“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.
John,
It seems resolution between significance and insignificance becomes the very limit through which we can understand God, man, and ManGod. That triple partition , that alluded to by Ec previously, may correspond to Your initial point.
But that is the point: they , space time’s gap can’t in any event, distinguish between before and after the event, therefore space time it’s self can not be assumed to be either, as an infinitely regressive continuum or, it’s negation.
The level of cosmic uncertainty would need to find an exit from a nominally defined box, and create a plurality , or else the state You described a-priori, that of a total and absolute disintegration , would/ could understandingly give shivers on any ones spine.
At this ‘point’ , if we were ably to affront it such, would/could a vindication for both: Atheism and Theism, and that is why ALL cosmological arguments end in stale.mate.
This is probably why Christ said, " Blessed are those, who can not see, yet believe."
The before and after can be distinguished in terms of causation and the arrow of time. The “gap” is not absolute nothingness, because God would still exist.
John, you know about binary I assume.
There’s actually a base called unary. It still needs some representation of zero! It still needs either spaces (otherness) or the enter button (to start a new line - again, otherness) if you use spaces and new lines, and zeroes and ones, it’s actually in base 4, not binary!
Just like even unary needs a different procedure, god needs otherness, god is DEPENDENT upon it! God is a dependent being!
‘Binary’ as people wrote it in computer code is actually base 4.
That makes sense only with an unsensed criteria of an implicit causation in tandem with an explicit one.
For this to occur, or, to imply a causal sequencing, albeit unsensible-not to confuse with insensible, the same near to the Absolutely both to concur,
In simultanity is a sine quo non matter of fact.
That actuality have to run concurrently and conspatially, and if so, that becomes arguable defenitionally , but not conceptually/ structurally, except by the mode demonstrated: vis affected and not effected causal definitions.
That affect demonstrates Your ’ affectance’ as well, by Your comment of “shivers down Your spine”.
Have I followed Your intrinsically shadowed argument as well, for surely a limited return (to Thomism) implicates a totally projected form of naive realism, that may have run it’s course, in need for at least a partially differentiated limit to the reduction.
If agreed progress(ion) to this limit, then on all other basis, I can not but not concur.
No, God does not cause in time. God’s cause is logical - not temporal - causation. God is timeless. Don’t forget your God 101. You clearly don’t like the concept of an uncaused metaphysical cause of physical reality. You’re constantly analyzing it in terms of the physical ignoring and presuming its non-existence. The OP gives you the reasons why you shouldn’t ignore it.
No of course not, however the digital problem is an effect of andnl has bearing on the connections , the analogies , the dialogues , and all the semantic/a posteriori —a priori differentiation that connect (existentialism with empiricalism).
The idea that the developmemt of the
logic system is tantamount and anachronistic with the Objective development of logic with developmental anatomy is long standing and consists of a above mentioned lobes through which the cerebrum context operates synthetically , synchronistocally as trait gainers.
The logic internal and external systems of logic have to parallel and conflate periodically to make sense of Creative processes which indicate the simultaneous objective reason behind Creation as a result of textual and contextual elements.
The textual logic may be contemoranious winthin the mind of God, without, which causation , as per extrinsic, seemingly senseless logic can manifest.
This is why the medulla obligate , the synapses mediate functionally and simultaneously.
Therefore, the logically uncaused mind of God, has to insure an eternal , intended continuum, with nexus that is both textually induced, and reduced toward the particular existential epoche.
The literal subtext are reformed into the figurative subjects, as per appearent accidents, such as the Revelation, the apple striking Newton’s head, all ‘accidental’ to pedicure the changing Covenant that befell Man, is his morphology was won’t to ready itself from representative reflection ( mirroring) through cognitive simulation through the context , to eventual enlightenment .
Narcissus’ guilt was symbolized inti a release to a seminal flower: .
Logic comes from God’s uncaused mind and uncaused power to create.
It makes perfect sense.
As you are probably aware by now, I do not think that’s how John defines infinity. That’s merely how I define it. I think that John defines it in Sense A. Here is what I mean by Sense A:
viewtopic.php?f=1&t=195793&start=500#p2769185
Perhaps noone realized it but in that post of mine I argued against John’s proof number four: The Beginningless Time Paradox.
I think that the following is an accurate paraphrase of a part of his argument:
If time has no beginning, it follows that the number of events that took place before the present day is equal to a number that is larger than every number (including itself.)
Note that I am replacing his use of the word “infinity” with “a number that is larger than every number (including itself)”.
I believe the above is a non-sequitur. If the universe has no beginning, what follows is that the number of events that took place before the present day is a number larger than every integer. A number larger than every number (including itself) is a number larger than every integer but it’s not the only number of that kind. In other words, there are different kinds of infinities. One of them can’t be exhausted i.e. reduced to zero (and it’s actually a contradiction in terms.)
Basically, what I am saying is that he’s committing a fallacy known as false dichotomy.
Yes but the atheistic forms of causation have been upended by the lack of substantive reasons why the Thetic forms of creation have not been transformed by the Second Covenant, because sans that, the road of salvation will obliterate the Creation It’s self , along with It’s author.
Is that what You are weary of?
I do not share that fear, because of the former attended to.
Why? God’s Covenant absolutely verified the complete integration into a Perfect Unity, as configured within the ancient symbol of the Trinity.
Such can not be a literal description, and can only be sustainable through the annals of the ages, through the Sacred Mysteries.
I don’t believe in infinitesimals.
Then doesn’t that make the discrete units continuous? What then is the difference between a series of consecutive discrete units of time and one long continuous stretch of time?
We’ve been over this.
You know what else has no scientific proof? GOD!
I might as well say: no there isn’t! 
But I’d prefer to address the reasoning behind the assertion. Care to do me the same favour?
What part of don’t imagine a starting point did you not understand?
That’s fine and dandy with me. So then you’re invoking the static picture of time. It’s like a 4th dimension akin to the spatial dimensions. Therefore, there should be no problem understanding it as infinite in both directions just like space.
Time dilation doesn’t prove a thing, except that things slow down the faster they move through space relative to an observer. If you don’t have time, you still have motion and change.
Yes, it was once real–but back then we called it the present–once it becomes the past, it’s only a memory. Cause and effect, change in general, can be understood as always in the present. It is the mechanism that governs change and how it unfolds.