There go my pig videos — Shawn

This little piggy went to market...

No, but that's not something in the world. It's something about things in the world. All the things that could represent that equation wont stay the same. — AmadeusD

Yes, but it's more than just "something about things in the world", it's a belief about things in the world. And the belief is that it is true, therefore something such as correspondence with reality must support that truth, as justification.

Now, the belief is that this "something" is something which does not change. You appear to be saying that if we exclude this "something" from "the world", then we can truthfully say that we believe there is nothing in the world which stays the same. But all you have done here is relegate this "something" which you believe in, to somewhere other than "the world". So unless you adopt some form of dualism, to give this "something" a place of being, then to avoid self-deception you need to accept that this belief is really nothing instead of "something".

In principle, that's the route which atheism takes with "God". God has no place in "the world", so we exclude God from our monist reality, which is allowed only to consist of things of "the world". Then, to be consistent, and avoid self-deception, we must deny belief in God. You have not taken this step, to maintain consistency, and avoid self-deception. You want to believe in "2+2=4", assert that it actually signifies "something", but you want to exclude that "something" from your world, so it would actually be nothing. That would be self-deception, insisting that "2+2=4" actually signifies, represents, or corresponds with nothing.

A notable feature of resource-conscious logics is how they naturally have "quantum-like" properties, due to the fact their semantic models are state spaces of decisions that are generally irreversible, thereby prohibiting the reuse of resources; indeed, the assumption that resources can be reused, is generally a cause of erroneous counterfactual reasoning, such as when arguing that a moving object must have a position because it might have been stopped. — sime

Can you explain a bit more thoroughly what you mean by "resource-conscious"?

Lot's of things stay the same as time passes. Look around you. Don't you notice a lot of aspects which are not changing as the time passes. But if that doesn't convince you, we could look at some simple arithmetic. Do you believe that the truth of "2+2=4" could change as time passes?

I don't think that's a solution - especially as I'm not clear what the problem is. We have two different ways of describing the world. End of story. — Ludwig V

Not "end of story". The two different ways correspond with two distinct aspects of the world. If it was simply a matter of two different ways of describing the same thing, we'd choose the best for the purpose at hand. But the two different ways correspond with two different aspects, that which stays the same as time passes, and that which does not stay the same as time passes.

Unsound argument means the premise was false, and also invalid reasoning was applied for the conclusion. — Corvus

Replace "and" with "or" here, and you'll see that if the reasoning is valid and the premise is false, then the argument is valid but unsound. So you should conclude "Hence the argument is unsound', instead of the following:

Here reasoning seems valid, but the premise was false, which led to the false conclusion. Hence the argument is invalid. — Corvus

https://iep.utm.edu/val-snd/

Your notion of "change" is untenable. I'm reminded of Heraclites' river.

Change is irrelevant to JTB. At time t1(insert well-grounded true claim here) and viola! — creativesoul

So, if knowledge is JTB, and change is irrelevant to JTB., am I correct to conclude that we cannot have knowledge of change, therefore?

My notion of change is untenable to you, because change is unintelligible to you.

Wrong assumptions lead to invalid conclusions. — Corvus

It's better to say that those conclusions are unsound rather than invalid.

An obvious wrong assumption? — Corvus

That assumption does create a measurement problem. So unless we think that measurement problems are good, then I'd say it's a wrong assumption.

But it does puzzle us still. Because if you think that we know everything about mathematical infinity, then I guess there should be an answer to the Continuum Hypothesis. — ssu

Again, "continuum" assumes something being divided. Simply saying that there is a number between any two numbers does not assume anything being divided, just like assuming that there is always a higher number does not assume anything being counted. These are simply pure mathematical axioms. But when we say things like "there is a continuum", "numbers are objects", then we introduce ontological premises into the mathematical axioms, which may or may not be true.

Is this a "misuse" in mathematics? We are talking about mathematics.

Pick two real numbers, and it can be shown that there are real numbers between them. Pick even two rational numbers, and you have rational numbers between them.

You would wander to the illogical, if you would to start to argue that it isn't so, that it's misuse or something. — ssu

That's not misuse, nor is it a problem.

The problem is in Zeno's application, when things like distance, and time, are assumed to be infinitely divisible. It is a measurement problem because instead of determining the natural constraints on such divisions (these constraints are unknown), it is simply assumed that divisibility is infinite.

Can you show me a physics text that does not use time? — Banno

How's that relevant? Physics uses mathematics, but that doesn't mean mathematics is physical.

Here I would side with Moliere. It is a logical problem. Or basically that the measurement problem is a logical problem, hence you cannot just suppose there to be "an adequate way of measurement". — ssu

Whether or not it is possible to devise an adequate way is irrelevant. The problem is that we do not have an adequate way. And the lack of an adequate way produces the use of an inadequate way. Therefore the problem is not a logical problem, it is a problem in the application of logic. Principles are applied where they are not suitable for the task which they are applied to. That is a measurement problem.

The problem is infinity itself. And that is a logical problem for us. — ssu

Infinity itself is not the problem. The problem is how the concept of infinity is developed and employed. In its basic form "infinity" allows that principles of measurement such as numbers, can be extended indefinitely so that in principle anything and everything can be measured. That is beneficial, it is not a problem. The problem is that there are many misuses of infinity, such as the idea that there is some type of thing which can be infinitely divided. That is not a problem with infinity, but a problem with its application, a problem of applying the wrong principles to the task, a measurement problem.

Zeno's paradoxes are very clearly problems of measurement. Like I explain above, if we had the appropriate way of measuring things like time and space, we wouldn't have to entertain the logical possibility of infinite divisibility. Then there would be no such paradoxes. The paradoxes are due to a deficiency in measurement capacity.

We're limited in terms of measuring -- but I want to say that Zeno's paradoxes are not problems of measurement at all. They are logical problems (which is why they evoke the difference between physics and logic and math, as the OP stated already) — Moliere

The logical problems are the result of not having an adequate way of measuring. We are reduced to logical possibility. If we had the proper way we wouldn't have to entertain those possibilities.

So for example, the true divisibility of every physical thing is determined by its physical composition. But if we do not know how it is composed we just assume the logical possibility of infinite divisibility. This is what happens with space and time, and before the atomists, matter itself. We do not know how these things are composed so we just assume the logical possibility of infinite divisibility.

A "non- physical" measurement of a physical quantity... what would be your non-physical units for the fuel left in the tank - not litres, since they are physical. — Banno

I was talking about the problems with the measurement of time (basis of the uncertainty principle), not the measurement of fuel. Show me how time is a physical quantity.

What I'm asking is more about Heisenberg's Uncertainty Principle, which as he interpreted it meant that reality itself doesn't allow for a precision of both, but rather demands aprecision, or position,* of any one particle. But due to cuz that's how nature works, not cuz how we measure it. — Moliere

It's due to the way that time exists, in conjunction with the limitations of our capacity to measure. We are limited in our ability to measure time by physical constraints. If we had a non-physical way to measure time we wouldn't be limited in that way.

Thanks Das, I'm going to hold off on any further reply right now and take a look at your essay.

Timestamps, while not sufficient, are nevertheless necessary for any attempt to articulate change. The shift from being to becoming cannot be described adequately through a chain of static states. As Aristotle argued, change is not captured by a succession of positions; rather, it exists between them. It’s a different kind of phenomenon—continuous, processual, and epistemically elusive. Yet without temporal markers, we would lack the coordinates needed to locate, compare, or even recognize shifts in state. Timestamps provide the necessary structure within which the insufficiency of static snapshots becomes visible. They do not capture becoming, but they allow us to trace its outline. — DasGegenmittel

I agree with this, and this use of time stamps to understand change is commonly found as cause and effect, which is a temporal ordering. In physics, the matter gets complex because special relativity employs the principle of the relativity of simultaneity. This allows that spatially separated events can have different temporal ordering depending on the frame of reference used. I believe it is common practise in cosmology for example, to choose the frame of reference according to principles of giving the proper temporal order to events which are known to be causally related. That is the "light cone" principle.

In this context, DK is not a lack of certainty, but an ideal in its own right. Knowledge is modeled as a limit process: not something one has, but something one approaches. The limit in the DKa and DKh formulas represents the asymptotic approach to ideal knowledge in dynamic contexts. It shows that knowledge evolves step by step, reducing uncertainty over time, but never fully reaches absolute certainty: see as well bayesian epistemology as complementary approach. It models the continuous refinement of justified beliefs under changing conditions. I distinguish two complementary dimensions: — DasGegenmittel

To me, this is equally problematic, because it sets out what knowledge ought to be as an ideal, without properly addressing what knowledge really is, in its actual existence, the ontology of knowledge. The fact that it "never fully reaches absolute certainty" indicates that knowledge never is the way that it is shown to be. So we are still stuck with the same problem that Plato demonstrated with JTB, we do not have a good understanding of what "knowledge" actually is, in its real existence.

Unless we address the issue of what knowledge actually is, how it exists as the property of particular individuals, we still have that ought/is separation between what knowledge ought to be, and what it really is. And, if we keep focusing on the ought, without addressing the is, the knowledge which is the property of individuals, might actually be progressing in a different direction and we wouldn't even know it. So for example, we may be allowing our criteria for justification to be getting more and more lax, so that the knowledge which individuals have may be actually getting a lower and lower degree of certainty, and moving away from the ideal, though we claim we are moving toward the ideal.

The "uncertainty principle" is an example of how we are inclined to allow ourselves to move away from the goal of certainty, allowing uncertainty right into our knowledge, as an acceptable part of it. The matter/form division of Aristotle relegated unintelligibility to matter, ensuring that only the aspects of reality which were designated as intelligible were allowed to be part of our formal knowledge. The unintelligible aspects were segregated, and excluded.

Elsewhere, I've argued that the inclination toward "formalism" is a cause of this trend, to allow aspects known to be unintelligible, to enter into knowledge. In its quest for absolute, ideal principles, (which is really impossible) formalism allows elements of uncertainty right into the basic premises, the axioms. This contaminates the entire formal structure, allowing uncertainty to lurk everywhere instead of excluding it from the formal structure, which ensures that valid logic produces certainty and relegates uncertainty to the truth or falsity of the premises. The formalist axioms already incorporate uncertainty.

JTC mirrors the structure of JTB—justification, truth, and belief remain essential—but reinterprets them dynamically. Truth is no longer static but contextualized within time. Justification adapts, and belief becomes a crisis-aware assertion. Together, these preserve the functional core of JTB while enabling knowledge to operate under uncertainty. JTC is not a rejection but a temporal simulation of JTB—an epistemic snapshot in motion, like Zeno’s arrow suspended mid-flight. — DasGegenmittel

This appears like you are trying to justify uncertainty. This would be a step in the wrong direction, as explained above, a movement away from certainty.

Personally, I find no issue between JTB and change. That's what proper indexing/timestamps are for. — creativesoul

Timestamps are not sufficient, because what is at issue is the fundamental difference between a describable state-of-being, and the activity of becoming. What Aristotle demonstrated is that we cannot adequately describe any activity as a succession of states-of-being because there is a basic incompatibility between these two.

If state A changes becomes state B at a later time, then the change has occurred in the time between A and B. If we describe the change between A and B as state C, then changes have occurred between A and C, and also between C and B. If we continue to describe changes in terms of intermediary states, we'd posit D as between A and C, and E between C and B, and we are on our way to an infinite regress of states-of-being, without ever describing the activity which is the change which occurs in the time between distinct states. Therefore we cannot ever adequately describe active change, or becoming, in terms of states-of-being.

You pointed out the tension between Parmenides’ being and Heraclitus’ becoming, referencing Aristotle, who saw these opposites as irreconcilable. Your proposed solution is a dualism that separates both aspects. This is precisely where my distinction between Static Knowledge and Dynamic Knowledge comes in:
• SK refers to timeless, secure knowledge (e.g., mathematics).
• DK is tied to changing conditions (e.g., the fastest route to work today). — DasGegenmittel

This roughly correlates with the division in Aristotle's Nichomachean Ethics, theoretical and practical knowledge. Each of those two is divided into branches and there is a differing degree of certitude expected from each different field. You'll notice though, that the two are not completely divided in reality, as practical knowledge consists of applying theory, and theoretical knowledge would be useless if there was no practical purpose for it. This is why intuition is assigned the highest position, because intuition is the type of knowledge which oversees these relations.

So in theory we divide the two, being and becoming, as fundamentally incompatible, but in reality, and in practise, the two continually intermix. If they weren't actually intermixing, we'd have "the interaction problem" commonly attributed to dualism. The reality of the intermixing creates the need for a third principle which provides the basis for describing the intermixing.

Immutable and timeless elements (see deduction) are often conflated with mutable and temporal ones (see induction), as is the case in many Gettier examples. The expectation that knowledge should work the same way in inductive contexts as it does in deductive reasoning is, as you imply, unfounded. The epistemic monism currently dominant in the field is therefore deeply problematic. That’s why I wrote my paper Justified True Crisis—because this issue often goes unrecognized. It’s reassuring to know there are people out there who think along similar lines. — DasGegenmittel

I believe that this is the issue of "understanding". Understanding requires the differentiation between the types. Conflating everything into a monism produces misunderstanding, and is itself a form of misunderstanding.

In relation to Plato’s Theaetetus, you argue that knowledge cannot be understood as “Justified True Belief” (JTB) because we can never completely rule out the possibility of falsehood. Therefore, “truth” cannot serve as a sufficient criterion, and JTB itself cannot be equated with knowledge. This interpretation reflects a typical post-Gettier skepticism, namely that the concept of truth itself remains “inaccessible.”

In my model, this doesn’t mean we discard truth altogether. Rather, the discussion around Gettier cases (e.g., the stopped clock) highlights the need to distinguish between static and dynamic knowledge. We still need “truth” as a goal and standard for knowledge, but we must accept that in DK-domains, our beliefs are constantly subject to revision, and we can never claim absolute certainty in changing environments. — DasGegenmittel

This is the complex issue, what directs the intermixing, the guiding light, the intuition. Notice that you say "we still need 'truth' as a goal". That itself, may not be true. The goal is the end, that for the sake of which, what Plato called "the good", and goals are freely chosen. So knowledge appears to have a deep pragmatic base, the practical side driving its advancements and evolution toward what is deemed as "good". You can see how modern science has developed toward prediction as its goal, and the capacity to predict does not require truth. Modern mathematics and other theoretical principles are designed toward statistics and probabilities, and the truth about what is going on behind the scenes of the things being predicted is unimportant.

The result is a separation between 'the good" which is the goal of knowledge, and "the truth" which is merely a possible goal. So epistemology may set out JTB as the goal for knowledge, an ideal, what knowledge ought to be in theory, but knowledge in reality is not an immutable eternal thing, it is actually evolving with practise. Because of this, "Truth" is replaced by other goals, and justification is relative to those goals, and there is a difference, or separation between knowledge as it ought to be, and as it really is.

The primary characteristic that makes the waking state feel real is its continuity (not in the strict mathematical sense; unless stated otherwise, the broader sense is to be understood) with preceding waking states. — Deep Kumar Trivedi

This realness is a creation of the conscious mind, through the use of memory. The consciousness uses chronology to create a sense of order which appears to it as rational and coherent. Through this appeal to coherency it dismisses the creations of the dreaming mind, which lack rational coherency, as unreal.

This characteristic is generally absent among dreaming states. Dreams are typically disconnected from one another. A dream begins abruptly, while a waking state always has a definable starting point. Even when a dream incorporates elements from the preceding waking state, it lacks full continuity.
For instance, suppose I am waiting for a friend. While waiting, I nap and dream that my friend arrives, and we share memories from the past. In this case, the dream exhibits a partial succession of events from the prior waking state. However, it remains a dream because the continuity of succession is incomplete. Upon waking, my friend would not recognize or verify the conversation we had in the dream.
Here, an interesting analogy can be drawn between the continuity of waking states and the mathematical concept of removable discontinuity (in its strict sense). In mathematics, a removable discontinuity occurs at an
x-value in a function where the two one-sided limits exist, are finite, and equal, but the function is not defined at that point. — Deep Kumar Trivedi

I don't think that you properly represent continuity and discontinuity here. The continuity which you describe as proper to the waking state is really a discontinuity, created from separate instances, separated by sleep. So the supposed coherent rational continuity is really false and incomplete because it is broken up by sleep. Therefore in reality the coherent rational continuity which is created by the conscious mind is not a true continuity at all. It is really a bunch of separate instances pieced together by what the mind believes to be rational principles of coherency, and this creates the appearance of a continuity.

Similarly, a dreaming state is like a point of discontinuity where the function (representing waking experience) is not defined, as the waking experience is not accessible to the dreamer. The preceding and succeeding waking states resemble the left-hand and right-hand limits, respectively. Both limits approach the same event, ensuring continuity. — Deep Kumar Trivedi

I believe you need to account for the inverse of this as well. The dreaming condition, and memories associated with it, cannot be included into the coherent rational continuity which the consciousness creates from its memories. Therefore all these memories (dreams) have to be excluded as some sort of fictitious memories, and that leaves a gap of discontinuity in the supposed continuity of the waking experience.

there are numbers that cannot be counted... — Banno

Only if you are a Platonic realist. Metaphysically, that's an issue with set theory in general, Platonism is presupposed.

And when abstractions such as numbers, are assumed to have independent existence just like physical objects, with no principles to differentiate between the abstract and the physical, we have the problem 180 mentioned:

confusing the physical and abstract. — 180 Proof

This is why the law of identity was imposed, as a principle of differentiation between physical objects and abstract objects. A physical object has an identity unique to itself, an abstract object has no such identity. Therefore all those assumed numbers which cannot be counted, have no identity.

ep. It is also connected and complete; it has a topological structure. Of course, not all the issues are ironed out and answered. If you want more you will need to talk to a mathematician. — Banno

Are you saying that topology adds something to the line, which is more than just the real numbers? What more could there be?

Anyway — Please let him just continue. It almost always guarantees a laugh whenever I check. — Mikie

NOS4A2 can be entertaining, but he seems to be get lazy, just posting a whole lot of X files now.

Do you guys fire-bomb Ladas to get back at Putin? — NOS4A2

In the 80's if you showed up to a party in a Lada, you had to park around the block.

They don't. The continuum is not just a set of points. — Banno

So are saying that there is more to the continuous number line than the points which are the real numbers? Can you explain that?

Treat it as points, or as a continuum, but not both. — Banno

Then why does mathematics combine the two? Real numbers are points representing a continuous number line.

Aristotle demonstrated that "knowledge", claimed by Parmenides as "being", is inconsistent with the reality of "becoming" which was asserted by Heraclitus. These two aspects of reality, being and becoming are simply incompatible. The solution to this problem is dualism.

Plato demonstrated in The Theaetetus, that "knowledge" as we know it cannot be described as JTB. This is because the possibility of falsity cannot be excluded, therefore we cannot hold truth as a criterion. In other words, the requirement of truth cannot be justified, therefore the idea that knowledge is JTB cannot itself be knowledge.

And if we remove the requirement of truth, we are left with justified belief, and this does not properly represent what we request from knowledge. So Plato concludes The Theaetetus with the proposal that trying to understand knowledge with the preconceived notion that it is some form of JTB is actually misleading.

The two are admittedly modeled as points, which works if you consider say their centers of gravity or their most-forward point. But by your assertion, do you mean that the tortoise is never at these intermediate points, only, the regions between? — noAxioms

I mean that if the tortoise is moving it is never at a point. This is because time is continuously passing, therefore motion is continuous too. So the closest thing we could truthfully say is that it is passing a point. To be at a point would require a stoppage in time. There is no time when a moving thing is at a point because that would a stoppage of time, which is a matter of removing the thing from time. That's the point of Zeno's arrow paradox.

Sorry to find a nit in everything, even stuff irrelevant to the OP, but relativity theory doesn't say this. In the frame of Earth, Earth is stationary. There's noting invalid about this frame. — noAxioms

I didn't say it's not valid I said that it's not true. Obviously the earth is not stationary. So that frame in which the earth is stationary is not true, it's an arbitrary (untrue) assumption, made for some purpose.

Take the zero-point energy, for example. In relativity it corresponds to the cosmological constant (lambda term) or 'dark energy' of the Universe. Besides the fact that measurement for the 'dark energy' does not match the theoretical predictions for the zero-point (the cosmological constant problem), we here have grounds for challenging relativity, based on the lambda term, given we affirm the validity of quantum. — Nemo2124

I believe "zero-point energy" is the consequence of relativity type thinking. Since relativity denies absolute rest, anything which appears like it ought to be rest, or is assigned "rest" (rest frame etc.), cannot actually be rest, to be consistent with the principle of relativity. Therefore assigning "rest" to something is actually a matter of assigning some form of unknowable motion to it if we adhere to relativity. This manifests in the Heisenberg uncertainty principle.

The tortoise moves harmoniously even by infinitisimals, at the end, taking an eternity to reach the finishing line, but reaching it in the end (because of the summation of geometric series). — Nemo2124

That the "summation of geometric series" will bring one to "the end", is actually demonstrated to be false by the need to assume "zero-point energy". The zero point cannot ever actually be reached in this way, and the practise of the summation of geometric series', is just a rounding off which does not represent physical reality. Since there cannot be any correspondence between the artificial end and any possible real end, due to the relativity premise which dictates that there is no end, then the end produced by summation is simply fiction. It's just a convenient way to avoid the problems created by relativity type thinking, but since it's fiction it produces useless metaphysics.

This is the problem approached by. If the abstract (ideal) is not representative of true reality, we need to understand and respect how this difference may mislead us. In this case, the physical reality of zero-point energy is evidence that the boundary applied by abstract thinking is not consistent with physical reality. So the series summation reaches the boundary (zero), but this is not representative of physical reality, and we are left with something real, called zero-point energy. The physical reality of what is actually represented by that name "zero-point energy" cannot be understood by this way of thinking because it gets swallowed up into the uncertainty principle, as an aspect of reality which cannot be understood.

We need a starting point here. Do we first take relativity to be valid or the absolute quantisation of space-time? Does the Planck constant suggest that there is a real fabric to space-time at the vacuum level? What is the nature of this fabric? These are questions that start to arise when we have a starting point, that is the discretisation of a space-time. In other words relativity has to make itself compatiable to quantum theory and not vice-versa. We just have to accept that the tortoise wins. — Nemo2124

The problem with this proposal is that there is too much relativity already baked into the procedural methods of quantum physics. Our understanding of energy and how electromagnetic radiation relates to massive objects is relativity based. So it's not a matter of making relativity compatible with quantum theory, it's a matter of falsifying relativity and starting from whatever that falsification reveals. This requires the appropriate attitude, as falsification requires application (experimentation) designed for that purpose.

Given an eternity and the fact that the tortoise keeps moving, I think that it will eventually cross any line that is set at a finite distance in the race. — Nemo2124

It cannot, by the premises of the example.

Physical space is not "infinitely" divisible like abstract space. Like most, this paradox is merely apparent – in this case it's derived from confusing the physical and abstract. — 180 Proof

What would you say that "physical space" is made out of? The divisibility of anything is dependent on what the thing is composed of. If you assert that physical space is not infinitely divisible you need to justify this with some principles, say what space is composed of, and how this limits its capacity to be divided. We tend to think of space as nothing, but then it's just an abstraction, and infinitely divisible. But if it's not nothing, then what is it made of?

The ancient Greek atomists limited the capacity to divide physical substance by positing fundament particles, atoms. The atoms would be indivisible. But Aristotle demonstrated the logical problems with this perspective. Each atom would have to be the same because internal differences would provide for different ways of dividing. And if all atoms are the same, then the differences between different objects could only be a matter of quantity, unless we assume something else to allow for qualitative differences between things. This is why the dualism of matter and form was required.

.

Sticking to the paradox, I don't think that Achilles can ever reach the tortoise, unless it reaches some sort of Planckian limit in distance and suddenly quantum leaps to become 'the winner'. That suggests that space-time is discretised, that you do reach a limit in physics that does not exist in mathematics. — Nemo2124

Maybe there are true, real limits within time and space, real quanta or discrete units of these, but use of the current way of modeling, which imposes an artificial limit or boundary, and uses calculus to show the approach to this limit, will leave us unable to find these real boundaries. And since relativity theory, which is the most common tool for physicists, assumes the fundamental premise that there is no such thing as absolute rest, modeling an object as reaching, or being at a fixed position in space, is inconsistent with relativity. Simply put, rest frames are imposed according to the purpose. By relativity theory, an object is always moving, and cannot actually be at a fixed position.

To be consistent then, if we employ relativity theory we cannot use the calculus which assumes a fixed position, the boundary or limit. If we quit using these artificially imposed limits, and model moving objects as truly continuous, instead of modeling them as approaching these fixed limits, then the issues and problems which emerge from employing principles of true continuity to the physical world, will reveal whether or not there are true boundaries to space and time. The point being that employing artificially (purposely) created boundaries, which do not correspond with true boundaries will just create confusion and unintelligibility, if we seek the true boundaries.

In the end, quantum leaps aside, although the tortoise moves at an imperceptibly and almost infinitely small pace, it still keeps moving and eventually will cross the line, given that there is no time limit. This seems to accord to what we perceive in reality, we are somewhat subordinated to nature's ultimatum. — Nemo2124

No, the tortoise will never cross the line if there is no time limit. Time will keep going forever, and the tortoise will always have more space to cover before it reaches the line. Therefore the tortoise will never cross the line. this is very similar to the way that Achilles will never reach the tortoise. The latter is a more complex presentation, the complexity designed to create more confusion when looking at the same problem.

Have they shιt all over Ukraine yet (again)? Reports a couple of months apart: — jorndoe

During the debate, prior to the election, Trump said that if he is elected, the war would be ended before he even takes office, because he knows Putin really really well.

I don't think the tortoise actually wins. In a similar way to the way that Achilles cannot catch up to the tortoise, the tortoise also cannot actually reach the finish line. To reach the finish line, the tortoise must first cross half the distance to it, then half the remaining distance, then half of the remaining distance again, and onward infinitely.

I think what this indicates is that this way of looking at movement, as proceeding from a start point to an end point, is somewhat incorrect. We ought to remove those points, those beginnings and ends, from the representation of the movement of the thing itself, and model the movement as moving past the designated points. Then we show Achilles as moving past the tortoise, and as moving past the finish line, instead of modeling the movement as ending at the specified point. I believe that this would resolve all such paradoxes.

To me, trial and error is a method of problem-solving, such that the solving of the problem is its entailed end. — javra

This would be one type of trial and error, to use it as a way of solving a specific problem. In the more general sense it is defined as "the process of experimenting with various methods of doing something until one finds the most successful". So it is a way of acting in which one is attempting to find "the most successful way", i.e. the best way. In this way, each attempt, each trial may solve the given problem, but we're looking for the best way to solve the problem.

Trial and error in no way overlaps with unintended, and hence accidental, discovery: if one, for example, accidentally discovers a valuable jewel underneath one’s sofa while cleaning one’s room, there was no trial and error involved in the process; on the other hand, trial and error, because it always seeks an end, is always purposeful, intentional, such that when the problem is solved by this approach, its so being solved is not an unintended accident. — javra

I see we really do disagree. Discovery by trial and error is an accidental discovery. That you can give an example of an accidental discovery which was not made by trial and error, does not indicate that trial and error does not produce accidental discoveries. If a person already knew what would qualify as the best way, they would not have to use trial and error. We cannot define what would constitute the best way, prior to the trial and error procedure, therefore the way which is found to be the best way, cannot be said to have been identified as the best way, prior to the procedure. So the thing found was not being looked for, and its discovery as "the best way", is accidental.

This is a matter of moving from the general to the particular. The general is "the best way". But the particular which is settled on, was not identified as the particular being looked for, only the general was being looked for. So that particular thing, as what fulfils "the best way", was found accidentally. In other words, we cannot go into a trial and error process with the idea that X constitutes success, because we do not know what will constitute success until we compare the trials. This is relevant to the point I made about how knowledge concerning the end prejudices a trial and error process, robbing it of objectivity.

on the other hand, trial and error, because it always seeks an end, is always purposeful, intentional, such that when the problem is solved by this approach, its so being solved is not an unintended accident. — javra

Of course the intention of the trial and error process is success, but that does not imply that when success is found, it was not found accidentally. The issue may be best illustrated this way. We can only try a finite number of ways. So if we try ways A,B,C,D, instead of ways W, X, Y, Z, and find that C is the best way, instead of finding that X is the best way, this difference is dependent on the random choice of the finite ways that we try, and it is therefore accidental. Any success found through a true trial and error process, is fundamentally an accidental success. This is due to the nature of choosing the trials. And if there is specific knowledge which prejudices the selection of trials, this is not a true trial and error process, but a process based in some prior knowledge about what constitutes the best way.

As to evolution being a trial and error process, I then find this to be a fully metaphorical application of the phrasing. Evolution is not a sentient being; and thereby cannot as process of itself intentionally problem-solve anything, much including via any trial and error means. More bluntly, what problem might evolution be intending to solve? This is not to then claim that evolution is not in large part a teleological process, but evolution is not the type of teleological process which applies to the intentioning of individual agents (and only to the latter can trying and failing and then trying again, this with a set goal in mind, apply). — javra

You are restricting your definition of "trial and error" to problem solving rather than allowing the more general sense of seeking the most successful way. If you allow the latter then you could consider the possibility that living beings are seeking the most successful way of living through the trial and error process we see as evolution.

In an Aristotelian model of things, “optimal eudemonia” (what you’ve termed “happiness”) is everybody’s ultimate end at all times – and not just for he who has agreed to uncover rocks for someone else. It will hence equally apply to he who wants the rocks uncovered for his own hidden purpose by the person who’s agreed to do so. And this Aristotelian conception of the ultimate end is only the most distal (distant) telos of an otherwise potentially innumerable quantity of teloi any person might be intending at any given time. And in so being, though one might get closer to it at certain times rather than others (when one is more at peace, or else joyful, for example), this ultimate telos of “optimal eudemonia which can only translate into a perfected eudemonia” is the most unreachable telos of all teloi out there. The most difficult, if at all possible, to actualize. It here drives, or else determines, all other teloi, this at all times, but it itself cannot be obtained for as long as any personal suffering occurs or is deemed to have the potential to occur. This includes some personal interpretation, granted, such as in what "suffering" signifies. But I still find it to be the only coherent way of understanding 'happiness as ultimate end'. — javra

It was your response to say that the person's end is to turn over the rocks. That would mean what the person wants and desires is to turn over rocks, so doing this would make the person happy. So clearly the person would be happy doing this, because doing anything else would interfere with what the person wants, and that is to turn over rocks. Therefore the person would be most happy turning over rocks.

Secondly, why did the person who’s agreed to turn over rocks so agree in this first place? — javra

That is the issue I got to later, about communication.

How's that relevant to what we are talking about, spatial expansion? If the distance between the object and the center of the earth is caused to change due to the effects of spatial expansion, this change is not included in the concept of energy. Therefore such a change in distance would not change the object's potential energy.

I don't see your point. Either the ball is at 2m or it is not. If it is falling it is not at 2m, it is moving. If it is at 2m then something is holding it there and a force is required to cause it to fall.

If it's distance changes due to the expansion of space, this change in distance is not included in the equations of the concept of energy, and so it is not considered to be "motion" as the term is applied in that concept.

I'm not sure about that. The potential energy between two objects *increases* with space. A ball 2m above the surface of the earth is said to have more potential energy than a ball 1m up. So perhaps it all adds up. — flannel jesus

I don't think so, because a ball at 2m will stay at 2m, as time passes, unless forced to change. However if space expands as time passes, the difference due to this expansion is not accounted for in the equations of energy. That is why a difference in distance, which is attributed to spatial expansion, is not classified as "motion".

I for one don't find reason to assume the observer is separate from the actor (here specifically as pertains to the act of choice making). — javra

The reason to assume a separation between actor and observer is that this separation is purposeful. The purpose is as I explained, it provides for a more objective trial and error process, by separating the judge who holds the principles for judgement (good), from the agent. This removes prejudice from the agent's choice of actions allowing that the agent will explore all possibilities, thus enabling true objective trial and error.

Do you agree that trial and error forms a significant part of a living being's activities, and that the process we know as evolution demonstrates a large scale trial and error process?

In the example you provide, on the other hand, I as the actor must for whatever (I uphold end-driven) reason first comply with your request if I am to at all act as you wish on your behalf. Once I so comply, then my actions will themselves all be end-driven - this not by your want to engage in trial and error actions whose end is unknown to me - but by my own then actively occurring want to successfully end up so "turning over all the rocks in a specific area". This in itself then being the end which teleologically drives, and thereby motivates, my actions.

So, at least in the example provided, I still find all activities to be end-driven and thereby purposeful. — javra

This is a good point to consider, and I think that the example is applicable. In the way you explained the example, you simply have a desire to turn over all the rocks, and that itself is your end. From my perspective that so-called end is just the means to a further end, to look for something which is assumed to be under one of them. As Aristotle pointed out in his analysis of ends and means, each specific end can be viewed as the means to a further end, and this produces an infinite regress if we do not designate an ultimate, final end, which he named as happiness. So this activity of turning over rocks is like your "happiness", you are fulfilling what you perceive as your ultimate end, you apprehend no reason for this act, or even doubt the possibility that there might be a further reason which you are unaware of, therefore you are satisfied in your acts, and you are "happy" fulfilling your desire.

However, like I explained, true understanding of "purpose" requires that we put the activity of the part into a larger context, and this means into a relation to other parts and the whole. So, in this respect, your understanding of your goal, the end which motivates you, is actually very deficient and incomplete. Your actions of turning over rocks, though this makes you very happy appearing to be the only thing desired, are completely meaningless, unless we put those actions into the context of the observer, and the judge who is judging them in relation to a further end. This larger context gives your actions meaning.

Now, the issue we need to consider is this relationship between you and I in the example. In this example, I am somehow able to set you about, in your motivated actions, which are actually carried out for the purpose of my goals, without you knowing that you are doing this for me, therefore a further end. So, I somehow communicate to you, what you must do, and motivate you to do it, for my purposes, without you even being aware of my existence as an agent myself, with intention.

Then we can apply this to the dream/awake relationship. We commonly believe that the dreamer is set free to go about the random process of dreaming, so that the dreamer would be like you, randomly turning over rocks, except given a wider parameter of activity, to dream up virtually anything. And, in this understanding, the dreamer is unaware of the conscious observer, who has set the dreamer to this task, so the dreamer does not realize that this is actually being done to facilitate a further end of the conscious mind.

So here's the key point. In my description, of the relationship between conscious awareness, and the dreaming unconscious, I've revealed that the common understanding is really a misunderstand, and we need to invert this relationship to understand what is actually the case. In reality, the unconscious is the true observer, who sets the consciousness to the task of performing random acts. And in sleep, the unconsciousness is processing the observations, allowing the conscious only glimpses of this process through dreams. This provides the consciousness a glimpse of the reality of the unconscious, but not enough for the consciousness to understand why it behaves as it does, and the true meaning in its activities.

As demonstrated by the example, there must be some relationship between the unconscious observer/judge, who sets the agent to work, in order for the consciousness to receive its marching orders from the unconscious, but this relation is kept to a minimum to maximize the objectivity of the trial and error process. So the consciousness receives different urges and motivations from the unconscious, having very little understanding of the true meaning of its actions, and why it is doing what it does.

Are you then suggesting that intentioning can occur in the complete absence of any intent? Such that X can consciously intend some outcome Z despite not being motivated by any intent/end - an intent/end which thereby equates to Z's successful actualization at some future point in time? — javra

I am suggesting that if we maintain a separation between means and end, i.e., the act and the desired result of the act, then X can consciously intend the act without being motivated by the end. Further, if we assume two distinct types of agency, one which communicates motivations to act, and the other which carries out the physical acts, then the agent which is motivated toward physical actions can consciously intend these actions without knowing the intended end of the actions. And this is not to say that there is no further end because in this scenario the agency which communicates the motivation to act is simply not revealing the further end, to the one which carries out the physical act.

But, again, I don't find reason to entertain what you've so far suggested. — javra

Do you agree that trial and error forms a significant part of the activity of life on earth, in a general way? If you agree that evolution is a process based in trial and error, then you might see the need to determine the nature of the trial and error process, and what principles are required to produce a true and objective trial and error process.

Neither of these, however, refute the purposiveness of each individual agency of a total mind concerned. — javra

The point was not to refute the purposefulness of individual agencies, but to question how we identify and locate the purpose or intention. If there is a group of agencies which work together, in a united way, it is not necessary that any one of them knows "the thing intended" by its actions. The goal or end to the agent's actions might be something completely outside the actions of the agent. This is a matter of how we identify the purpose of an action, by placing the action within a larger context. What gives the action its purpose is the larger context, so that the purpose of an agent's actions are not necessarily something which is derived from the agent itself. Therefore we cannot accurately say that the agent is trying to accomplish something.

Accordingly, we cannot accurately describe acts of intentional agency as acts motivated toward accomplishing something. And, an agent may act in a completely accidental way, not intending to accomplish anything. This means that we cannot exclude the possibility that an act of agency may be fundamentally accidental.

As to trial and error processes, I can so far only disagree with such being purposeless. — javra

I agree that it is impossible for an act of trial and error to be purposeless, that would be contrary to the meaning, therefore self-contradictory. The point is that the purpose may be something completely independent of the agent making the trial and error act. If we assume that the observer in the trial and error act is separate from the acter, this becomes very evident.

Suppose I assign to you the task of turning over all the rocks in a specific area, because I am looking for something underneath one. You, the acter only know the specified act, without any knowledge of what constitutes success or failure, only I, the observer, knows. We can take what that analogy demonstrates, further, and assume an agent which has been endowed with the capacity to act "freely", in any way possible, instead of being assigned a specific task. This free agent simply acts randomly, without any goals or intentions, and like the example of you turning over rocks while I observe, it has no specific idea, of the "intention" of its acts, inherent within itself, but it is being observed, and its actions are being judged by the observer in relation to some principles of success and failure.

The trial and error actions of the agent in this scenario, are from the perspective of the observer, very purposeful. But from the perspective of the agent there is absolutely no purpose for its actions. If the agent allows any sort of purpose to direct its actions then it is not fulfilling its true purpose, as assigned by the observer, and the trial and error experiment would be corrupted.

What I propose, is that to have a truly objective trial and error process, the purpose must be separated from the agent in this way. If the agent grasps the intention in any way, this would contaminate the trial and error process by guiding the agent's actions in a subjective way.

So doing would then be evolutionarily unfit. And so it would not then be as common an activity in lifeforms as it currently is. On the other hand, whenever we as conscious humans engage in trial and error processes it is (as far as I know) always with a purpose in mind. — javra

This is a correct account of trial and error. However, there is another factor to consider. Since error is highly possible, and it could be injurious or even fatal to the acting agent, it is beneficial to the one proceeding in a trial and error process, to have someone else carry out the actions, and simply observe the other. So when we separate the agent from the observer in this way, trial and error takes on a completely different appearance. There is a fundamental form of deception which the observer must impose on the agent, to withhold information from the agent, concerning the intent of the agent's actions. True objective trial and error requires a separation between agent and observer such that the agent does not know the intentions of the observer.

While I grant that our unconscious doings might at times seem random to us, I can so far find no reason to entertain that any intention-devoid agency can occur. I acknowledge the possible reality of randomness in relation to agency at large, but will deem it to be the outcome of discordant agencies, each intention-endowed, whose interactions results in outcomes unintended by any. This be the agencies individual humans or else the individual agencies of a singular total human mind. — javra

What I am suggesting is that randomness is a necessary aspect of true trial and error. The higher the degree of randomness there is in the actions of the agent, the higher the quality of the trial and error process. This is due to the nature of the trial and error process. To be a true trial and error process, no foreknowledge (constituting prejudice) can be assumed. Since no foreknowledge can be assumed, then there can be no relevant guidance provided to the agent.

Further, this implies that "intention-endowed" actions are not necessarily guided in any particular way. That is due to the fundamental deception described above, which forms the basis for true objective trial and error. The separation between the observer and the agent, which allows for the occurrence of true trial and error, also implies that the agents act with no apprehension of the intention. And although the agents are "intention-endowed" they are not guided or directed in their action by that intention, being intentionally deprived of that information by the fundamental deception.

Perhaps it does have an effect on the void. Space expands and light loses energy as it travels through expanding space. Maybe space expands proportionally to the energy lost to it — flannel jesus

That's similar to what I think as well. But do you see what this implies about the concept of energy? In application the concept of energy is applied to movements within a non-expanding space. However, the conception is deficient because it does not account for the true expansion of space. Then some energy must be said to get swallowed up by space, to account for this deficiency in the conception.

Of course this is he same as the amount of energy being constant while the amount of energy available for work decreases over time. — Banno

This demonstrates the contradiction I mentioned. Energy is defined as "the capacity to do work". To assume that there is energy within a closed system which is not available to do work, is simple contradiction.

The truth is that the energy would actually be lost to the system. But to create the appearance that the law of conservation is true, the lost energy is said to still exist somehow, but in a form in which it cannot do any work. Of course that's nonsense, because that is just saying that it's energy which exists, but is in no way detectable as energy. So it's energy which does not fulfill the criteria of "energy". Hmm, energy which is not energy, an interesting concept.

What about friction, heat loss, things like that? When a machine loses energy, it doesn't just lose it into the void, it gets transferred to other things in its immediate environment. — flannel jesus

Never has 100% of the energy been all accounted for. You can speculate about where it all goes, but inevitably we have to admit that some simply gets lost "into the void". This poses the question of what does the void consist of, which allows it to swallow up energy without that energy having an effect on the void.

Can you think of a different reason why perpetual motion machines would be impossible? — flannel jesus

No I can't. The only viable reason for the impossibility of perpetual motion is that in reality energy is not conserved as time passes. This fact is folded into the concept of entropy.

Whereas the conservation laws are metaphysical and true and helpful, determinism is metaphysical and potentially false and not helpful. — Banno

Conservation laws are very helpful in many applications. But if we do not respect the fact that they are ideals rather than truths, they are metaphysically misleading. As ideals, we can compare them to other ideals like "the circle". The irrational nature of pi (Happy Pi Day everybody!) is indicative of the fictitious nature of the perfect "ideal" circle.

Aristotle addressed eternal circular motion in his discussion of the assumed divine, eternal orbits of the heavenly bodies. He showed how this ideal, eternal circular motion is logically possible. If the moving thing adheres to a perfect circle, there can be no possible beginning or ending point to that motion. Therefore eternal circular motion is logical possible, as an assumed ideal. However, he claimed that the thing moving in the eternal circular motion must be composed of matter, and was therefore generated, and will corrupt. In this way he demonstrated that real material existence does not correspond with the ideal. The ideal is false.

From this, we can see that the application in which the ideal is the most useful is when we examine how the actual physical reality varies from the ideal. The discrepancies from the ideal, when studied, reveal the true nature of the thing modeled by the ideal.