Hi Adam,
That's a good question. It's excellent to try to think things through as far as they'll go, and to be daring! Congratulations. But be careful not to let your theoretical speculations spoil your relationships or work or grades, at least until they're very well formed and well tested. I'm going to suggest that they are not, at present, and so I hope this will help you in your investigations.
To start, I think you noticed one reason not to just die--it's hard work unless your time has come! You can't just go to sleep and not wake up. Your father's sperm needed no justification to search out your mother's egg, nor did the resulting embryo need to explain its divisions to itself prior to acting. But you could use the question as a basis for insight. You might try sitting in meditation and going through the process of dying. Attempt to do as little as possible while maintaining awareness of the disassembling of all active functioning. It's the lazy man's meditation--awareness of awareness. Try to use your syllogism to deactivate your activity/reactivity. Just rest, without doing anything, in awareness. Find out what the difference is between being dead and being alive.
But it's still an interesting question. I think you've confused yourself about logic, though. Pure logic is without content, meaning or referent. You're engaging in practical reasoning, which means it always has a semantic content. So what? Well, you probably know this, but the difference is that an inference, practically speaking, is only as meaningful or true as its premises (although, it's worth noting that a true conclusion can have false premises--1) all men are dogs; 2) all dogs have oppose-able thumbs; C) all men have oppose-able thumbs). Unfortunately, the premises are the conclusions of previous syllogisms/arguments. And the premises of those previous syllogisms are the conclusions of still more antecedent syllogisms/arguments,
ad nauseum.
This problem could be solved with axioms, but then we're just assuming things. Alternately, we could discover the most wonderful of wonderfuls--the
self-evident proposition! I challenge you to discover it, young knight. Neither of these are very satisfying (or the second one isn't because no one has found a self-evident proposition). In math, the axiom system is used, without assuming that the axioms are uniquely true. In practical reasoning/coffee-shop discussion, we (ideally) argue back premises until people tire of it or find points of agreement from which they can proceed. This is more or less the Socratic dialectic, and it does not yield final answers, as may be suggested from Socrates famous dictum, "All that I know is that I know nothing."
What's the upshot? Well, in one sense, it suggests that even reasoning is empty of intrinsic essence. And so is emptiness, of course. In addition, it means that you should never get too worked-up about a particular conclusion you've derived. If you seek truth, you can act as your reasoning leads, while using that reasoning as the basis for further exploration of reality and your own understanding of it. Let's take your syllogism as an example:
1. Action can only be justified by reference to objective value.
2. Objective can't exist because it is a logical contradiction.
therefore
3. No action is justified.
I guess I'll explain points one and two again so as not to be accused of working with false assumptions.
1. - The reason to do something is that it has some positive effect on value. Every action one does is aimed at increasing amount of value. There is no reason to do an action that doesn't improve value of some sort.
2. - Value is simply a system of comparison, and as such can only be measured by some sort of standard. This standard is necessarily subjective, that's the nature of a standard.
So you've noticed that your premises/assumptions require explanation. In fact, if you're going to go the logic route, they deserve their own syllogisms. Now, when I challenge premise 1, I go look at your explanation. In the explanation, there are many semantic problems, e.g., you haven't defined "positive effect," "value," "improve," etc. Also, your explanation is logically invalid since you use important terms in your conclusion-- "Action can only be justified by reference to objective value"--that can't be found in your explanation, e.g., "justified," "reference," and "objective." To a certain degree, you define "objective" and "value" in the explanation for the second premise, but they're pretty gauzy definitions for such important concepts. This means that you haven't really argued for your premises. Which means that you would be well advised to try to look more deeply (and without becoming too rigid) into the meaning of these concepts.
But I think that I know what you're getting at with this whole thing, so I'll release you from the logic lesson (if you're even still reading). Here are a series of possibilities that would overturn your syllogism. I'm not saying that I necessarily believe any of these, but they're all viable premises.:
1) Action can only be justified by reference to subjective value.
2) Some actions have aims (those executed by a human being with a plan, at least), and some do not. A bacterium swimming up a sugar gradient probably doesn't have an aim, but we "explain" its actions with such descriptions.
3) Objective and subjective are heuristics that do not have real referents--all existent phenomena are transgress the distinction and make up the class of "real" things.
4) The nature of standards is not always subjective--there exist absolutes or essences, and comparatives evaluate the relative participation in those absolutes.
5) Compassion is the fundamental nature of reality as seen from a perspective or point of view, but it is not easily perceived as such.
6) Justification arises from imagining worlds we desire, and people we desire to be in those worlds. Our actions are "justifiable" if they concur with actions that fit into those ideal worlds.
7) Value comes from awareness, not from objects. That does not make it a subjective property (e.g., if awareness is objective), but a conditioned one.
8) An action with justification is a particular kind of action. Justified actions are only better or worse than unjustified actions by means of some system of values.
Etc.
So, anyway. There are lots of ways to get around the problem you're having, or to doubt that it's a real problem. Keep wondering, and keep thinking things through as far as they go. Read Spinoza's
Ethics, Plato's
Symposium and
Republic, or Christine Korsgaard's
Sources of Normativity, to see some alternative ideas. Or read Nietzsche's
Beyond Good and Evil, or the works of the early logical positivists, and begin to see where your ideas are originating. Hillary Putnam tries to break down the fact/value distinction, too, I believe. You might try out some of his papers. But do like Descartes--observe and obey the fine grain of conventional morality while you're engaging in these investigations. Don't let the ideas poison your life. And keep coming back to awareness--it's the "thing" that makes your questions/experience/value possible. So, what is it!?
Here's a poem that I really love, and that you might find enjoyable (not that the fact will justify any actions!):
MY own heart let me have more have pity on; let
Me live to my sad self hereafter kind,
Charitable; not live this tormented mind
With this tormented mind tormenting yet.
I cast for comfort I can no more get 5
By groping round my comfortless, than blind
Eyes in their dark can day or thirst can find
Thirst ’s all-in-all in all a world of wet.
Soul, self; come, poor Jackself, I do advise
You, jaded, let be; call off thoughts awhile 10
Elsewhere; leave comfort root-room; let joy size
At God knows when to God knows what; whose smile
’s not wrung, see you; unforeseen times rather—as skies
Betweenpie mountains—lights a lovely mile.
-Gerard Manley Hopkins
Enjoy,
Brule