Values and perspectivism

There was once a famous person (forget who) long ago that remarked that if music could some how be recorded and available to everyone, life would be all glory and rose petals for everyone. It would be utopia. But we know that ain't so. The universal availability of music has not made life heaven on earth. As soon as something desired is widely available, its value in our eyes seem to diminish according to some pattern or other of diminishing return. I think behavioral economists have names for this but I don't know what the literature on it is.

Now consider if we are to solve all of the world's most pressing issues of global injustice, energy problems, racism, sexism, etc. Maybe other problems which we may not see as that pressing now would take their place in our valuation systems. We might develop irrational fears of death even from old age or disease, etc. We may even develop whole new neuroses we can imagine fretting over now. Our value structures would change and problems once that pressing might not be seen as such and problems not so pressing relatively speaking. Alternatively people in the future may see our present concerns as neurotically intense or even irrational compared to theirs.

My question is that does this perspectivism threaten the claim that values are objective and non arbitrary? If so How far does it go in that direction? Will we see all our current worries as just neuroses? Maybe all of our values are arbitrary and largely determined by perspective. That would harm claims that go to the heart of the good life it seems by making all conceptions seem trivial.

Life's worth

It seems to go against many of our egalitarian and liberal sensibilities for someone to say that a person's life is inherently more valuable than another's. However, some of our intuitions seem to suggest that we do hold this. Mine for example, in a hypothetical where Confucius's life is compared to the typical Nazi's. I will choose Confucius's life and moreover, I believe that my decision is justified. That is, that Confucius's life is worth more. There may be many situations, plausible ones, that may obtain in real life where lives are in the balance in such a way that we may have to choose (consider who gets a rare vaccine for some disease) which is more worthy of being saved even apart from practical or consequentialist considerations. Now many of us are hesitant to value lives but this may be because of limitations on epistemological considerations and for the fact that most people are relevantly equal on many aspects up for consideration in valuating lives. I suspect that moral worth is paramount in such weighting. If souls were more transparent, our intuitions may not be so egalitarian.

Short story

Inspired by a conversation with Carl on the comments section on one of the posts.

When Cantor was on his death bed, still haunted by the ghost of the continuum hypothesis, the Devil appeared by his bedside. The Devil wanted Cantor's soul and offered him this deal: your soul for the truth of the continuum hypothesis. Cantor agreed on the condition that he stipulates the condition of his time in hell. He wrote his demands in a sealed envelop and gave it to the Devil only to be opened after the Devil tells him the secret that has racked Cantor's professional life. The Devil knew that hell was a place of infinite durations of suffering and knew that Cantor knew this as well so what can Cantor stipulate in his demands that would make this deal not go terribly bad for Cantor? Because there are few logicians and philosophers in hell to enlighten him, the Devil agreed.

The Devil tells Cantor the truth of the Continuum Hypothesis which the Devil stole from God's math notebooks (the Devil could not have came up with the truth of it himself due to his lack of mathematical and logical training). Cantor then dies a happy man with the truth of the CH. While in hell, the Devil sees Cantor and is about to stick his pitchfork into him. Cantor reminds him of their agreement so the Devil opens the envelop to see what stipulation Cantor had for his permanent stay. It read:

1. I am to have one minute of joy without being tortured for every 100 years of being tortured.

2. I am to have all my moments of joy consecutively.

3. I am to start on a minute of joy.

New York Times does free will

The NYT has an article by John Tierney on free will and X-PHI. It's a shame that though the article mentions that most philosophers today ascribe to various versions of compatibilism, it fails spectacularly by not giving the substantial reasons why philosophers do so. This may have the effect of making the NYT reader think that philosophers are a wishy washy bunch who's capricious beliefs are dependent on extra rational processes and are out of touch with the latest science. There is no mention of the quality of will approach, the reflective self-control approach, the higher self approach and the dispositionalists approach or any contemporary compatibilist approach all of which are compatible with the truth of determinism.

Of course there are some weaknesses to all these approaches but that doesn't mean they do not provide very good reason philosophers have for supporting compatibilism. These positions can be explained so that any reasonably intelligent and educated person can understand them which I suspect many readers of the NYTs are but they may very well be well beyond the scope of the journalist in question.

Olson on rate that time "flows"

Some philosophers have taken the metaphor of time's flowing to be literal. But does time flow and if so how fast does it flow? Some philosophers have said it must flow at exactly one second per second!

Eric Olson responded to this claim in his paper, "Rate of Time's Passage". His counter argument basically says that it is impossible for time's flow to pass at one second per second because rates of anything is a ratio between two values. In the case of one second per second, you would not get a rate (because the second units would cancel) and you'd be left with just a number as quotient, namely one, which is not a rate of anything. Olson concludes from this that not only does time not flow but that any A-theory of time must be false because A-theories entail times passing at some rate or other.

This doesn't seem like a good argument at all. The reason why we cannot gauge time's passage as a quantifiable rate is because we have no standard to measure it against. The rate of change for anything (movement, temperature etc) can be measured against certain standards such as the movement of the clock's hands but what will we gauge the passage of time against?

Olson anticipates this answer and says that it is no good because we can use time to gauge its own passage such as we can use something's length to know its own length but it would still turn out to be nonsense by getting numbers instead of true rates. He says that it makes sense to say that the Standard Meter is one meter long and we know this because it is the same length as itself.

Here's my response: First of all, length is not a rate, it is a property of the thing itself (a genuine property in fact). Rates are comparisons or relations between events so right off the bat, there is a false analogy. Second, if we had a suitable measure for time's passage such as a "supertime" we could gauge time's passage or flow against supertime and get something like 1 second per supersecond which is a rate and not a number because the units do not cancel since they are in different units (time vs supertime). But what wouldn't supertime need a supersupertime to use as a standard to measure the flow of supertime and so on ad infinitum? No. Because supertime may use time as a standard; it's arbitrary what we will use. Third, scientists use time to gauge time's passage all the time without any problem.

Consider relativity. I am at rest relative to you and you are on a fast spaceship going to Mars. For every 4 seconds my clock registers, your clock registers only 1 second (time dilation). Call my inertial reference frame R1 and yours R2. In this case, your clock passes at .25 seconds per second (you can use the Lorentz transformation to calculate how fast you'd have to go for this time dilation to occur). But the "seconds" in the divisor and dividend do not cancel because they are relative to different inertial reference frames. We get something like .25 R2 sec per one R1 sec and that is not problematic at all.

We cannot gauge time's passage as a whole because we have no available and suitable standard but that doesn't mean there is no possible one. The problem is analogous to the old ponderous childhood puzzle of if everything became twice as large at the same time, how would we know? In this case, if everything flowed at twice its normal rate (assuming there is a normal rate), how would we know? That's an epistemological problem to be resolved with the appropriate standards.

Lies once more

I once mentioned that some philosophers of language such as Don Fallis and Roy Sorensen seek to replace the traditional philosophical conception of lying which includes an intentional deception as a criteria with an intentional violation of a Gricean norm. What prompted them to do so? It's the counter example of bald-faced lies. Bald-faced lies. One commits a bald-faced lie when when is not attempting to deceive anyone such as the case of the person on the witness stand saying "I don't know, nothin'" when everyone in the court including herself knows she knows who did it but don't want to incriminate the defendant (presumably because the defendant has threatened her). Fallis' definition of lies are as follows:

You lie to X if and only if: (BNL)

1. You state that p to X.

2. You believe that you make this statement in a context where the following

norm of conversation is in effect:

Do not make statements that you believe to be false.

3. You believe that p is false.

However, here's a counter example:

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.

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.