- Achilles will not reach the tortoise before the sequence is completed
- The sequence is never completed.
But the idea of completion suggests another argument. Every day I wake up from sleep, that 'little slice of death', and become conscious. Imagine the following thought-experiment. I wake up an infinite number of times. Could I have a conscious moment after that infinite sequence? Is it possible that there could be a waking moment belonging to my consciousness such that there are an infinite number of waking moments before that? Surely not. I can't think of an argument to prove it, rather, it seems an irreducible part of my idea of consciousness that I cannot conceive of an actual or 'completed' infinity of conscious moments. (Complete in the first sense of 'already happened').
You object: what if I failed to wake at some point, an infinite number of days passed, and then I woke up? I reply: physical time and conscious time are different. If I go to sleep on Saturday, and an infinite number of days pass, and I wake up, it is no different for me than if I had woken up on Sunday. I cannot conceive of a sequence of infinite waking moments that I can ever 'escape from', in the sense that every one of those moments was behind me. Perhaps there could be some consciousness after such a sequence, but it would not be my consciousness.
Thus any two waking consciousnesses of mine must be connected by a series of finite waking moments. Which leads to the following paradox. Given that every moment of my consciousness is in a sense a waking moment - the only difference being the lapse of physical time which we assume occurs during sleep, and which we assume does not occur when we are waking - and given that any series of conscious moments belong to my consciousness must be finite, how is it that are consciousness also appears continuous. i.e. there are no obvious gaps or 'flickers' in consciousness such as we see in the early movies? How can consciousness be both discrete and continuous?
6 comments:
What do you have in mind with 'terminated'? Do you perhaps mean that the sequence, considered as an ordering, has no last element? Maybe the paradox gets its force because people expect the sequence to end with the event of Achilles finally(!) coinciding with the tortoise. But we could dismiss that argument by asking why anyone would expect that a subset of the events on A's worldline constructed in this way would include this final event. One might as well choose any subset, finite or infinite, that doesn't contain this point and say Look, the final point isn't there; ergo A never reaches the T. The more I think about this the more trivial it seems to become. The only interest comes from trying to understand why anyone should find it problematical.
I'm not at all sure I've grasped your consciousness thought experiment. Doesn't it show that the cinefilm metaphor for the stream of conscious 'moments' is seriously misleading? My own consciousness seems highly discontinuous, like the proverbial butterfly on the buddleia. The external world does have some continuous aspects. Why do we not see our own blind spots?
>> The only interest comes from trying to understand why anyone should find it problematical.
Agree so far.
>>I'm not at all sure I've grasped your consciousness thought experiment.
Do you agree with my point that I can only be conscious of a finite number of previous days? That my consciousness cannot survive the infinite?
If you do, then do you agree that this conflicts with the thesis that consciousness is 'continuous'?
Well, if each day's memories grow geometrically dimmer with age then infinitely many days' memories might be contained in a finite mind. There is no doubt some threshold beneath which a memory is effectively void. But one might imagine a prosthetic memory that gave one an infinite but fictional past life. Not all 'remembered' days would be different, of course, but randomly chosen forgetting's could make them seem different. However, for the sake of exposition let's take it that I can be conscious of only finitely many previous days. Now what do you mean by the continuity of consciousness?
>>Well, if each day's memories grow geometrically dimmer with age then infinitely many days' memories might be contained in a finite mind. There is no doubt some threshold beneath which a memory is effectively void. But one might imagine a prosthetic memory that gave one an infinite but fictional past life.
This was not quite my point. Let me think about this and write some more next week. Thank you for your contributions. They are always well-thought out and provoking.
>> Now what do you mean by the continuity of consciousness?
I mean that it's 'smooth'. Not jumpy like the 1890s film clip I linked to. This suggests that for any two conscious moments, there is a third that we can interpose between them. Continuous in the sense that the rationals are continuous (correct me if I am wrong).
>> This suggests that for any two conscious moments, there is a third that we can interpose between them. Continuous in the sense that the rationals are continuous.
This property is usually called 'denseness'.
I think we have to be very careful here. I suppose that if I'm awake between t1 and t2 then one could say that every t in [t1, t2] counts as a conscious moment. But that doesn't mean that at some t*>t2 I can recall my state of consciousness at some t in [t1, t2]. In fact, I'm not at all sure the notion of 'state of consciousness at some instant' makes sense. In so far as I can identify distinct states they seem naturally to span finite intervals of time, perhaps from 1/10 second to 1 second in duration.
I agree that aspects of phenomenal consciousness are smooth. I see the outside world seemingly smoothly changing. But my attention is decidedly jumpy. Visual information reaching the brain is spatially gappy because of the blind spot, but phenomenal consciousness seems to 'interpolate' within the gaps (though Dennett argues against this way of seeing it). Likewise, the smoothness we find might be interpolated between temporally discrete 'samplings'. After all, when watching a film or TV the perception is smooth yet we know that the information arrives in discrete frames. And animal nervous systems can extrapolate from smooth motion---essential for catching moving prey.
I look forward to your further thoughts.
>>Visual information reaching the brain is spatially gappy because of the blind spot, but phenomenal consciousness seems to 'interpolate' within the gaps (though Dennett argues against this way of seeing it).
Likewise, there is no perceptible gap at the perimeter of the 'visual field' and the stuff we can't see. Ernst Mach famously tried to draw the visual field - presenting it in such a way that there was a visible boundary at the perimeter. And as Wittgenstein commented (probably with Mach in mind), it just doesn't look like that.
I wonder if this is a similar problem.
On denseness vs continuous, these are mathematical terms. 'continuous' in its more general non-technical sense just means 'unbroken'; no gaps.
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