Thursday, March 31, 2011
Values and perspectivism
Life's worth
Wednesday, March 30, 2011
Short story
New York Times does free will
Tuesday, March 29, 2011
Olson on rate that time "flows"
Lies once more
John is married to Jane and knows her well; Jane is a brilliant philosopher. One day, Jane does something that really irks John and he tells her that she is an "idiot" out of spite.
John believes that what he said is false and that the norm of conversation to not make false statements is in effect. He seems to be making a "statement" when he says, "You're an idiot". But he doesn't seem to be lying.
Friday, March 25, 2011
The Abyss and the Tao
After Cantor recovered from a stint in the insane asylum for mental breakdowns suffered while trying to prove some (we now know) intractable problems in set theory, he had a stroll with his good friend and colleague Dedekind. Dedekind asked Cantor what he pictured in his mind when he thought of sets. Dedekind remarked that when he thought about a set, he pictured a clear bag containing objects inside which are the set's elements. Cantor responded that when he thought about a set, he pictured an abyss.
In a previous post I remarked that some abstract objects occupy space and have relevant properties of concrete material objects and thus there may not be any philosophical (epistemological or otherwise) problems in dealing with them such as knowing them or having them cause and be caused by physical phenomenon. In mathematics, we have pure sets built from the null set from iterative or otherwise “mental operations.” The old joke that the mathematical universe is an entire infinite universe begotten from nothing (the contents of the null set) is illustrative of the counter-intuitiveness of this idea.
Thus, as the story goes, from the null set, we have everything we need for mathematics. But since these objects of math are all purely abstract without concrete properties (as opposed to abstract objects with concrete elements) which may take part in the causal epistemological chain, how do we know them if e.g., the causal theory of knowledge is correct? If mathematics is built on such foundations, we cannot appeal to impure sets such as sets built on singletons of everyday objects to resolve these epistemological lacunae. Mathematics foundationally built in such a way thus may be metaphysically and epistemologically counter-intuitive to many precisely because of the knowledge problem or some other problems with causally inert properties of pure sets or the begetting of things from nothing. Metaphysically, it is problematic as the old joke suggests, it is a infinitely high house of cards built on top the foundations of an abyss. I want to ask here if there is another alternative system that is built on firmer and more intuitive metaphysical foundations.
Now consider the classical Chinese conception of numbers. Many philosophers of the school of names and the neo-Taoist school inspired by the I-Ching (such as Wang Bi) thought that from some object, we may, by some mental operation, form the class (they did not have a modern notion of set obviously but did have a notion of what we would term 'class') containing that object. Now we have two objects, namely the object and its singleton class. One can go on forming more and more objects this way until one has all the objects needed for one's numbers and thus to furnish one's mathematical universe. This would generate the positive integers instead of the natural numbers including zero as modern mathematics would have it. There is something to be said about the Chinese system; it is iterative like the modern conception of numbers but it starts off from one (the singleton set of some concrete object) instead of zero (the null set). This system is ontologically well-founded on something as opposed to nothing and is concrete "from the start." Specifically, what the Taoist founds his theory of numbers on, the original object on which all his classes are built on, is just the Tao.
More formally, we have according to the Taoist conception: Tao, {Tao}, {Tao, {Tao}}, {Tao, {Tao}, {Tao, {Tao}}}. Now, either the Tao or {Tao} may be arbitrarily designated as the number one.
Let's say that we choose the former. One is unlike the other numbers in that 1. it is not a class (set). 2. for all numbers n other than one contains n elements while one, not being a set contains no elements.
Or one can designate the Tao's singleton {Tao} as the number one. But then all subsequent numbers will contain the Tao which is not a number to generate all successive numbers.
Alternatively, one may have 1=Tao, 2={Tao}, 3={Tao, {Tao}}.
This last interpretation seems to be the one Wang Bi favored.
Significantly, as Wang Bi makes the point in both his Yijing and Laozi commentaries, in this sense “one” is not a number but that which makes possible all numbers and functions. In the latter (commentary to Laozi 39), Wang defines “one” as “the beginning of numbers and the ultimate of things.” In the former (commentary to Appended Remarks, Part I), he writes, “In the amplification of the numbers of heaven and earth [in Yijing divination] … ‘one’ is not used. Because it is not used, use [of the others] is made possible; because it is not a number, numbers are made complete. This indeed is the great ultimate of change.”
However, here, each number will contain n-1 elements instead of the Von Neumann formulation of modern mathematics which has for each number n, n elements.
Thus Chinese mathematics can be impure and would have no problems with the epistemological problem of knowing abstract objects built on the singleton of some concrete object. Everything that can be proven in the modern system of mathematics can be proven in the Chinese system per Lowenheim-Skolem theorem or one of its corollary theorems (since the two number systems are equinumorous and isomorphic). Zero thus is redundant for mathematics. There remains only orthographic problems of how to write numbers and mathematical formula down and the technique the classical Chinese used was to use a non referential “placeholder” in place of '0' or the cipher.
But this system is just as counter-intuitive as the modern for there are problems of its own. If I start off from the singleton set containing my computer and you start off from the singleton set containing your right foot, we would have two different notions of the numbers one and thus all subsequent numbers built on it. But 1=1 is true and it is necessarily true. Modern mathematics does not have this problem because it is easy to prove that there is one and only one null set and thus it and all numbers built on it are identical.
We may be able to obstruct this problem by introducing a single “arbitrary object” which can stand in for any object and starting from the singleton of it and define it as the number one. However, is this arbitrary object concrete or abstract? It might make sense to say of an arbitrary object that it is concrete or abstract with causal properties. I don't know. But if concrete where is this object? It may not have a specific location but since it could “stand in” for any concrete object, it may make some sense to ascribe to it causal properties even if it may be abstract much as the singletons of concrete objects. Kit Fine has defended arbitrary objects has having such common properties of concrete objects.
Alternatively, as pointed out above, Wang Bi and some of the other classical Chinese philosophers thought that the original object which one is is just the Tao, which in turn is itself not strictly definable and may be a ineffable "primitive" (I guess maybe like the term 'nothing' or perhaps 'arbitrary object') or its singleton. The Tao certainly seems to have causal properties and may certainly be said to influence causally the world on their conception whatever it may be.
Still, the Chinese system may not wholly escape some of the counter-intuitiveness associated modern math. It is only slightly less counter-intuitive than the modern system because instead of begetting the whole mathematical universe from nothing, it begets it from one thing. An infinitely high house of cards is built on the flimsiest of foundations instead of on an abyss.
Thursday, March 24, 2011
Hate speech
Tuesday, March 22, 2011
Infinite lives
Monday, March 21, 2011
Movie suggestion
Thursday, March 17, 2011
Meaning of life again
Saturday, March 12, 2011
Abstract objects and causation
Thursday, March 10, 2011
Wagering for one's soul and the possibility of Divine Evil
In the previous post, I mentioned that the “God” of the Bible is at least a possible, if not actual being that is very evil. If the description of him is empty, he is a possible being of some possible world (closest to ours with relevant changes) that fits the description. If he is an actual being and “God” of the Bible denotes him, the description may or may not be accurate. The Bible may be wrong about his attributes. He may not be the evil being he is described. In which case it may be that people have mistaken his attributes or it may be that he is actually an omnibenevolent being that has constructed the Bible as a kind of moral test for us. If we resist the Biblical version of him which is on many philosophical accounts is a description of an evil being, we “pass” and if we fall for it by worshiping the Biblical description, we “fail.” What is the consequence of these possibilities?
Consider these four possibilities. Either there is at least one evil being that fits the Biblical bill (henceforth, I will refer to this possible being as "Dog") or there is not. Additionally, either there is at least one omnibenevolent and omnipotent being or there is not (I will call this being just "God" not to be confused, of course, with the Dog which is the Biblical God). There are four total possibilities and they are mutually exclusive: there are at least one Dog that fits the Biblical bill but no God. That both exists. That God exists but Dog does not and that neither exists. In what follows, I will simply ignore the possibility of more than one of each kind of being (it will not affect the argument).
Many philosophers since Augustine have made maltheistic arguments against the Biblical (Abrahamic) God. If we are to interpret the Bible literally, we find that it's inescapable the conclusion, if we are rational, that the being called 'God' there is actually something monstrously evil. His actions in the Bible of causing/inciting/endorsing/ordering genocides, mass murder, "natural" catastrophes, child and wife killings, etc are well known. Even some of our Founding Fathers have remarked how despicable and evil the Abrahamic god is. Jefferson once said (paraphrasing) that a unbiased and reasonable man would have to conclude that the Biblical god is evil or a demon after reading it.
David Lewis in his paper, “Divine Evil” has gone even further in suggesting that the evils perpetrated in these well known examples from the Old and New Testament pale in comparison to the infinite evil of Divine Evil (for all former evils are finite while Divine Evil is infinite). Divine evil is the evil of punishing those to an eternity of suffering (damnation) for facile reasons such as vanity. Yet it is precisely for reasons such as vanity that the Biblical God has given in the Bible (and Koran) for sending people (many of whom presumably lived very virtuous lives) to an eternity of suffering. Making someone suffer infinite torment for an infinite amount of time for facile reasons constitute evil par excellence. It is hard to even imagine what could be more evil. It is infinite Divine Evil. I wholeheartedly agree with this Divine Evil hypothesis, that is, that the being described as the God of the Bible appears to be very evil.
Lewis uses the hypothetical example of a Nazi named "Fritz" to argue his case and who does not act in an evil manner but wholeheartedly supports the Nazi cause of invasion, aggressive wars, and genocide. He admires Hitler very much. Now most of us I think will consider Fritz very evil even if he has not done acts of evil. He is evil simply in virtue of endorsing and advocating those evil acts. He is vicariously evil. That was Lewis's main argument, that people can be vicariously evil in regards to obeying the Biblical commends to worship the evil Biblical being that sends people to torment for eternity for vain reasons much as Fritz can be evil just by admiring and endorsing Hitler. Notice that this vicarious evil need no real object to imbue it with its evil; even if Fritz is a brain-in-the-vat and the Nazi leaders and desired world he endorses is an illusion created by some neuroscientists, he would still seem to be evil in endorsing such evil illusions. Fritz, after all, has no control over whether his world is real or an illusion and if he is guilty of evil in a real world, he is so in a illusory world which is phenomenally identical to that real world. Whether he lives in a real world or an imaginary but phenomenologically identical world is a matter of luck outside of his control and which he presumable is not responsible for.
Assuming that Lewis's argument for the Divine Evil of the Abrahamic God is true, what has this got to do with us? Other than what it has to our moral status there seems to be prudential concerns we must also deal with analogous to Pascal's prudential arguments for believing (or trying to cultivate a belief) in his god.
If the the Abrahamic God is such an infinitely evil being, what prudential arguments analogous to Pascal's wager can we devise to take into account such a conclusion?
In the following table, I will argue in similar decision theoretic terms for what we should believe or disbelieve and maybe be against (that is, cultivate a antipathy or something like it) so that we may avoid eternal damnation and end up with the best chances at getting into heaven.
I have also avoided tricky technical issues with interpretation of the wager and with issues between infinite and finitary decision theory. Alan Hajek employs interesting methods using kinds of ordinal infinite numbers called surreals to remedy the usual problems associated with infinitary decision theory such as problems with mixed strategies (i.e., since run of the mill infinity is reflexive under multiplication of finite probabilities, any mixed strategy will yield infinite utility thereby making a mockery of Pascal's wager), and infinitesimal degrees of beliefs and Roy Sorensen uses more traditional conceptions of (cardinal) infinity to make the wager as fitting as possible to the tasks at hand.
One may also employ very large finite utilities to stand for heaven (and inversely, large negative utilities for hell) but I prefer the infinite strategies as it is closer to our religious and philosophical notion of the utility of heaven and hell but other problems with the nature of non standard uses of infinite numbers inevitably rear their heads making trouble for Pascal's interpretation of the wager as Hajek shows. Since juggling infinite utilities seems to cause technical trouble (tractable or intractable is a matter of dispute) so I will try to avoid such technical issues with the ambiguous utilities of -H (which is hell and may or may not be infinite negative utility) and +H will mean heaven (which may or may not be infinitely positive utility). I think the wager can still be analyzed rationally using just the notion of dominance from decision theory.
-H and +H, even if finite, will likely be under any plausible interpretation, very, very large utilities in opposite directions. One is to be avoided at nearly all costs and the other, desired at equally far reaching costs. I will use “Indeterminate” to be somewhere between these utilities as it is indeterminate what our reward/punishment will be under some such scenario. However, indeterminate leaning towards some direction (such as -H or +H) as it may be will lean towards that direction. So we have the current utility spectrum from least desirable to most (for us).
(-H) is less than (Indeterminate) is less than (+H)
I will use the palindrome "Dog" to denote the Biblical god and assuming that Lewis's argument for its evil is true (and in fact, it may be a sort of analytical truth that a being displaying those qualities are evil as I think Lewis would agree). I will also use "God" to denote a possibly existing being who really is omnibenevolent, omnipotent, omniscient, etc; this is the being with the properties traditionally thought to belong to God's. Thus my terms are:
Dog=Abrahamic/Biblical god=Devil
God=Omnibenevolent, creator...etc
I have assumed (much as Pascal and Hajek's versions of the wager) that your subjective probability for all these possibilities are positive (or all >0). The first three columns of this table denotes the possible situation when God is all powerful with ability to send people to heaven/hell but Dog does not have such powers, and this would correspond with many of our understanding of God and the devil. Dog may claim to hold such powers to be able to send people to heaven/hell as he does in the Bible (if the Divine Evil conclusion is true as we are assuming). The fourth and fifth columns represents possible scenarios where both God and Dog have powers to send us to -H or +H. We have the following 2 by 6 decision matrix:
| God & Dog exists | Dog only | God only | God & Dog exists (both equally powerful) | Dog only (Dog has power to send people to -H) | Neither exists |
Wager for Dog | -H | Indeterminate
| -H | Indeterminate (but leans towards -H) | Indeterminate (lean towards -H) | Indeterminate |
Against Dog | +H | Indeterminate | +H | indeterminate | -H | Indeterminate |
The columns represent these exhaustive possibilities. Either both God and Dog exists, or Dog exists but God does not or God does and Dog does not or neither exists (last column).
When God and Dog exists but Dog lacks powers to send us to -H (first column), it is prudent to wager against Dog. When Dog exists without God but Dog lacks the requisite powers to send us to -H (merely bluffing to, e.g.) as is the case in the second column, the results are indeterminate much as what happens when we die in an atheist's world. When both God and Dog exists and both are equally powerful, it is indeterminate who will get our souls but I am leaning towards -H for those who wager for Dog as both God may want to punish us for our vicarious evil in wagering for Dog and Dog may want to punish us just because he is Dog. He may repay our good turn for our wagering for him with an evil turn. He is evil after all! In that case, both God and Dog will agree on our fate. But he may also wish to reward us for our wagering for him but God may have other ideas as he may wish to punish us. Anyway, I am leaning towards Against Dog as the rational choice in this scenario even though I have labeled it indeterminate what our fate is if we so choose for that reason.
In the fifth column, only Dog exists and he has the power to send us to -H. If we wager for him, he may show us some good will and not send us to -H. But he may also lie (again, he is evil after all!) and decide to send us there anyway against his promises in the Bible to send all faithful to +H. If we wager against him he will certainly send us there.
The last column is where neither God nor Dog exists and in which case we just die and what happens to us is indeterminate or likely we just get a utility of nothing.
Notice the asymmetry. If we ignore the fifth column where Dog has the power to send people to -H and there is no God to check his powers, we have a decision matrix that is dominant for “Against Dog”. That is, if we ignore the possibility that Dog is the only power in the heavens without God to check his evil ways, we would be irrational not to wager against Dog. Even if that columns is true, we may only have little prudential reason to choose to wager for Dog as he might deceive us and send us to -H anyway. It makes sense that the devil pays a good turn with a bad one so given this there is little reason we should decide to wager for him even if this column is in fact the case. This (especially combined with the moral reasons) suggests we should wager against Dog.
Sunday, March 6, 2011
What does 'god' denote?
There are instances of "reference fixing" where a proper name is attached to a description and so that the proper name is rigid. Consider "'Hesperas' shall be the name of the brightest non lunar object in the evening sky." Hesperas is a rigid designator.
There are also cases of the use of descriptions to fix non rigid references to proper names such as the example given here.
You find an old painting. After engaging in some convoluted discussion about legal ownership, you decide to clarify your terms: “Let the expression ‘Originalowner’ designate, for any possible world w, the original owner in w of that painting” (you point at the painting). You have causally grounded ‘Originalowner’ by means of a baptismal ceremony; but the referent varies from world to world, depending on who first owned the painting. The term is not rigid.
If 'God' is empty in this world, there is a possible world (it seems to me, the closest possible world to our's with only the relevant differences) where the description of him given in the Bible holds. The name will attach to that being through the description. It may be a weighted description of conjuncts. His leading of Moses and the Jews out of Egypt, being the Creator, being very powerful etc may all be taken into account as the description describing him in that world.
So if 'God' is an empty term, it will still refer to a non rigid possibilum in that ceteris paribus world. Talk of him will be like talk of Santa Claus, etc, meaningful in some sense but strictly speaking, empty. All subsequent talk causally related to the term and through intention ("Allah" e.g.) will designate such a possibilum. This is how we can talk about possibilia and make meaningful distinctions between fictional "truths" and "falsehoods" (Santa Claus has a beard and Santa Claus is a mouse, respectively, for example) and how we know we are "talking about the same thing" in conversations about possibilia. I will talk about the implications of this talk of possibilia as it relates to the (actual) status of our souls and to Pascal's wager in my next post.
Saturday, March 5, 2011
Is life worth living for the hedonist?
Most have tried; but it seems that living such a life is a matter largely of luck. If so, the honest-with-herself hedonist must admit that it would be unwise to go on to live another life (or even to continue with her current life) as prospects that it will turn better for her so that she will live such a life or if she is lucky enough to currently live such a life, not turn bad at some later time is slim. She will also refuse to have children on such conclusions.
But is life worth living? Who will still want to go on living? Who will still have purpose under such bleak prospects? Who will still have meaning and value? It is precisely the Moral Saint or those who try to be one through cultivation.
Friday, March 4, 2011
Is there such a thing as excusable rape?
The law recognizes extenuating excuses such as these and often hands out much lighter sentences, sometimes replacing jail terms with long parole combined with psychological counseling. Our reactive attitudes of blame, indignation, anger etc towards these people also seem greatly attenuated.
But would we feel the same if we found out that many rapist may also rape because of uncontrollable passions? To my understanding, the psychological literature on rape is undecided at this point whether many who do rape do so because of uncontrollable urges and "passions" of this kind. If there are such cases, would we be justified in excusing partially or fully those who rape under such excuses? Some cases of rape such as some cases of statutory rape, the law recognizes as excusable for obvious reasons such as when it is reasonable that the rapist believed at the time the victim is of age. I'm not of course, talking about these obvious instances of excusable rape.
Tuesday, March 1, 2011
Of vices and rainbows
Now I think vices and virtues themselves are objective (they may be dispositions etc) but how are people in whole to be morally evaluated under such perspectival considerations? Are our attributions of moral worth like our seeing rainbows or are they more like seeing colors; that is, with a substantial personal coloring (no pun intended) but still objectively evaluable? If the later what standards will we judge people by? Maybe the lines will be shown to be wholly arbitrarily drawn. It may be that the lines and standards are dependent on the society to a large degree in that certain societies make becoming good (or bad) easier or harder and it is that standard that we have to measure people against (relative to the place and time they live under) but is this the kind of objectivity that will do the job for a robust moral realism?
One possible response to this kind of perspectivism is that we may have to orient our blame at character traits and motivations (ill or good will, etc) instead of individuals which may have varying degrees or combinations of good and bad traits. This would mean giving up of contempt for contempt seem to be an attitude fundamentally attached to persons as a whole and not merely character traits. But this seem to be at odds with our most deeply held intuitions concerning the seeming fact that there really are bad (or good) people in the world, not just bearers of traits which are bad (or good) and that that the bad does deserve something like contempt. The sacrifice to shift to that reorientation of our moral outlook may be too much to give up that intuition. It would also push to problem back to traits instead of persons for we can always ask what is the standard for minimal amount of combination of good vs bad traits for moral decency? Maybe only purely moral saints, those who are morally perfect, are the ultimate standard to avoid the arbitrariness of it all. I would hope for all of us that that is not the case.
Alternatively, we may wish to draw the lines at those who either endorse/identify or are against their vices or endorse/identify with their virtues. Those who do the later are deemed good persons while the former are deem bad. This would mean that many if not most people we now regard as good may actually be bad because they do not try to go against their vices and may even endorse or identify with many of them. But this would also save the distinction of good/bad people. However, I don't think this will do much as there are varying degrees of endorsing and identifying with one's vices and virtues, both in degree of strength of endorsing, how often it occurs consciously, and which vices and virtues we do so. So we may be back at where we started. Some people may be largely against their vices but do not identify with their virtues or vice versa. Some may only rarely consciously be aware of where they stand with regard to their values and moral beliefs. There are so many combinations that lines may have to be arbitrarily drawn.
Are racists today, in our society, worse than racists before?
This is because our culture has far more epistemic resources available to defeat racist views than 1930s Germany. Not only is information dispelling racist views much more common and available but the skills necessary to dismantle those views (and other views such as aggressive militarism, etc) are available to almost anyone who desires to acquire them. All one of reasonable intelligence needs to do is pick up a study a critical thinking book to acquire such skills. Holding everything else equal, the Bystander Nazi and the everyman/woman racist today, are not equal in their moral worth. You would have to display far more vices, especially ignorance, hatred, prejudice, lack of empathy, etc to be a racist today than someone in 1930s Nazi Germany. Since such a person has more vices, it is reasonable to see this person as more contemptible and blameworthy as well.