless algorithms cannot discover cause at all.

End of proof.

“Very funny, Briggs. Most amusing. But you know you left out the most important element.”

I did? What’s that?

“The data. No algorithm can work without data. It’s the data from which the cause is extracted.”

Data? Which data is that?

“Why, the data related to the event your algorithm is focused on.”

Say, you might be right. Okay, here’s some data. The other day I was given a small bottle of gin. In the shape of a Dutch house in delft blue. You weren’t supposed to drink it, but I did. In defense, I wasn’t told until after I drank it that I shouldn’t have.

“What in the name of Yorick’s skull are you talking about? That’s not data. You have to use real data. Something that’s related to your event. What’s this Dutch gin house have to do with that?”

Well, you know what Napoleon did in Holland. And what’s my choice have to do with anything? We want the algorithm to figure out the cause, not me. Shouldn’t it be the business of the algorithm to identify the data it needs to show cause?

“I’m not sure. That’s a tall order.”

An infinite one, or practically so. Everything that’s ever happened, in the order it happened, is data. That’s a lot of data. That tall order is thus not only tall, but impossible, too, since everything that’s ever happened wasn’t, for the most part, measured. And even it if it was (by us men), no device could store all this data or manipulate it.

“Of course not! Why in the world are you bringing in infinity and all this other silly business? You can be obtuse, Briggs. No, no. The data we want are those measurements related to the event you picked.”

Related? But don’t you mean by related those measures which are the cause of the event, or which are not the direct causes, but incidental ones, perhaps measures caused by the event itself, or measures that caused the cause of the event, and that sort of thing? Those measures which a prominent writer called in his award-eligible book (chap. 9) “the causal path”?

“They sound like it, yes.”

Then since it is you who have partial or full knowledge of the full or partial cause of the event, or of other events in the causal path of the event itself, isn’t it you and not the algorithm that is discerning the cause? Any steps you take to limit the data available to the algorithm in effect makes the algorithm’s finding of cause (or correlation) a self-fulfilling prophecy. By not putting in my gin means you are going all the work, not the algorithm. It means you have figured out the cause and not the algorithm. That makes the cause in your mind and not the data, doesn’t it?

“Perhaps.”

The best any algorithm can do is to find prominent correlations, which may or may not be directly related to the cause itself, using whatever rules of “correlation” you pre-specify. Your algorithm is doing what it was told in the same way as your toaster. These correlations will be better or worse depending on your understanding of the cause and therefore of what “data” you feed your algorithm. The only way we know these data are related to the cause, or are the cause, is because we have a power algorithms can never have, which is the extraction of and understanding of universals.

“I guess.”

And all that that is even before we consider predictive ability or, more devastating to your cause (get it? get it?), under-determination, Duhem, Quine, and all that. The idea that even if we think we have grasped the correct universal, and have indeed used our algorithm to make perfect predictions, we may be in error and that another, better, explanation is the truly true cause.

“That seems to follow.”

Then it also follows is that the only reason we think algorithms can find cause is because we forgot the cause of causes, or rather the cause of comprehending causes, which are our own minds.

Note that this explanation, which is a proof, does not explain why most use algorithms in the hope of finding “causes” to repeated events, or events which are claim to be repeated. That’s a whole ‘nother story, which involves, at the end, abandoning the notion probability is a real thing.