Ah, you are showing some colour, John.
Thank you for taking the effort to represent me honestly - though I refer to continuity spatially as well as temporally.
An objection of mine, as this explanation of yours continues, is towards your analogy by movie film. Indeed the movie film “simulates” a continuous experience whilst instead being a rapid succession of discrete frames, and humans cannot distinguish rapidly presented frames from continuity beyond a certain threshold. Does it then follow that all sensory data is therefore discrete and merely interpretted continuously by the human?
I contend no by virtue of the formal logical fallacy: “affirming the consequent”. ((P\to{Q},Q)\to{P}) where P denotes the presention to a human of a rapid succession of discrete frames, and Q denotes the experience of continuity by humans.
I also applaud your reference to Occasionalism. I was familiar with the concept, but not the term.
Do I need to go much further than reminding you of the term “Falsificationism”? Let me know.
Can you expand on your statement “the lack of time in the “gaps” does not mean it is continuous”? Surely the quoted words are true by definition? Unless you mean to imply “perceived” continuity? To this I refer you back to my mention of affirming the consequent and Falsificationism.
The continuous is mentally modelled through infinitesimals (denoted by discretes), which is different to it actually being made of infinitesimals.
You can quantify every possible increment between 0 and 1 infinitely. Every single instance is presentable as a discrete number. There are an infinite number of these possible numbers, even between 0 and 1. They are all discrete. This is in spite of the true continuous progression between 0 and 1. One can still only represent any snapshot of this continuity as a discrete quantity.
Okay, and thanks again for confirming my point against you… - keep going if you prefer?
- The infinitesimal magnitude “hazily” conceived as a continuum…
- “In something LIKE the same sense” is a discrete entity made up of its individual units - such as 17th century mathematicians conceived them.
- “The coherence of a continuum” mirrors exactly what I said about the need to represent the continuous in terms of the discrete in order to model it, despite it being in fact continuous.
- Obvious contradiction: given that each of the connected parts of a continuum are divisible, they can at no point be part of a continuum. I.e. given “continuum” therefore “not continuum”. The author should have been more careful here.
- Infinitesimals “as parts of continua” can’t be (discrete) points - yes, my whole point. But this is the only way in which to mentally model them, even though they are “nonpunctiform” due to the continuous nature of what these “points” are intended to be abstracted from (continuity).