I think that Silhouette is using these words (“continuous” and “discrete”) in a different way than you do (and perhaps even everyone else.) I for one have absolutely no idea what he means by those words.
Continuous means comprised of infinitesimals. Continuous means you can continuously subdivide without end. Discrete means comprised of a finite number of discrete units. Discreteness means you cannot continuously subdivide without end.
Mathematics is continuous. A number line is continuous.
Physical reality is discrete.
Yes, that’s how you and I (and other people) define those terms. But you and I and other people (except for maybe Henri Bergson) are not Silhouette.
Many people, especially atheists and non-believers, think that physical reality is continuous. This is a major misconception, but understandable in light of the fact that physics uses mathematics which it must, but mathematics is continuous. This is why it is important to understand that math is not physical reality. Some people also think that reality can be infinitely subdivided, but nothing could be further from the truth.
See it’s stuff like this that annoys me so much about the education level of this forum.
Discrete in science is the opposite of continuous: something that is separate; distinct; individual.
I mean, I use basic technical terminology and everyone is like HUHH?? 
WUUUT? 
like I’m some kind of alien for knowing how to use the correct words correctly.
My bad, I misread you specifying “one”.
Also, I’m sure you meant how John is defining infinity, but you’ve entered the fray arguing your definition of the word infinity - forgive me for inducing that you did this to assist with this definition of infinity, since you judge one of his arguments to unavoidably and precisely rest upon?
@John, if you’re reading - kindly “define infinity” for us as precisely and exhaustively as you can, if you please?
Oh did I? Are you sure? Are you sure it wasn’t you who got it completely wrong again?
Continuous i.e. “without break” means there’s no division - especially not infinite division into infinitesimals…
Again - how do you manage to be so completely backwards? I don’t get it. It’d be okay if you were aware of any potential shortcomings and if you came here so that you could learn, but you’re so goddamn sure of yourself on top of being so completely wrong that it’s insufferable.
I repeat, continuous does NOT mean comprised of infinitesimals - it means without break. No division, especially not infinite divisions. An infinitude of discrete units is exactly how the real number line is broken down. In this case you can subdivide infinitely into smaller and smaller discrete quantities, but continuity is one-ness.
And where are the gaps of nothingness between real things? It’s a continuous experience. You can artificially break it up into discrete parts to mentally model it - that’s the only way to do such a thing, but in doing so you compromise on its fundamental continuity. Even experiencing the smallest perceivable particles is a continuous experience. Beyond that it’s all mental conceptions, all the way into the quantum realm - and even there we speak of continuous wave functions that describe probability distributions.
Mathematics is not “continuous” - there is an entire branch of mathematics called “discrete mathematics”, and I contend that even with respect to the continuity of things like the real number line, one performs operations on operands that are extracted as precise discrete values. One even models continuous progressions e.g. like curves as a discrete function through differentiation. You approach this via infinitesimals, but this does not mean the final result is infinitesimal. What you approach is continuous one-ness.
I think it has to do with the fact that if the number of points between (t_1) and (t_2) is infinite that means that in order to go from (t_1) to (t_2) you must cross an infinite number of points. And you can’t do that because no matter how many points you cross, there will always be more points to cross.
I am surprised that you believe in the so-called actual or completed infinity given our exchange in that infamous thread.
But I guess you’re no longer the same Gib. You are now AN ALIEN GANGSTER.
Zeeeeeeeeeeeeennnnnnnnoooooooooooooooooooooooooooo.
plato.stanford.edu/entries/continuity/
“The usual meaning of the word continuous is “unbroken” or “uninterrupted”: thus a continuous entity—a continuum—has no “gaps.” We commonly suppose that space and time are continuous, and certain philosophers have maintained that all natural processes occur continuously: witness, for example, Leibniz’s famous apothegm natura non facit saltus—“nature makes no jump.” In mathematics the word is used in the same general sense, but has had to be furnished with increasingly precise definitions. So, for instance, in the later 18th century continuity of a function was taken to mean that infinitesimal changes in the value of the argument induced infinitesimal changes in the value of the function. With the abandonment of infinitesimals in the 19th century this definition came to be replaced by one employing the more precise concept of limit.
Traditionally, an infinitesimal quantity is one which, while not necessarily coinciding with zero, is in some sense smaller than any finite quantity. For engineers, an infinitesimal is a quantity so small that its square and all higher powers can be neglected. In the theory of limits the term “infinitesimal” is sometimes applied to any sequence whose limit is zero. An infinitesimal magnitude may be regarded as what remains after a continuum has been subjected to an exhaustive analysis, in other words, as a continuum “viewed in the small.” It is in this sense that continuous curves have sometimes been held to be “composed” of infinitesimal straight lines.“
Errr… thanks for confirming my point against you?
Yeah in the later 18th century you’d have been in fashion until the 19th century - as you quoted in your first paragraph. Limits being precise discrete values that came to replace infinitesimals…
The second paragraph just clarifies what is meant by infinitessimals, which I already explained.
Again, you can analyse a continuum “in the small” to be as though it was constructed of infinitesimal discretes, even though the continuum remains continuous…
Thanks again…
If the education level of this forum annoys you, perhaps you shouldn’t be on this forum.
I think it’s not a good thing to get annoyed when people tell you that they do not understand you and that they believe (rightly or wrongly) that you are working with idiosyncratic definitions.
My apologies but I do not really understand what you’re saying here.
I know this is written in response to John. I just want to chime in and say that this is where you lose me. What does “gaps of nothingness between real things” mean? What does “continuous experience” mean?
I understand that these terms are part of your philosophy (and I know how you call your philosophy) but I have absolutely no idea what they mean.
To make it worse, these terms don’t appear to be used by anyone other than you. I can’t Google what they mean and I can’t find other people who use them.
I know Henri Bergson (and perhaps a number of other philosophers) work (or used to work) with similar terminology but the problem is that they are quite obscure, and so, of no help.
Maybe you should make a thread of your own (if you haven’t already) where you clarify your philosophical concepts to those who are unfamiliar with them.
“Closely associated with the concept of a continuum is that of infinitesimal. An infinitesimal magnitude has been somewhat hazily conceived as a continuum “viewed in the small”, an “ultimate part” of a continuum. In something like the same sense as a discrete entity is made up of its individual units, its “indivisibles”, so, it was maintained, a continuum is “composed” of infinitesimal magnitudes, its ultimate parts. (It is in this sense, for example, that mathematicians of the 17th century held that continuous curves are “composed” of infinitesimal straight lines.) Now the “coherence” of a continuum entails that each of its (connected) parts is also a continuum, and, accordingly, divisible. Since points are indivisible, it follows that no point can be part of a continuum. Infinitesimal magnitudes, as parts of continua, cannot, of necessity, be points: they are, in a word, nonpunctiform.”
The continuous is made of infinitesimals. The discrete is made of indivisibles. There is no such thing as infinitesimal discretes.
Because there is no time between indivisible units of reality, then there is no “nothingness” gap in the sense of observable spacetime. However, the lack of time in the “gaps” does not mean it is continuous. See Occasionalism.
Off-topic post directed at Silhouette:
I know what “continuous motion” is. It simply refers to an object that is moving (i.e. changing its position) constantly, without ever stopping.
I can be more precise than that. Here:
An object continuously moving in the universe where time is finitely divisible simply means that for every two adjacent points in time the object is at different positions in space.
An object continuously moving in the universe where time is infinitely divisible simply means that there is no period of time consisting of more than one point in time where at every point in time during that period of time the object is at the same position in space.
But what does “continuous experience” mean?
I have no idea.
Maybe “non-stop experience”? E.g. never losing consciousness? But I am sure that’s not what you mean.
To continue is to persist, or better yet, to repeat. That which is continuous repeats. If we’re working with that definition, then to say that the contents of our experience is continuous is to say that something within it (perhaps even everything within it) repeats. What exactly repeats? What’s the thing that repeats? Everything? But it’s not true that everything repeats. I can see my fingers moving as I type this post. Their position in space is changing, it is not repeating.
Yeah, I know…
But I put a lot of years into this forum, y’know? Fun fact - my account is even older than Carleas’. I certainly wasn’t always this clued up - this forum actually helped me get to where I am now and I never really connected with a different one - obviously I should try harder.
I use this opportunity to try and teach here, but people don’t like being taught by some rando on the internet. They themselves, randos on the internet want instead to assert their opinion and fight their corner - would you disagree, on balance? And statistically since there’s no qualifications necessary to post on an internet forum, it’s not surprising when the majority of these same people aren’t of elite intelligence and education.
Perhaps I should save it for your thread on the “purpose of this forum”, which you already know I’ve taken an interest in.
The annoying thing is not when people tell you they don’t understand and/or err on the side of probability in dealing with a random sample of faceless people.
Everyone is a student. Everyone ought to seek guidance and inspiration to improve. Certainly myself, and certainly everyone else here - that’s to be encouraged, I think we agree.
The annoying thing is when people present themselves as perfect experts when someone like me is around who can academically destroy them, and they don’t even understand what happened when I do so, and assume I’m wrong by default. Some of the more intellectually capable among the remaining posters have recognised what’s going on with me and respect it, but of all the former posters who could have maybe stood to debate on my level, they’re simply not here anymore.
Okay.
Well I thought you were bringing up your definition of infinity (“A number larger than than every integer”) and subsequently claiming the definition of this word “is precisely what one of his (I mean John’s) arguments rests upon” because you wanted to help John out with this definition of infinity, so as to get to the bottom of this argument of his. A crude assumption on my part - of course.
Does that make sense now?
That’s fine - I always wanted you to appreciate that I am open to questions about what I mean, rather than mere assertations that what I mean is wrong. It’s the outright assertion that I’m flatly wrong when I know I’m not that bugs me.
Simple experiment: observe your surroundings. Consider the scientific explanation of what is going on: light bounces off everything, and the rays that enter your eyes’ pupils project a flat image onto your retina. What you “see” goes on in your brain with regards to the flat information that your retina passes on. It’s a 2D area of vision of various shades, and if like me you’re lucky enough to not be colourblind, various colours too. The image is a continuous variation of shades and/or colours. A competent artist will instruct you never to draw black lines to distinguish one feature from another if you want to paint or draw a realistic looking picture. Photographs are the same - there is a contuous variation of shades and/or colours with no “gaps” in between. It’s like a continuous steady fluctuation of visual data. You have to focus on one “part” of it to distinguish it from another, but whenever you go to lengths to distinguish it from another part, there is never a distinct dividing line. This is actually a huge difficulty for AI technology - the distinction of sensory data is infamously difficult to parse.
The same goes for sounds, touch, smells, tastes - the entire sensory plethora that constitutes overall “experience”. It is continuous, thus “Continuous Experience”.
Let me know if that helped or not.
Yes, Experientialism is my own unique philosophy - it’s the one area where I have introduced my own terms, which I have on many occasions tried to define and explain on this forum - but by no means do I expect everyone to be familiar with them by now. I know Fixed Cross ought to be by now, we’ve discussed it at length spanning the course of many years, albeit broken up by long gaps. I’m still not convinced anyone else can yet truly represent it satisfactorily - an ongoing work of mine.
Thank you for introducing me to the name Henri Bergson - I am unfamiliar with him. Yes, I ought to make an official Experientialism thread, but I am in constant debate with myself over how best to begin to explain it in an official capacity. I’m sure I’ll get round to it at some point.
By “continuous experience”, he means no gaps in between moments of time. But, as I pointed out, those “gaps” are timeless, which means you can get a feeling of continuous experience despite the indivisible unit of time like in a movie film. Each frame is a discrete indivisible unit that when played in sequence gives the sensation of “continuous experience”.
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).
I’d hate to be the kill joy to burst the beautiful bubbles most everyone is riding sky high on, including near infinitely reduced affective arguability, in stead of ‘effective’.
But regardless this appearent near approaching final epoch, of almost epic like proportion, let me be the one please to remind You and you, that this argument which has gone on ceaselessly for generations, numerically coincidental with the many turtles resting upon each other’s back, that…
well, that is, the inversive nature of the law of contradiction , demand the simplest modicum of truth.
That truth, the complexity of a series of infinite number of turtles, is very prone in intermittent series, as if totally, absolutely reliant on literally counting them one turtle at a time.
To sequence them as such, literally by totally dismissing one unfortunate turtle who was left in the lurch, may create as many sequential sets, as probabilities can account for.
Sure it is not merely inconvenient to discount such a rare occuramce, and De-politicisedl the odd man out, the third man, the man in the grey flannel suit, cause he resides in shades almost fading to pure white.
Almost white is the inconvenient truth, as the presupposition that it is merely a glitch, a very odd man indeed, who dares to proclaim that He may be identifiable by all that near to very near approach to the pure white.
That is the problem here: we only hear what we want to hear, but can’t or don’t want to sense the big picture within which we have to re-represent ourselves as the Author of the very thought re presentation, as if suddenly realizing that we are the authors of our own created self image.
That may be simpler to see, then to try to get out, exit, where we feel hemmed in by the ’ No Exit’ sign.
If unwilling, to reduce to this unfounded , insinuated level of authenticity, how can we come up by a quantified quality, that can overcome and rule out any distinction between knowledge and and it’s method.
Cantor, Nietzche tried, and their reason was undermined by the then current boxed in dimensions of existence.
They had to reduce their understanding within a scintilla of an non measurable ’ eigenblick’.
But if that reasoning could be sustained, then those limits could again structurally disintegrate, therefore paving the way to total structural disarray, where a cognitive domino effect can compel Prometheus to totally unbound.
Who can ever in hell face that personal responsibility unto themselves?
Even all the tricks in Faust’s jack in the box could never untangle the ness, let alone identify the culprits, the other demons, and then surely would not be left any others to debate or argue with, lest to seek to vindicate one’s self as Dostoevsky tried in “Letters from Underground” No one dared, except at the outset of the last great world war, Sartre, who could only are by and with himself in “Nausea” until…
I have a post for Magnus…
Let’s say you have an infinite number of 3’s…
This logical definition is that this only equals infinity
3+3+3+3…
If you take one three away … does that mean it equals infinity minis 3?! No fucking way! And thus, Magnus is refuted
An indivisible unit of spacetime that is destroyed, and then re-created, has no spacetime in the “gap” between the destruction and re-creation, because the spacetime was destroyed before re-creation. The lack of spacetime in the “gap” means spacetime appears continuous, but is not because each spacetime slice is indivisible.