Everything that exists
My understanding of comtabilisim is that under certain circumstances you can make your own free will choice which is not deterministic. It is a bit like 'eating the cake and having it' but many philosophers
agree with it.
To get rid of the paradox, you need only to assume that time is not continuous.
And that time is not continuous is supported by the recognition that the past is substantially different from the future. Once the future is recognized as different from the past, the present must be understood as something other than the continuity of future/past, it must be understood as a divisor between them. Then we are left with three distinct things, past, present, and future.
This is only derived from the faulty definition of "the present" explained above. If we abstract our thoughts from the subjective experience of time, to think about time as it really is, independent from this subjective experience, this conclusion can be seen as completely unwarranted.
To take your example, how do I distinguish a signal indicating the existence of a condition causing pain from a signal that says only that a pain receptor is firing? Since they are one and the same signal, I do not see how I can.
can response to stimulus be an indicator of consciousness
In Descartes' Error neurophysiologist Antonio Damasio argues that our knowledge of the external world started as neural representations of body state and evolved into representations of the external world as the source of changes in our body state:
I see three problems with this otherwise plausible hypothesis: (1) It requires one neural state to encode multiple concepts. (2) There seems to be no mechanism thise "solution" could have evolved. (3) Neural states do not represent as other signs do.
For those of us who are not physicalists
What does "ds/dt" mean?
A cosmic DNA?
According to the hard deterministic view, there is an inevitability about the evolution of the universe that is the result of the causal chain of events. That chain started at the singularity of the Big bang. In my opinion, that implies that everything in our universe down to my writing these lines was somehow inherent in some initial specific properties of the Big Bang; sort of a Cosmic DNA. Not being a determinist I cannot come to term with such possibility, but logically I find it hard to refute it.
Your description is not really consistent. If the first instant only fades to 50% by the time the conscious person is aware of the second instant, then you can't really say that "a single photograph represents your conscious instant", because the person is conscious of part of the first, and the second, at one conscious instant.
The thread topic is not the infinite divisibility of time, or even the continuity of time, but the reality of time
Suppose instead that Achilles and the tortoise are riding in trains on parallel tracks. The tortoise is initially 100 feet ahead and proceeding at 20 feet per second, while Achilles is going 40 feet per second. After 2.5 seconds, Achilles is where the tortoise started, while the tortoise is now 50 feet farther along. Nevertheless, after another 2.5 seconds, Achilles overtakes the tortoise.
Zeno's false assumption is that continuous motion requires an infinite series of discrete steps, which is precisely what I deny--there is no need to divide space or time infinitely in order to traverse a finite distance during a finite lapse.
I guess you forgot that I defined five properties that are jointly necessary and sufficient here.
The line is not composed of parts and thus potentially infinitely divisible, but that by itself is not sufficient to make something truly continuous. What part is confusing you?
Sure, but when you mark an instant to divide one second, you get two half-second lapses; and when you mark two more instants to divide those, you get four quarter-second lapses; and so on ad infinitum. In other words, we artificially insert discrete instants to create the parts, which are always continuous lapses.
Again, the paradox is based on an incorrect concept of continuity as merely infinite divisibility. Time is not isomorphic to the rational numbers, or even the real numbers in my view.
Put another way, Zeno's assumption is that Achilles must complete an infinite series of discrete steps, each of which consists of traversing a smaller and smaller distance in a smaller and smaller interval of time, in order to overtake the tortoise--which is obviously false.
Recognizing continuous motion as the fundamental reality, rather than discrete and sequential positions and instants, dissolves the paradox because Achilles merely has to achieve an average speed that is greater than the tortoise's average speed.
It would infer the likelihood that time is more arbitrary than not, no?
And I'm saying time is subordinate to change.
Okay, please educate me. Show me how one of Zeno's paradoxes applies to what I have presented in this thread so far. I am actually well aware of them, but it is always possible that I have missed something.
Positing points already presupposes discreteness, even if there were infinitely many of them.
No, the Planck time is the duration required for light to travel the Planck length in a vacuum, and the Planck length is the distance below which our current physics equations are no longer valid. In other words, I understand them to be mathematical limitations on marking and measuring time and space, not real properties of continuous spacetime.
Which one of his paradoxes would you specifically like to discuss as relevant to the thread topic?
Google says "forming an unbroken whole; without interruption," so nothing about being infinitely divisible. Again, the rational numbers are infinitely divisible, yet not continuous.
For me, infinite divisibility is just one of five properties that are jointly necessary and sufficient for true continuity; here is how I am presenting them in a forthcoming journal paper:
Rationality - every portion conforms to one general law or Idea, which is the final cause by which the ontologically prior whole calls out its parts.
Divisibility - every portion is an indefinite material part, unless and until it is deliberately marked off with a limit to become a distinct actual part.
Homogeneity - every portion has the same dimensionality as the whole, while every limit between portions is a topical singularity of lower dimensionality.
Contiguity - every portion has a limit in common with each adjacent portion, and thus the same mode of immediate connection with others as every other has.
Inexhaustibility - limits of any multitude, or even exceeding all multitude, may always be marked off to create additional actual parts within any previously uninterrupted portion.
The application to time is that the portions are lapses, the limits are instants, and the one general law or Idea to which every lapse conforms is an indefinitely gradual state of change.
Of course he made assumptions, as all of us do.
If they were "all one and the same concept," then we would not have three different terms for them.
I acknowledge that analog and digital loosely correspond to continuous and discrete, respectively; but again, infinitely divisible is not synonymous with continuous.
Events would be mental snapshots, or categories, of the continuous flow causation. Minds break up the analog signal of the world into binary bits that are meaningful to our goals. The separation/discontinuity only exists in our minds.
Imagine a series of instantaneous photographs to be taken. Then, no matter how closely they follow one another, there is no more motion visible in any one of them than if they were taken at intervals of centuries.
— Peirce, c. 1895
If this is the case, it does have an effect on the argument, because it would indicate that the perspective of the conscious human being spans numerous instants of time. If consciousness were restricted to one instant, the present instant, then we would observe a succession of instants. To get the "blur effect", the conscious being must be observing numerous instants in what appears (from the perspective of the consciousness) as "at the same time". The consciousness is observing numerous instants "at the same time", and is incapable of detecting the division between them.
This is evident from the fact that we are consciously aware of motion. Motion requires a period of time, so if we are consciously aware of motion, then consciousness must span a period of time.
I disagree with describing it "narrow". It is parsimonious, but leaves nothing unaccounted for. It's reasonable to methodologically treat abstractions as independent existents, but that utility does not depend on an ontological commitment.
Emphasis on the qualifier "independent", because this parsimonious ontology doesn't deny the existence of triangles and right angles, it just denies that they exist independently of the things that have those properties. The angles between the walls of my bedroom are 90 degrees - and this angle does actually exist, just not independently of the walls. Many other things have this exact same property, and that's why "having a 90 degree angle" is a universal.
My issue is that there's no good reason to assume "90 degree angle" exists independent of the things that have it. Sure, we can think abstractly about this property without considering the things that have it, and that's a product of our powers of abstraction.
Everyone is always making some assumptions, and again, infinite divisibility is necessary but not sufficient for true continuity.
The rational numbers are infinitely divisible, yet no one seriously claims that they are continuous.
Considering Peirce's remarks on this topic in general and about ultimate parts in particular to be gibberish, along with suggesting that being continuous is synonymous with being infinitely divisible, demonstrates quite conclusively which one of us does not understand what "continuity" means.
On the contrary, we directly perceive the continuous flow of time.
In fact, if we did not directly perceive the continuity of time, then we would have no concept of continuity at all.
On the contrary, Zeno's paradoxes are only dissolved by recognizing the continuity of both space and time.
All the arguments of Zeno depend on supposing that a continuum has ultimate parts. But a continuum is precisely that, every part of which has parts, in the same sense. Hence, he makes out his contradictions only by making a self-contradictory supposition. In ordinary and mathematical language, we allow ourselves to speak of such parts--points--and whenever we are led into contradiction thereby, we have simply to express ourselves more accurately to resolve the difficulty.
— Peirce, 1868
In a 1908 paper that established the parameters for many of the debates within the philosophy of time ever since its publication, John Ellis McTaggart argues for "The Unreality of Time." His basic claim is that time cannot be real because it is contradictory to predicate past, present, and future of the same moment or event; and he alleges that the obvious rejoinder--that a moment or event is past, present, and future only at different times--is viciously circular. McTaggart's implicit assumption is that time is a series of discrete positions, which are what he calls moments, and an event is the discrete content of a particular moment. In other words, he treats any single moment or event as an existential subject, which is why it is precluded from having incompatible determinations.
Generally, you could explain it through a simple mathematical formula (time= distance/speed).