the axiom of choice:
Zermelo stated (1904): given any set of mutually exclusive nonempty sets, there exists at least one set that contains exactly one element in common with each of the nonempty sets.
note: 2 mutually exclusive sets are disjoint from one another, that is to say, they have no elements in common. for example, let A be the set of all apples, let B be the set of all oranges. A and B are clearly mutually exclusive, because there is no apple that is also an orange.
it is then easy to see that if we construct a set C to be the set containing exactly one each of every type of fruit, then we will be able to find in it an apple and an orange. this set satisfies the characteristic of the axiom of choice, as it contains exactly one element in common with A and exactly one element in common with B.
free will
philosophers refer to the concept of choosing between courses of action as free will.
this is not to say that all will is free: for example, the desire to indulge for the 100th time in blasting heroin during a 50 day period seems to have an air of inevitability about it. some smokers may claim that even after 5 years of smoking a pack a day, they still choose to smoke as opposed to their continuing to smoke beyond their will. to be a smoker is a course of action. it might consist of many seemingly independent instances of actually smoking, but each instance shares the characteristic of smoking.
it's repetitive behaviour like this that creates pathways in the brain related to the idea of a habit.
my point
in line with earlier rantings on
syllogistic raising (which in certain contexts is related closely to the
fundamental attribution error), i would like to make this observation, as simple as it might seem (although i claim that it is notoriously hard to prove):
- there is no real choice (despite what we may tell ourselves). the only decision that we may make is usually related to the negative.
example: (after perhaps in introductory period) a person does not choose to smoke. they may elect not to (and suffer the customary withdrawals), and so at any point there is not really a choice in the sense that both options present as equally weighted, but rather a drive toward a "destiny" of smoking (habit) which may be counteracted by a sudden requirement that they do not smoke.
example: you have a bag containing an apple and an orange. if you have never had either of them, you have a choice. if you have had either of them, you no longer have a "real" choice. most people are not indifferent to what they would prefer: some people have a greater taste for citrus, and others prefer apples. you may "choose" to try something different: an apple person may decide this time i'll have an orange, for something different or you may elect to keep doing the same thing you always do. the latter election does not seem to actually constitute a choice, since if oranges don't rate for you there never really was a choice in the first place.
returning to this as a syllogistic raising
it is the assumption that 2 options automatically leads to 2 choices which has me curious. here the fact is that you have option P and option Q. your background history usually goes with option P. at what point when given the option do we actually choose?
example: you have an almost full packet of cigarettes remaining at the end of the day. you fall asleep. when you wake up, you have 2 options: to smoke again or to never smoke again. which do you choose? most people continue smoking. some people will give up. but how many people actually make the decision to give up right then and there, when they have the goods at their disposal?
it seems to be a syllogistic raising because option Q might be the "choice" (ie habit) of smoking, and option P might be the "choice" (ie option) to not smoke (taking the negative). to not smoke is, by definition, being a non-smoker. so in this case, the syllogism is that deciding at any time to not smoke automatically leads to being a non-smoker. try it and see: option P is not really a choice because, perhaps, it is not really a fact.
summary
i suggest that deciding to change a course of action comes some time before being presented with the option. this amounts to knowing what the option will be, ahead of time. but since it is usually to not do something that you currently do, you are simply taking the negative.
compare that with being presented with opportunities in life. an opportunity arises that you did not expect. since you didn't expect it, you didn't see the option coming. the option arrives, but you miss it because you continued doing whatever it is that you normally do, either through habit or some other constraint. most people would agree that when some big change takes place in say, a friend's life, it was not entirely unexpected for those observing. "you were showing signs," they might say after it happens. "you were restless" and so on.
so then, might we ask: how free is free will?
or is free will merely a construction we present to ourselves to help us sleep easier at night?