Showing posts with label logic. Show all posts
Showing posts with label logic. Show all posts

Thursday, July 30, 2009

The "ultimate" articulation of a nihilist's ethics in a floating opera


Here's a rather seductive argument that I just read in Barth's The Floating Opera, a wonderfully nihilistic novel about Todd Andrews intellectual descent into the wrath of his own mind.

I recommend it as a read if you're into cynicism. Anyway, his logic, in the final chapters, is certainly noteworthy:

<-- begin -->

I. Nothing has intrinsic value

II. The reasons for which people attribute value to things are always ultimately irrational


III. There is, therefore, no ultimate "reason" for valuing anything (including life).


IV. Living is an action.


V. There's no final reason for action (just as there is no final reading for valuing anything).


VI. There's no final reason for living.


<-- abyss -->

Questions raised:

1. Is 'value' a valuable concept?
1.1 Do we need 'value' to have will? In other words, does Andrew's rhetoric destroy our will to power? Our will to anything?
2. What are intrinsic qualities of anything? Mustn't intrinsic qualities be ascribed by the very people who claimed those qualities to be intrinsic?

3. What is an "ultimate reason" at all if there are no "intrinsic qualities"?
3.1 Ultimate reasons are indeed meaningless if there is nothing to be ultimate about them (this isn't a question I realize)
4. Can reasons for actions be relative instead of ultimate?

5. If there's no reason for living, is that necessarily a good reason for not-living?


The first to refute this argument, on logical or rational grounds, gets a present.


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Friday, June 26, 2009

Forking Hume


Today I find myself wrestling with Hume's fork - a wonderfully cogent skeptical argument that suggests there can be no certainty in our statements about the world. Hume dichotomizes all propositions into two types; first there are statements about ideas, which are analytic in nature, and knowable through logic and deduction. Kant would later dub these statements (such as "1+1 = 2" or "all men are mortal") a priori, or knowledge that can be known in absolute certainty without empirical (worldly) experience.

The second kinds of statements are statements about the world, such as "the sun rises in the east" or "gravity makes rocks fall to the earth." These types of statements are synthetic, a posteriori propositions. A posteriori knowledge comes from empirical data - as we watch the sun continuously rise in the east, or rocks fall to the ground, we come to see the truth in these statements to the extent which they square with our future expectations of the world.

Future expectations, in this case, are the key to understanding why Hume was such a skeptic. In order for us to claim that "every rock dropped will hit the earth" we, of course, need the premise "every rock I've ever dropped has hit the earth." We also need another premise, one Hume is not willing to grant us, and rightfully so.

Hume argues that, implicit in all synthetic a posteriori claims, is a premise that the future always resembles the past. Ironically, we come to realize empirically that this isn't true, and therefore if I can't say with any certainty that the future will resemble the past, I have no good reason for expecting the rock to fall to the ground the next time I drop it. If you were to rebuff me and say "Gravity will always pull the rocks down", I could just as easily say to you "and how do you know that gravity will act the same in the future as it has in the past."

Ultimately, Hume forces us to realize that intrinsic to any of our expectations that we claim to know about the world is a degree of hopeless faith which ostensibly says "I believe that I know X because I have faith that all previous occurrences of X will resemble all future occurrences of X." How ridiculous, in this sense, it is to say that you know that the rock in your hand, when dropped, will fall to the ground, because you believe that this rock, and all rocks that have been dropped and will be dropped, act the same? Surely this is not now we want to go about claiming to "know" things...

So I'm left with a logical argument that makes perfect sense but with consequences that make me very unhappy. According to Hume, statements about ideas (a priori), may be certain, though they cannot truly pertain to the world. This is because we cannot be completely certain about anything in the world, and hence, if we are certain that "a triangle has three sides", we can also be certain that this tells us nothing about the world.

On the flip side, if we cannot be certain of statements about the world; we cannot use our ideas and analytics in matters of fact. Abstract relationships, therefore, cannot be consistently used to express or evaluate material objects/process. What does this mean for physics and applied math? Does this invalidate the very strength of empirical science?

Or does this, once and for all, settle the argument that philosophers are truly useless to the world, just as much as the world is useless to philosophers? I'll leave the conclusions up to you... suffice to say, Hume forked us good.

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Wednesday, June 24, 2009

A Rejection of Carnap's Rejection of Metaphysics


Rudolph Carnap is one of my favorite logical positivists because he is able to write passionately and with conviction about numbers, symbols, and form. Yet one of his most important seminal works - "The Rejection of Metaphysics" - is not without its own metaphysical problems. For better or for worse, here's some criticism:

Ruling out the possibility of a fact-only world
(Pardon the format; Wittgenstein has been rubbing off on me.)

Carnap's argument:


1. All facts, as we regard them, must be always be True to be facts.

2. Anything that is not a fact, say an opinion or conclusion, might still be interesting, but cannot have an objective meaning.
2.1 Without objective meaning, there can be no definite 'sense' ~ i.e. the same thing is not meant by the statement every time
3. Opinions, Reflection, and Convictions (as with other types of non-facts) hence do not have any 'sense.'
3.1 This is not to say that they can't have sense, just that they don't. The 'sense' of a non-fact can change depending upon context
3.1.1 Take for instance the opinion that 'Drugs are bad.' This has no anchored sense; I could be talking about legal drugs, illegal drugs and the sentence would
change if I was saying it in a counselor’s office or at a frat party.
4. If we are concerned with facts, we are concerned with separating facts from non-facts that appear as facts.
4.1 A fact might be 'the sky is blue' a non-fact that appears as a fact might be '"LSD can save endangered species.'

5. All facts must be verifiable in order to qualify as facts.
5.1 The only way we can identify facts, as such, is by testing them empirically.
5.1.1 If we want to test whether or not the sky is blue, we can take pictures of it, ask people, look at the sky, compare the sky's blue to other blues, etc...
6. If only facts can have sense and meaning, and we can only identify facts by empirical means, all facts can only be proven empirically.
:. (therefore)
7. 'Facts' presented as such (such as 'moral facts') which are not empirically demonstrable, testable, or otherwise observable cannot be qualified as 'facts' because they cannot necessarily be proven as facts need to be proven.
:. (therefore)



8. Metaphysical truths, moral facts, epistemological claims, psychological analysis, and all other opinion-driven intellectual pursuits are therefore not facts, and therefore do not have any objective meaning or anchored sense.


My Refutation:

Let's start with Carnap's conclusion, and then work backwards to his definition of fact

1. " 'Facts' presented as such (such as 'moral facts') which are not empirically demonstrable, testable, or otherwise observable cannot be qualified as 'facts' because they cannot necessarily be proven as facts need to be proven. "

2. If the above statement is true, it is a fact about facts.

3. Statement 1 cannot be tested, is not "empirically demonstrable", nor can we observe it.

4. Statement 1 is not a fact.

5. Statement 1 is not always true.

6. Statement 1 is not true, than it is also not true that "8. Metaphysical truths, moral facts, epistemological claims, psychological analysis, and all other opinion-driven intellectual pursuits are therefore not facts, and therefore do not have any objective meaning or anchored sense."

:.

7. Carnap's 'verifiability' thesis is itself an unverifiable proposition.


QED? We'll see...








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