- 09 Feb 2018 16:16
#14887454
I'm looking for some feedback in considering this Zeno paradox in part because it seems of particular interest to Marxists that claim an some level of affinity with dialectics. This doesn't have a clear goal, but just wanting to put it out and see what comes of it, trying to work through it as it was something that came up unexpectedly in a past discussion and left me overstretching myself into the unknown for a lack of education with certain concepts around motion.
Here is a summary of the Arrow Paradox explaining how it seems to make motion incomprehensible.
Why is this paradox of relevance, well it seems there is a charge laid against formal logic of having certain limits which it'll inevitable end up in contradiction.
http://redlibrarian.github.io/article/2017/07/17/hegel-marx-dialectic.html
The idea for dialectical as I understand it, following Hegel, is that a contradiction is meant to be negated and raised to a higher conception free of the initial contradiction instead of the Kantian response.
https://broodsphilosophy.wordpress.com/2006/12/20/hegel-change-and-contradiction/
- Source
This has played out particularly in certain debates between logicians of the formal sort and dialectical camp.
But to the above I wonder if it misses the point or whether dialectical are indeed engaging in sophistry.
In regards specifically to Ajdukiewicz's treatment of Zeno's arrow paradox specifically, Henri Wald writes
The above point seems to not be perhaps unique to Henri Wald.
This seems to be in accordance with one interpretation of Marx's sense of motion expressed by Bertell Ollman.
Which points me to a differing ontology in which time is perhaps treated as an independent thing external to objects that acts upon them.
Time as Abstraction
https://plato.stanford.edu/entries/change/#IncMot
To me it seems that time doesn't have ontological primacy but things in themselves are seen in a state of flux.
And there is probably good reasons to emphasize the primacy of things being in flux rather than time as an external thing.
DHARMAKI¯RTI AND PRIEST ON CHANGE
Which I assume is amicable with the idea that whilst in a mathematical formulate there is perhaps not sense of future, in reality we have entropy to always press us 'forward.
Entropy (arrow of time)
Here is a summary of the Arrow Paradox explaining how it seems to make motion incomprehensible.
Spoiler: show
Why is this paradox of relevance, well it seems there is a charge laid against formal logic of having certain limits which it'll inevitable end up in contradiction.
http://redlibrarian.github.io/article/2017/07/17/hegel-marx-dialectic.html
An interesting example of how dialectical and formal logic can be seen as antagonistic is in Zeno’s arrow paradox. For Zeno since, at any discrete moment in time, the arrow is at rest, the arrow is at rest at every discrete moment throughout its flight. The arrow is both moving and always at rest: a paradox. For Hegel, the problem is with halting the arrow in its flight in order to “grasp” it at every distinct moment, much as we do when we capture a “piece” of data. It is clearly impossible to build up motion from a collection of moments at rest. However, if you start from the fact of motion, it is obvious that every moment of rest is merely a convenience, a way to “grasp” the arrow for analysis, but does not represent the truth of the arrow in motion. From a socio-political point of view, whenever we try to “grasp” a concept, institution, or phenomenon, we have to hold it still, violating the fact of its motion (i.e. how it changes over time); we also have to make it distinct (A and not not-A) by shearing it of all its relationships. Both of these operations do violence to the complexity and reality of the phenomenon under analysis. It is to try to resist this violence that dialectical logic is still important.
The idea for dialectical as I understand it, following Hegel, is that a contradiction is meant to be negated and raised to a higher conception free of the initial contradiction instead of the Kantian response.
https://broodsphilosophy.wordpress.com/2006/12/20/hegel-change-and-contradiction/
The Kantian solution, namely, through the so-called transcendental ideality of the world of perception, has no other result than to make the so-called conflict into something subjective, in which of course it remains still the same illusion, that is, is as unresolved, as before. Its genuine solution can only be this: two opposed determinations which belong necessarily to one and the same Notion cannot be valid each on its own in its one-sidedness; on the contrary,they are true only as sublated, only in the unity of their Notion.
- Source
This has played out particularly in certain debates between logicians of the formal sort and dialectical camp.
Spoiler: show
But to the above I wonder if it misses the point or whether dialectical are indeed engaging in sophistry.
In regards specifically to Ajdukiewicz's treatment of Zeno's arrow paradox specifically, Henri Wald writes
Spoiler: show
The above point seems to not be perhaps unique to Henri Wald.
Spoiler: show
This seems to be in accordance with one interpretation of Marx's sense of motion expressed by Bertell Ollman.
This is not to say that dialectical thinkers recognize the existence of change and interaction, while non-dialectical thinkers do not. That would be foolish. Everyone recognizes that everything in the world changes, somehow and to some degree, and that the same holds true for interaction. The problem is how to think adequately about them, how to capture them in thought. How, in other words, can we think about change and interaction so as not to miss or distort the real changes and interactions that we know, in a general way at least, are there (with all the implications this has for how to study them and to communicate what we find to others)? This is the key problem addressed by dialectics, this is what all dialectics is about, and it is in helping to resolve this problem that Marx turns to the process of abstraction.
...
Even today few are able to think about the changes they know to be happening in ways that don't distort—usually by underplaying—what is actually going on. From the titles of so many works in the social sciences it would appear that a good deal of effort is being directed to studying change of one kind or another. But what is actually taken as "change" in most of these works? It is not the continuous evolution and alteration that goes on in their subject matter, the social equivalent of the flowing water in Heraclitus' river. Rather, almost invariably, it is a comparison of two or more differentiated states in the development of the object or condition or group under examination. As the sociologist, James Coleman, who defends this approach, admits, "The concept of change in science is a rather special one, for it does not immediately follow from our sense impressions . . . It is based on a comparison, or difference between two sense impressions, and simultaneously a comparison of the times at which the sense impressions occurred." Why? Because, according to Coleman, "the concept of change must, as any concept, itself reflect a state of an object at a point in time" (Coleman, 1968, 429). Consequently, a study of the changes in the political thinking of the American electorate, for example, gets translated into an account of how people voted (or responded to opinion polls) in 1956, 1960, 1964, etc., and the differences found in a comparison of these static moments is what is called "change." It is not simply, and legitimately, that the one, the difference between the moments, gets taken as an indication of or evidence for the other, the process; rather, it stands in for the process itself.
In contrast to this approach, Marx set out to abstract things, in his words, "as they really are and happen," making how they happen part of what they are (Marx and Engels, 1964, 57). Hence, capital (or labor, money, etc.) is not only how capital appears and functions, but also how it develops; or rather, how it develops, its real history, is also part of what it is. It is also in this sense that Marx could deny that nature and history "are two separate things" (Marx and Engels, 1964, 57). In the view which currently dominates the social sciences, things exist and undergo change. The two are logically distinct. History is something that happens to things; it is not part of their nature. Hence, the difficulty of examining change in subjects from which it has been removed at the start. Whereas Marx, as he tells us, abstracts "every historical social form as in fluid movement, and therefore takes into account its transient nature not less than its momentary existence" (My emphasis) (Marx, 1958, 20).
Which points me to a differing ontology in which time is perhaps treated as an independent thing external to objects that acts upon them.
Time as Abstraction
2. A theory which takes on itself the task of explaining away change by what is abstracted from change, namely the time and the different values of the property that changes, will get into the kind of paradoxes as those presented by Zeno. No matter how you try to connect those abstractions mechanically from outside, you can never succeed to construct change from them,as those are not parts which are there by themselves merely connected in notion of change. For a particular change – a movement which can be described by the s=v*t formula, that mathematical description is merely an abstraction of how the potential measurements in some given framework happen, but the theory about time and values separate from change, about time and position separate from movement, will try to say that what is first is t and x. That there are ontologically existing positions, and ontologically existent times. And in the moment t1, it is in position x1; in moment t2 in position x2 etc… And in such theory there is no movement, just sequence of position in sequence of times, and there the movement appears as a merely nominal concept.
It is also imagined that the difficulty of Zeno’s paradoxes can be overcome by adding infinitesimals to the story. But often it is the “bad” notion of infinitesimals which is used, the one where the infinitesimals are something ontologically primary – again the abstract moments of time are imagined, but now which are infinitely close, i.e. where the distance between two moments is smaller then any given “distance”, but yet it is not zero. But this infinitesimals understood this way are yet another contradiction. And while it is true that calculus gives good way to solve the Zeno’s paradoxes, it is not through this contradictory interpretation of infinitesimals connected to the contradictory notion of change as aggregate of moments.
The mind left within the confusion created by combining those two notions (or interpretations), each contradictory in itself, is hoping that there is something about putting two things which mind can’t comprehend together, and through that – the magic of change comes about. And what the mind does in such situation is to blame the reality and our limited power of understanding for this weird state of affairs, as if the best we can do is to catch the pieces which reality throws to us. And while our minds are really to blame, it is not because our comprehension is limited, but for wanting to make our abstractions the basis of reality, instead of seeing them for what they are.
https://plato.stanford.edu/entries/change/#IncMot
Many of the above themes come together in Graham Priest’s inconsistent account of motion in In Contradiction (1987). Priest sets up the opposing consistent account of change as what he calls the cinematic view of change. This is the view that an object in motion does no more than simply occupy different points of space at different times, like a succession of stills in a film only continuously connected. He attributes the view to Russell and Hume. It is an extrinsic view of change, in the sense that change is seen as a matter of a relation to states at nearby instants of time. The best-worked-out version of this view is the usual mathematical description of change of position by a suitable function of time; and then motion as velocity, that is rate of change of position, is given by the first derivative, which is a relation to nearby intervals.
To me it seems that time doesn't have ontological primacy but things in themselves are seen in a state of flux.
And there is probably good reasons to emphasize the primacy of things being in flux rather than time as an external thing.
DHARMAKI¯RTI AND PRIEST ON CHANGE
In order to examine Dharmakı¯rti’s account of change in light of Priest’s inconsistent theory, we need to revisit Dharmakı¯rti’s notion of momentariness. Here I follow Georges Dreyfus’ authoritative reconstruction of Dharmakı¯rti’s philosophy from a Tibetan point of view.20
Dharmakı¯rti follows Vasubandhu’s view of momentariness as well as most of Vasubandhu’s metaphysics and ontology, in his Abhidharmakos´a.21 According to Vasubandhu,
Destruction of things is spontaneous. Things perish by themselves, because it is their nature to perish. Since they perish by themselves, they perish as they are produced. Since they perish by themselves, they are momentary.22
According to Dreyfus, Dharmakı¯rti elaborates on this ‘‘process view’’ of ontology in two ways: the argument from disintegration and the inference from existence.23 Dharmakı¯rti presents the argument from disintegration as a refutation of Nya¯ya ontology, according to which the term ‘‘disintegration’’ describes ‘‘the state of an already disintegrated thing.’’24 This Nya¯ya view of disintegration posits substances that undergo disintegration in dependence on causes of destruction (vina¯s´ahetu). Against this view, Dharmakı¯rti proposes a dilemma: is the disintegration of a substance an event that the substance undergoes or is it of the substance itself? If the former, it is difficult to see how all qualities disintegrate as soon as they are produced. If the latter, the substance itself must bring about its own disintegration. This means that one can infer the effect, that is, disintegration, from the cause, that is, substance. But for Dharmakı¯rti an inference from cause to effect is a fallacy. Hence, one cannot posit substances separate from their disintegration. Instead, we must think of the term ‘‘disintegration’’ as referring to the process of disintegration. What this means, by using Mortensen’s terminology, is that each spatiotemporal point is not occupied by a substance undergoing disintegration but by a process of disintegration itself.25
Dharmakı¯rti’s inference from existence goes as follows:
[T]hings truly exist insofar as they are able to perform a function. To function is to be capable of producing an effect, a faculty possible only if the object is constantly [ceasing to exist].26 A static object is not acting on anything else nor is it being acted upon. Therefore, that something exists shows that it is momentary.27
What this means is that if something exists, then it exists only momentarily. Hence, Mortensen is correct in saying that for Dharmakı¯rti every existing thing occupies only a spatiotemporal point
Nonetheless, Mortensen seems to underestimate the importance of Dharmakı¯rti’s process view of reality. For Dharmakı¯rti, if something exists, it occupies only a spatiotemporal point. But what exists is not really a substance that undergoes change. Rather, it is the process, or the change, itself that is at a spatiotemporal point. Once we understand Dharmakı¯rti’s view of momentariness in its full extent, it becomes unclear whether or not Dharmakı¯rti has enough resources to reject Priest’s argument for the inconsistent theory of change. This is what I will show below.
Dharmakı¯rti versus Priest
As we saw above, for Dharmakı¯rti there is no distinction between the object and the state in which the object is: the object is said to occupy a spatiotemporal point only to the extent that it is in the process of disintegration or cessation. Now, this view of reality rings a bell. It is a very similar view to Priest’s, if not the same, that a changing object must be in a state of flux at each spatiotemporal point. I examine in this section whether or not Dharmakı¯rti can resist the temptation of Priest and reject an inconsistent theory of change.
Which I assume is amicable with the idea that whilst in a mathematical formulate there is perhaps not sense of future, in reality we have entropy to always press us 'forward.
Entropy (arrow of time)
https://www.ethicalpolitics.org/ablunden/pdfs/For%20Ethical%20Politics.pdf#page90
-For Ethical Politics
-For Ethical Politics