Do Hume’s Problem and Zeno’s Arrow Paradox have the same solution?

Question

Both Hume’s Problem and Zeno’s Arrow Paradox freeze an observation in time. Do they have the same solution?

To show that the future may not be predicted from the past, the test that David Hume applies is whether, given a series of observations and a set of expectations for a given result, a differing result is nonetheless “conceivable” (Enquiry Concerning Human Understanding, §25; Treatise of Human Nature, I, 3, 3). He answers no. On such an assumption, Hume cannot predict anything. Nor can he know what event might have come before, as any preceding event is also conceivable. In relation to the present moment, any cause or effect, however arbitrary it might appear, is still conceivable. Hume knows nothing beyond one static bit of data.

Seen in this way, Hume’s Problem seems related to Zeno’s Arrow Paradox. At any given moment, Zeno’s arrow is stationary in the air, and so it never moves. As Zeno’s arrow can never move forward, so Hume’s knowledge can never reach beyond the present.

Zeno and Hume were certainly raising different questions. But they seem to have arrived at the same place while doing so. So do Zeno’s Problem and Hume’s Arrow Paradox have a common solution?

Answer 1

I do not think these two problems have same content ,though at first glance they appear to deal with issue of time variation.

Zeno’s Arrow Paradox freeze an observation in time

So then, nothing moves during any instant, but time is entirely composed of instants, so nothing ever moves.

But—assuming from now on that instants have zero duration— the arrow travels 0m in the 0s the instant lasts, but 0/0 m/s is not any number at all. whether it is in motion at an instant or not depends on -

whether it travels any distance in a finite interval that includes the instant in question. The answer is correct, but it carries the counter-intuitive implication that motion is not something that happens at any instant, but rather only over finite periods of time. Think about it this way: time, as we said, is composed only of instants. No distance is traveled during any instant.

So when does the arrow actually move? How does it get from one place to another at a later moment? There’s only one answer: the arrow gets from point XX at time 1 to point YY at time 2 simply in virtue of being at successive intermediate points at successive intermediate times—the arrow never changes its position during an instant but only over intervals composed of instants, by the occupation of different positions at different times.

The Hume's problem of induction is the philosophical question of whether inductive reasoning leads to knowledge understood in the classic philosophical sense,[1] highlighting the apparent lack of justification for:

1. Generalizing about the properties of a class of objects based on some number of observations of particular instances of that class (e.g., the inference that "all swans we have seen are white, and, therefore, all swans are white", before the discovery of black swans) or

2. Presupposing that a sequence of events in the future will occur as it always has in the past (e.g., that the laws of physics will hold as they have always been observed to hold). Hume called this the principle of uniformity of nature.[2]

The problem calls into question all empirical claims made in everyday life or through the scientific method.

Karl Popper ,philosopher of science, sought to solve the problem of induction.[27][28]

He argued that science does not use induction, and induction is in fact a myth.[29] Instead, knowledge is created by conjecture and criticism.[30] The main role of observations and experiments in science, he argued, is in attempts to criticize and refute existing theories.[31]

According to Popper, the problem of induction as usually conceived is asking the wrong question: it is asking how to justify theories given they cannot be justified by induction. Popper argued that justification is not needed at all, and seeking justification "begs for an authoritarian answer". Instead, Popper said, what should be done is to look to find and correct errors.[32]

Popper held that seeking for theories with a high probability of being true was a false goal that is in conflict with the search for knowledge.

Therefore the Zeno's Paradox and Humes Problem are far from being identical or parallel.

https://plato.stanford.edu/entries/paradox-zeno/#Arr ref.-https://en.wikipedia.org/wiki/Problem_of_induction#Karl_Popper

Answer 2

The basic problem in the Arrow paradox is that it refers to the arrow's position but completely omits the arrow's momentum. I.e an arrow in motion has more physical properties than just a position at any given moment, but the description of the situation doesn't acknowledge this (which is understandable, as it took a long time before people even conceived of momentum as such). Phrased differently: Abstracting the world (in part) as a 'point' in 'position-momentum space', then given any position a stationary arrow and a moving arrow at that position would in fact occupy different 'points' in that abstract space, but our perceptual apparatus only allows us to 'project' everything onto the 'position' axis.

Hume's point has the same underlying problem. It is correct that one cannot predict the future given the present, but it MAY be possible to do so given the present plus some indication of which way things are going. A concrete example of this is the motion picture: One cannot infer motion from a single still photograph, but one can infer motion from (the right kind of) a sequence of still photographs.