Thank you for the kind words! I find the ego typically gets in the way of finding the truth, though to give the Devil credit where it’s due, it’s probably from the ego my obsessive need for truth comes. But yeah, the happiness and relief I get from learning something new far outweighs any negative emotion I may feel from being proven wrong. I am lucky to have that. I think my more recent years of philosophizing has been a crucible. I’ve philosophized all my life, but I’ve only gone really hard into analytical philosophy and formal logic the past 5 years. The combination of being egoically attached to certain untenable positions and also being driven towards truth is a very burdensome inner conflict. I even became depressed during one period of this path due to the inner conflict of being so attached to a position that the force of truth was showing to me was impossible.
After finally letting go of that position (this was sometime in 2024), it kind of opened Pandora’s box. I saw what could happen if I put aside my ego as much as possible when searching for truth, and the amount of Eureka euphoria that a less obstructed stride towards truth generates just dwarfs the discomfort and pain of constantly changing my mind. It is a skill that requires practice however, and I seem to be developing it still. There have been periods of my philosophizing were I underwent staggering revolutions of thought every week, perhaps once every day. And often I would return to old ideas in new forms over and over. The fear of just uselessly going in cycles sometimes hits me, but I don’t give that fear much credence. I seem to be going somewhere, because the collection of beliefs that are seemingly useful and long-term is only growing larger and larger.
When I’m finally able to fully formalize my currently under-construction formal system, I will enter a new era, I believe. I suspect I’ll probably redefine it a few times, but it will be easier then, because it will be from the vantage point of having something more solid to stand on. Right now I am running around in philosophical quicksand, and the only solid ground I have is the soles of my own two feet. And I am not discontent with that, because it is a necessary phase.
Indeed, taking sets as fundamental is a bad move, I believe. That said, \mathsf{ZFC} is a great system. In many areas of math, equality is reduced to having the same structure. That makes sense for mathematics, because I believe it is the study of structure itself.
So, I believe \mathsf{ZFC} is largely correct on the structural level, but it seems to imply certain ontological positions that are problematic to me. Tokens are not prior to universals, because we cannot even pick out tokens without universals. It is when universals (predicates, that is) unify in salient ways that a token emerges from their co-inherence. Of course, this is not at all a sufficient account. I mean, take the conjunction of two predicates, and you just get another predicate. To go from the general to the particular requires either enough predicates, or the right predicate(s), to “weigh in”, such that their conjunction is no longer just a more specific universal, but now an actual particular. I don’t yet know exactly what that particularizing addition must be.
My system is more and more achieving a structural similarity to \mathsf{ZFC}, but it is doing so without taking sets as fundamental, but rather using predicates as somewhat equivalent to them. This isn’t ground-breaking at all, but I just thought I’d mention it, because I agree that we cannot conceive of tokens as logically prior to their universals.
I don’t believe in the real number line as corresponding to anything real. Not in the literal sense at least. I am not sure if I believe in absolute infinity, but if there is such a thing as absolute infinity, then it solves nothing anyways. Cantor showed that there are always bigger fish to fry. If you start dealing with transfinite numbers, then your need for true boundlessness just reappears higher (and higher yet) up on the infinite hierarchy. Any final, self-contained solution that uses absolute infinity will nonetheless wind up working primarily because it properly grapples with potential infinity.
So, if the real number line corresponds to anything real, it corresponds to what is always a discretized number line that can be iteratively given a higher and higher resolution. The density of the real number line, at best, corresponds to an activity on the true number line.
For any number x and y, there is a number between them… if we decide to look for it, to construct it. I am not sure if this is really how it is, but this is just the best case scenario for the real number line’s correspondence to anything real.
Either the measure of space and time is just statically discrete, or it is dynamically discrete, perhaps with an arbitrarily increase-able resolution, but never an infinite resolution. Density and continuity are always a work-in-progress, God fills in the blanks if and when he must.
But, as you rightly mention, quantum physics seems to stop that work-in-progress right in its tracks. The jury is still out on the correct interpretation of this IMO, but it definitely could mean that time and space are simply statically discrete, or perhaps dynamically discrete but with a limit to its resolution nonetheless.
I view mathematical absolute infinities and the real number lines as static idealizations of what must instead be eternally dynamic. And I think Cantor would ultimately agree, because the paradoxicality of the class of the entire hierarchy of infinites, often denoted as ת, is the logical proof that any and all infinite measure is an unfinishable work-in-progress. The destination is the journey, the finality is to be a process, because if we correctly classify processes as processes, then they are complete as such. There’s a beauty to that. And this is part of the reason why I don’t think time is an extralogical matter, and why I am very against trying to model truth and reason with these ideally static systems. I mean, all logicians know for a fact the systems aren’t, on a practical level, actually static. But, they say they are static in an ideal sense. I believe it is a Platonic move, and I think it is wrong.
No static system could ever formalize a dynamic reality. Our systems are meant to be mirrors of reality, and so they must move in sync with reality. The system’s are not merely dynamic at the practical level, because the system’s do not exist beyond the practical level. A formal system is an activity, called formal only due to its rigid structure.
I wonder, what do you think of this? I went on this tangent to build on my interpretation of what you are talking about above, but I could have misinterpreted the point you were making. Or even if I didn’t, you may still disagree with some of the details of my account here.
This is incredible interesting! It connects to stuff I have been thinking about, especially recently, but it frames it in a slightly different way. I don’t think I have ever heard or thought about the present as an overlap of the future and the past. Right off the bat, I like the thinking, because it removes the present as an additional primitive, instead defining it in terms of the future and the past. Before I try to analyze your idea above here, I’d like to offer some of the context with which I receive it.
As explained above, I believe in the discreteness of space and time. However, that immediately raises the question: what are the quanta of space and time?
A discrete view of time usually treats time like a video. It is a video, a discrete sequence of pictures stitched together. But, there is a building intuition within me that this may perhaps be problematic. I can’t quite explain very well yet why I think so, and why I think the alternative might be better, but here it is:
What if time is a video made from stitching many tiny, indivisible videos together? In an earlier post, I warned against change across the span of a moment. And I still believe in that we should be wary of this; we should make it explicit whether we are ultimately professing such a thing or not.
But perhaps this is the only thing that makes sense. What if the moment IS the change? Each quantum of time (each moment) is really a quantum of change? With static moments, we create this duality between the static contents of moments and the mystical change between them, whatever that means. But perhaps we should just accept change as the fundamental content of moments? This may seem like I am returning to my former view that change is what kills and not time, but I would argue this is a separate matter, and so it isn’t a return. I will get back to that.
I am not well read on Hegel. I, like most people, do not understand him at all (if there even is something to understand). But in SL, he mentioned something that I found to be very interesting and profound. He says measure is the unity of the duality between quantity and quality.
That makes sense, because there is no way to get a measure from quantity unless there is a quantity of something. And that something, that gets quantified; that is the quality. The qualia of the matter. The qualia of the length that we’ve just decided is a meter. The qualia of the duration that is a second…
As you can see, I believe a temporal logic must be intervalist. I believe temporal intervals are more fundamental than temporal points, because the latter is really an unreal, idealized abstraction from the former.
Now, that stance perhaps does not directly force the idea that the quanta of time are themselves dynamic; like an atomic video. But, I think it at least helps motivate this move. If the quality of time was the static breadth of a moment… then there’s this extra layer of how the phenomenology of time somewhat mystically arises as being dynamic from the progression of static quanta. But… as a phenomenologist, this makes me uneasy. It just doesn’t feel like that. The static moment feels like a mere abstraction, utterly impossible to sense or even properly conceive, already gone before it had time to be. If time were truly a video stitched together by still pictures, then why doesn’t it feel like that?
Now, this does not imply I am returning to an idea that change is fundamental. Time is still divided up into quanta, and it is the force of time that brings forth the quantum in which I am dying. The only difference is that instead of time bringing me from a moment in which I am alive, into a moment in which I am dead, time is instead bringing me from a moment in which I am living, into a moment in which I am dying. Then after that, I am being dead. So, I see this as a separate matter, not as a return to change as logically prior to time.
The content of every moment is itself an indivisible action or activity. Every moment is a quantum of change. But this then immediately forces me to ask; what is in-between moments then? Well, I must conclude… nothing. Instead, moments overlap.
If a moment is an activity, then we can abstract from it its idealized start- and end-points. But these are not really points, but rather the sub-regions of overlap with the preceding and succeeding moments (respectively).
Moment 1 overlaps with Moment 2, and Moment 2 overlaps with Moment 3, but Moment 1 does not overlap with Moment 3. And it is this intransitivity that allows all moments to really be entirely overlapping with other moments, and yet moments are still distinguishable from each other. Moments always share their content with other moments, and find their distinction from other moments in that they have different relations to other moments.
And this growing intuition of mine thus clearly connect to what you are claiming here… It seems my philosophy is pushing me towards thinking about the overlaps between moments, and you’re talking about the present as an overlap between the future and the past.
And you then connect that to the breadth of the present. I’ve always known there had to be some kind of breadth to the present, but I didn’t know what it was. Now, it seems like that breadth is a quantum of change, a quantum of duration, or the qualia of duration… And this breadth consists of the overlap of the past and the future…
The more I think of it, the more obvious it seems. It gives a kind of qualitative and even logical continuity to a progression of time that is nonetheless structurally discrete.
What do you think? Am I interpreting your idea here correctly, and if I am not, then what do you think of this idea I am proposing?
Indeed, placing the future as kind of prior is wonderfully ironic, but really intuitive once it is grasped. The deepest truths often tend to be ironic, I have noticed.
Though, there is kind of* a force moving in the opposite direction, the conventional direction. It is the force of logic, where the presence of antecedents in the past force the universal presence of their consequents into the possibilities of the future, which means that regardless of which possibility gets picked, the consequent will be a part of it. We can model this as a force from the past acting on the future/present.
*But, that is a simplification. The logical force from the past to the future is at most a transferred force. Really, there is a kind of parallel force acting on time, acting on the present; the force of God’s selection of which potential gets actualized. God picks a certain antecedent, and God enforces logic, so God thus indirectly forces the universal presence of the consequent in all future possibilities.
We can model this as a transferred force from the past onto the future, because it is practical, but it may be very misleading. It may be misleading because the transference implies a kind of delay between God’s selection of the antecedent, and the emergence of the consequent’s presence in all possibilities.
…But perhaps there is a delay? I wonder if God is omniscient in the sense that his thought, his realization of the world, his computation… is the speed limit (equal to c, I would assume). I don’t know. I view reality as a work-in-progress, and I wonder if God is simply the one who works it all out before us, with even him too being constrained by some speed of computation, of discovery, of self-realization.
If so, there may be a kind of transference of force, because maybe when God picks an antecedent, he must compute its consequents, and once he does, the realm of future possibility is shaped accordingly. His choice of an antecedent forces aspects of his possible future choices, and in this way, there is a transferred force from the past to the future, mediated by God.
But this is just a possibility that I am exploring.
I take this as an agreement that the breadth of the present is not static, but rather dynamic; some quantum of change? And the section quoted above perhaps explains what you think the quantum of change really is. The quantum of change is the selection of one possibility over another, which is the same as the actualization of one possibility and equivalently the non-actualization of all the others.
Would this be a correct interpretation?
I agreed with this back when I wrote my last response, but I just didn’t want to jump into a discussion of what is doing the selection yet. I wanted first to understand the other aspects. When I said:
I did not mean that the potential was singular. I’m a big fan of the following riddle: What is that when you have one of it, you have none of it?
I meant that the potential was a plurality of mutually exclusive possibilities, and time was the force that forced one of them into actuality. But the force that picked which one was a force I wanted to remain quiet on, for that time being. I have long thought of God as the selecting force in reality. I plan on trying to prove God’s existence and nature in my formal system once it sufficiently matures. I think one of the most important proofs of God’s nature will be the proof of his supremacy, which will follow from a proof that reality is indeterministic, and yet the present moment is determined… so, there must be a mechanism that takes us from one to the other. Intuitively, that would be God.
I agree that determinism removes the very purpose of the present and thus, through parsimony, implies eternalism. Or worse, the implication of eternalism from determinism may in fact be fully a priori. Either way, I believe in neither.
Yes, but the consequent is a selection that is inseperable from the selection of the antecedent. God does not violate logic. If you want a more detailed view of my stance on this, I refer you to this discussion: God and the Paradox of the Stone
Logic determines the relations between God’s selections. But it does not fully determine God’s selections. Logic is just not strong enough to determine everything, so at the end of the day, there is a beautiful, indeterminate, divine, magical choice of one thing over another.
I don’t know if God plays dice, but he sure as hell doesn’t just play Sudoku…
I thank you back for your words, and the pleasure is mutual! Minds resonating together reach amplitudes utterly unreachable when alone 