Now you are claiming that builders are houses. — Dfpolis

You continue to be ridiculous. In the hypothesized scenario there is a builder building a house and there is a house being built. A proper description refers to both, but this obviously does not imply that builders are houses. In that hypothesized scenario, the description of a builder building refers to the very same situation as the description of a house being built.

Again, that is the point. Actions are identically passions from a different perspective. That does not make causes (builders building) the same as effects (houses being built). — Dfpolis

The effect of the builder building is a house, and the house is posterior in time to the builder building. The effect of the builder building is not a house being built, as these are one and the same thing. The effect is the house.

You are stipulating a separation between the "builder building" and the "house being built", in order to claim that there are causes and effects which are simultaneous and not chronologically ordered. I disagree, and so I am demonstrating that your argument is simple sophistry. Your argument amounts to employing two distinct descriptive styles to describe the very same activity, and then claim that one description is of the cause, and the other is of the effect, when both descriptions are really descriptions of the very same thing.

The house has some existence = a partial existence as a work in progress. Once building has begun, the house has a partial existence. If you do not like the term "house," substitute "house in progress." The logic works as well as it depends on the facts. — Dfpolis

Perhaps we can make some progress here, by breaking down the coming into being of the house, into parts. Do you agree, that when each part comes into existence, it does so as an effect, from the prior activity of the builder which is a cause of it, and the activity of the builder is always prior in time to the existence of the part? So, for instance, the foundation comes into existence, and it only exists after specific activities of the builder. There is no simultaneity of cause and effect here, the effect, which is the existence of the part, is always posterior in time to the cause, which is the activity of the builder. Can you agree to this simple principle?

Doing is causing and being done to is being effected. — Dfpolis

Right, but "being done" implies finished, complete, the end. And "being built" implies unfinished, and this is completely incompatible with "being done". Further the concept of, "being done to", "being effected", as is your claimed meaning of "passion", which is really "passive", requires an object which the action is being done to. In the hypothesize scenario, this object is supposed to be the house. But the house does not exist, and this is why your proposal is nonsensical and impossible to understand. If you would propose a passive object which the action is being done to, then we'd have a place to start. However, you insist that the passive object which supposedly suffers the passion, is the activity of "being built", and this is nonsense.

All the rest of us are able to distinguish builders building from houses being built even though they are inseparable. — Dfpolis

That's unabashed bullshit. Provide for me an accurate description of a house being built which does not involve builders building. The only difference is as I explained earlier. Since "builders building" is more general, there is no necessity that the builders building are building houses, yet there is necessity that houses being built involves builders building. This, as I explained to you, is the nature of final cause, the free willing agent has choice, which is most general, and decision moves toward the more specific without necessity. So there is no necessity between cause and effect in this direction. But when we look from the direction of the more specific, "houses being built", there is the necessity of builders building.

If we were discussing causation completely, yes. However, you asked about efficient causes and that is what I am explaining here. — Dfpolis

There is no such thing as efficient causation in which the cause and effect are simultaneous, concurrent. You simply use a sophistic trick of description in an attempt to prove that there is.

"House" is being analogically predicated. It does not mean the completed house, but the work in progress, which does exist. — Dfpolis

So the object which suffers the passion is a predicted object? How can it suffer the effects of the activity it doesn't even exist, and is only predicted to exist?

https://www.jstor.org/stable/26170042 — Dfpolis

If you believe that this text is consistent with your claims, then provide some references from it. I think you and Duns Scotus are talking about two different things, but using the same terms. You have an odd way with terms, as is evident from your use of "passion".

So why don't you conclude that the use in the context of the law of identity violates the use in the context of set theory? It seems to be an arbitrary choice. — Ludwig V

I'd agree except that the law of identity was first, set theory came along after. So set theory violated the law of identity, which was already established. If it was the other way around, then we'd want to look at the reasons why someone would be trying to enforce the law of identity, which seems like a useless, obvious, self-evident tautology, in violation of how set theorists were defining "same".

Well, if the law of identity is an obvious self-evident tautology, then it appears like there must be something wrong with set theory if it's in contradiction with what is obvious. We can see something like this in Aristotle's work to establish the law of identity. He claimed that the law of identity was necessary to battle against sophists who could logically demonstrate absurdities. If the base axioms of a logical system are contrary to what is self-evident tautology, then that system will be able to prove things which are contrary to what is obvious, one can prove the absurd.

The meaning of "same" depends on its context. — Ludwig V

Very true, but we need to pay attention to subtleties to avoid deception. Suppose you and I both drive the same make and model of car, and same year and colour as well. Notice, that "same" is being used in a qualified sense, referring to different properties "same make", "same model", "same year", "same colour". Now, suppose I say that I drive the same car as you. This would be incorrect. But why is it incorrect, because everything about it seems to be the same? The thing is that everything about it is not the same, only those named qualities are the same, and that's why it's incorrect to say that it is "the same" in that unqualified sense.

Now, when we say that "two sets are the same", this is incorrect for the same reason. Not everything about the two is necessarily the same, only the stipulated required qualities. So it is incorrect to say that the two sets are the same, in the unqualified sense, because some features like the ordering of the elements may be different.

The builder building is the cause. The house being built is the effect. Of course they are concurrent. That is the whole point. — Dfpolis

As I explained, "the builder building", and "the house being built" are just two different ways of describing the exact same thing. There is no distinction of cause and effect here, and that is why there is concurrency, there is not separation. They are the same.

But, building is not being built. so the cause is not the effect. — Dfpolis

Yes, "building" is "being built". Why can't you comprehend this? The two are the very same, identical activity, described in two different ways. As I said in my reply to Tim, "building" has the builder as the subject, and "being built" has the house as the subject. So the two are just different ways of describing the exact same activity. One way is to describe a builder building, and the other way is to describe a house being built. But both are descriptions of the exact same activity. There is no separation of cause and effect because there is only one activity being described.

Further, since "the house", as subject does not yet have any existence, it cannot suffer any passion, or have any properties at all. And that's why your claims make no sense. At the time of "being built", the house exists only as a plan, a goal or end. This is why "the house" which is implied as the subject of "being built, can only be referred to as a final cause at this time, not an efficient cause. The house exists in the mind of the builder only, as a goal or end, and the cause of the builder building. This is just like Aristotle's example of final causation, where "health" exists in the mind of the man walking, as the cause of him walking.

You do. I don't. In essential causality they are inseparable. In accidental causality (time-sequence by rule) they are separate. That is why there are two kinds of efficient causality. The first is necessary, the second is not. — Dfpolis

Now you are just being ridiculous. If the cause is inseparable from the effect, then how do you know that "being built" is not the cause, and "building" is not the effect? And maybe it constantly switches back and forth, with the two continually changing places, each being sometimes the cause and other times the effect. If the cause is inseparable from the effect, then there is no principle by which you can say one is cause and the other effect.

Do you see why I say that your claim is ridiculous? You claim to be able to distinguish "building" from "being built", one the cause the other the effect. Yet you also claim that the two are concurrent and the cause is inseparable from the effect. Therefore whenever you describe the scenario, there is no way to know whether the description is of the builder building, or the house being built. In reality though, it is just one activity, and you've devised this elaborate way to say that it is two distinct activities, one cause and the other effect. And when it comes to telling me how to distinguish one from the other, you admit that the cause cannot be distinguished from the effect, "they are inseparable".

By referring to a good dictionary when you see a term used in a way that is new to you. — Dfpolis

I referred to my OED, and "passion" is said to be a noun. The nearest definition to fitting your usage was: "4a strong enthusiasm (has a passion for football). b an object arousing this." There is nothing anywhere similar to your usage in my OED. However, there are definitions of "passive" which are similar. For example: "1 suffering action; acted upon." I think maybe you confused words, and meant "passive". However, if you tried to talk about the passiveness of the house being built, this would more clearly reveal the nonsense of your expressions. So you try to hide it behind a strange use of "passion".

Yes, I am but I am not saying it is a completed house, but a house under construction. — Dfpolis

OK, let's ignore all our differences, and start here, where we agree. Do you agree that at the construction site, there is not a house, there is activity which we can call "the construction of a house", or, "a house under construction". Both these phrases refer to the exact same thing, and "the house" only exists as a plan, a goal, or the end of that construction project. Do you agree that to talk about causation here, we need to include "final cause"?

And continuing, corresponding to the action of the builder building, is the passion of the thing being built. And all of this makes perfect sense. — tim wood

How does this "make perfect sense to you"? The passion is in the builder, not the thing being built. And even if we take "passive", which means "suffering action; acted upon", instead of "passion", the passivity is in the materials which the builder works with. The "thing being built" doesn't even exist, it is an idea, a goal in the builder's mind.

The substance, then, is the house. The accident applied to it in this case is passion. Not that the house is doing anything, but rather something is being done to the house: it is being built. — tim wood

You're missing the point tim. The house does not exist, it is a goal in the builder's mind, existing as a formula. The accidental properties of the house only come into being after each part of the house is built.

This is out of context, and misapplied by Df. What is described in your quoted passage is the difference between accidental and essential properties of things. How Df is using the term is as a property of an activity, "the passion of being built". Df states that being built is something which has the property of being acted on (passion). That is a category mistake.

Df is not saying that there is a house which is being acted on, and this "being acted on" is a passion of the house, because there is no house, the house does not yet exist, it is being built. What there is, is a project, a goal, intention, or end, which is being acted on. Df takes this final cause, and attempts to convert it into an efficient cause, through the category mistake mentioned above.

Df applies Aristotle's distinction between accidental and essential properties of things, to activities of causation, to create the appearance that acting and being acted on are two separate properties of a single activity which is called "building" or "being built" depending on whether the subject is the builder (building), or the house (being built). But the house is not yet built, it exists as a goal, and that goal acts as a final cause. Therefore the house cannot be described as a thing being acted on (having a passion). What is "being acted on" is the project, or goal, the end.

If you can make sense of what Df is saying, other than as the category mistake I describe above, then I would be very grateful to see your explanation. Df simply reasserts what has been said, which makes no sense to me because it appears as a category mistake.

In set theory, two sets that are equal are the same set. — fishfry

Conclusion: set theory is in violation of the law of identity. I've explained to you why this is the case. Do you agree with me?

Again, you are missing the point. The necessity is not in the decision to build, but in the relation between the act of building as cause and the passion of being built as effect. — Dfpolis

This doesn't make any sense Df. Passion is emotion, feeling. The phrase "the passion of being built doesn't make sense. You claim "passion in the technical sense", but Google doesn't even come up with any such thing.

If we remove "passion", then all we have is "the act of building", and "being built". But these two are exactly the same thing. Of course they are concurrent, as they are two different ways of saying the same thing. But there is no cause and effect here, they are one and the same thing. If we add "passion" into the scenario, then we are talking about the passion of the builder, and this acts as a cause, not an effect. And, the ambition to build is prior in time in relation to the acts of building which follow from it.

The concurrent necessity between building and being built is being asserted, not a necessity in the choice to build. — Dfpolis

The only necessity here is that these two expressions "building", and "being built", both refer to the exact same thing. Look: "we are 'building' a house", or "a house is 'being built'. They are both just different ways of referring to the exact same thing, the house that we are building. There is no cause or effect here, just one thing, described as a house being built, or the house that we are building. In one case "builders" are implied and in the other "builders" are explicit.

If you want to separate cause from effect, you separate "builders" from the act of building, as the cause of that act, or the act of building from the house, as cause of the house. But you cannot divide the act into "building" and "being built", and say that one is cause and the other effect, because they both refer to the very same thing. And the fact that they refer to the same thing is the reason why you can say that they are concurrent. But it's also the reason why they are not cause and effect.

That does not mean that the activity of producing the effect (e.g. building) is prior to the passion of the effect being produced (e.g. being built). — Dfpolis

Again, you are speaking nonsense, attributing "passion" to "being built". Passion is a human emotion, feeling. In no intelligible sense, is "passion" used to refer to what "being built", or "being produced" feels like.

Try assuming that I know what I am talking about and see if you can make your interpretation of my words fit that assumption. When I say I am only discussing efficient causality, I mean that I am only discussing that one of the four causes. I do not mean that there are no other causes. It is only by looking for ways in which I might be wrong that these two ideas can be confused. — Dfpolis

How can I possibly assume that you know what you are talking about when you use "passion" in that way? Please, at least try to explain what "the passion of being built" could possibly mean. The only way that you separate the act of building from the act of being built, to say that being built is the effect of building, as a cause, is by saying that being built is a passion. Clearly though, you have this backward. The builder has a passion for building, and as such passion is a cause in the building process, not an effect.

Making a commitment is not an isolated event. It sets up a committed state. If I am walking and decide to stop, that commitment (the state of being committed to walking) ends, as does my walking. — Dfpolis

But it is not concurrent, it is prior. The state of being committed to walking ends before the walking ends, even if it's only a fraction of a second, it's still prior, and causal.

So, you are claiming that building and being built are not concurrent? If so, we have no common basis for continuing. — Dfpolis

The activity of the builder, as builder, is prior to the activity which is the house being built. This is because the builder must study and understand general principles (and this qualifies as activity of a builder) prior to the activity which is the particular house being built.

I see we have no common basis for continuing. You insist on nonsensical use of "passion" which makes passion the effect of the builder building rather than use a true description which recognizes passion as a cause of the builder building. And you assert that what you argue is Aristotelian.

I never claimed that any and all acts of the builder are concurrent with being built, but only the act of building. Please do not extend what I say to make it wrong. I never denied that builders plan or have free will. — Dfpolis

OK, have it your way, only the acts of the builder which are identical to the acts described as being built, are concurrent. Of course, they are one and the same thing. So there is no cause/effect here.

No, it does not. I do not have time to deal with your negativity. You can take my word for it or Google it. — Dfpolis

You claimed to have quoted Aristotle's definition of change. A quote requires a reference.

We need not use the word same if it bothers you. — fishfry

Great, I prefer the word "equal". It's better suited for that purpose. "Equal" generally allows that the two things which are said to be equal are not necessarily the same. "Same" is defined by the law of identity as indicating one thing only. That is the commonly expressed difference between "same" and "equal". "Equal" indicates a similarity of two things by both sharing an identifiable property, while "same" means that you are referring to one thing only.

Then why are you disagreeing with me? — fishfry

Generally I disagree with your wording, as indicated above. The axiom of extensionality indicates what is required for two sets to be equal, yet you state this as "the same". That I take as a mistaken use of words.

And if you say it's a useful deception, that's fine. — fishfry

I didn't say that though. I simply gave an example of how fiction is useful, one that was obvious. Many times fiction is used in ways not intended to deceive, like the use of counterfactuals in logic, for example. So, the issue is complex, because mathematics, like fiction in general has many uses.

May I ask, is chess similarly a useful deception? Language? You didn't respond to my point earlier that language is also a formal symbology that attempts to capture, however imperfectly. some aspect of abstract thought. — fishfry

These are broad generalizations which I can't relate to because I do not accept them as valid generalizations, so I do not reply. For example, you say that language "attempts to...". But language doesn't attempt anything, individual people attempt to do things with the use of language. And, there is such an extremely broad range of things which people attempt to do with language, that it doesn't make sense to make the generalization that what people attempt to do with language is to capture "some aspect of abstract thought".

What is wrong with that? — Ludwig V

I don't see how recursion qualifies as an infinite activity.

2 + 2 and 4 symbolize the same set. You are the one strawmanning the claim that somebody says they're the same thing. — fishfry

My point has always been that "same" in this context is not consistent with "same" in the context of the law of identity. So, to say " 2+ 2 and 4 symbolize the same set" is to use "same in a way which is in violation of the law of identity.

Whether we are talking about "same thing", "same set", "same number", or "same kick in the ass", is irrelevant. The point is that this specific use of "same" is very clearly in violation of the law of identity. If the law of identity indicates that only a thing can be said to be "the same", and you do not believe that a set is a thing, and you want to say that a set is the same, then I suggest that you do not agree with the way that "same' is used by the law of identity. Is this the case? Do you believe that mathematicians have a better definition of "same"?

If math is a flagrant fiction, why's it so darn useful? — fishfry

In case you have never noticed, fiction is extremely useful. I suggest you begin with a look at the obvious, deception. Deception demonstrates that fiction is very useful in convincing others, to help us get what we want from them. And, so is mathematics.

The necessity is bilateral and in the present tense. There can be no builder building without a building being built and vice versa. — Dfpolis

The necessity is not bilateral because from the perspective of the builder, to build is a freely willed choice. The so-called necessity of "a building being built" is a feature of the way that you describe the agent, as "a builder". If the agent decided to do something other than build, this would not negate the existence of the agent, it would negate the descriptive term "builder".

So the relation of "necessity" between builder and building involves two distinct senses of "necessity" and the conclusion that "the necessity is bilateral involves equivocation. From the perspective of seeing an existing building, or even a building being built, it is logically necessary that there is a builder. But from the perspective of the builder, the building is "necessary" in the sense of something needed, desired as an end. These two senses of "necessary" are very distinct. The builder is a "builder" whether that person decide to work on this particular project or not therefore there is no logical necessity between the builder and the project, from the builder's perspective..

Furthermore, it is very clear, from the nature of planning, that there truly is a builder acting on the project, by preparing for the possibility of it, "without a building being built". That is to say that the builder acts on the project before the project even exists, and this is a matter of gaining experience.

This is proven by the fact that plans are most often general, and the general plan for a type of building, a house, preexists actual building of the particular house. Therefore the builder is building, studying general plans and building codes, for some time before there is actually a building being built.

To deny the temporal priority of the general formula, or plan, for a house, in relation to a particular house being built, is to completely ignore the principal problem being dealt with by Aristotle in his Metaphysics. This is the issue brought forth in Plato's Timaeus, the question of how it is that a general idea, a universal form, in its temporal priority, acts to determine the form of the particular, when that particular comes into being. To take Aristotle's example of the potential of an acorn, the general form, or universal type of "oak tree" precedes the growth of the seed, and determines the type of thing which the particular will be, prior to the existence of the particular.

Your way of portraying the actions of the agent as concurrent with the effects of those acts, and as a bilateral necessity, completely obscures this issue, of how it is that an intentional agent can work with universal principles, a general formula, to create particular individuals of that type.

Baloney. The builder is an efficient cause, and that is the only cause I discussed. — Dfpolis

You described an instance of the act of building, and this act is caused by final causation, intention, as per Aristotle's description of the four senses of "cause". That you call this "efficient cause" only indicates that you do not understand Aristotle.

Read what I said. I said it is a passion of the house being built. It is not a passion in the emotional sense, but in the technical sense of suffering an action. — Dfpolis

The act of building is prior to the house, as efficient cause, and the will or intent to build is prior to the act of building as the final cause. If we look backward, at the house's coming into being through a causal chain of efficient causes, the end of that chain (which is the beginning in time) is the final cause, the intent of the builder. That is how a freely willed act works, the agent desires something and causes (through final causation) the efficient causes which are seen as required, as the means to that end.

If I do not wish to build now, I will not build now. Planning may be prior, but the commitment to act now is concurrent with acting now. — Dfpolis

No, this is a false description. The act follows the commitment (decision) which is prior to, as cause of the act. The two are not "concurrent". I decide to walk, and the activity of walking is the effect which follows from this cause. The person may deliberate, and decide to act at a very specific time, but the physical (observable) act is posterior to the mental (unobservable) decision to act.

I did not deny that because I did not discuss final causation, but efficient causation. — Dfpolis

Your failure to take into consideration the role of final causation is what produces the faulty description that there is a "bilateral necessity" and that the acts of the builder, and the building being built, are concurrent. They are very clearly not concurrent because the planning of the building is an act of the builder which is prior to any building being built. If you would take into account the role of final causation you would understand that there is no such bilateral necessity, and no concurrency. In reality, if you just look at the actions of the builder, you might not even know that there is "a building being built", until the builder is well into the project. You refer to the end, the final cause, "the building" when you say that there is "a building" which is being built. So you refer to final causation yet claim you do not discuss final causation.

Again, there can be no building a house now without a house being built now. — Dfpolis

Yes there is activity of the builder as "builder" of a house, now, without a house being built because the planning, which requires understanding of general principles, is a part of the activity of building which is prior to the activity that is referred to as "a house being built". This is the difference between what is observable and what is not observable. The planning is a part of the builder's activity of building which is prior to the observable activity which is described as "a house being built. That the two are distinct is true and proven from the fact that the planning may be generic, while "a house being built" is particular. And learning the general principles is a necessary part of "building a house" while it is not a part of "a house being built, because the former refers to the general and the latter refers to the particular. Therefore it is very clear that there is activity of the builder which is prior to, cause of, and necessary for, the particular instance of "a house being built".

I quoted Aristotle's definition of change, not mine. — Dfpolis

That would require a reference.

...then buy Twitter, now known as X... — Shawn

That's a cool name, "Twitter, now known as X". When will the sublimation be complete?

Aristotle and the Scholastics distinguish two kinds of efficient causality: accidental, which is the time sequence by rule Hume and Kant discuss, and essential. Accidental causality involves two events separated in time. Because they are separated, an intervening event can prevent the cause from bringing about the effect. Hence Hume was correct in arguing that time-sequenced causality lacks necessity. — Dfpolis

I do not agree with this interpretation. Aristotle did not distinguish accidental efficient causation from essential efficient causation in the way you describe. Nor did the scholastics. Aristotle classed luck and chance as accidental causation, and the four commonly referred to causes are the essential conditions for change. Efficient causation is an essential condition, described by Aristotle as "the primary source of change" and it follows the time sequence described by Hume.

It is from the perspective of the effect that the efficient cause is apprehended as necessary. If the building has been built, it is necessary that there was an act of building.

In essential causality there is one event, and cause and effect are concurrent. Aristotle's paradigm case is a builder building a house. The cause is the builder building. The effect is the house being built. Yet, the action of the builder building the house is identically the passion of the house being built by the builder. — Dfpolis

Here you conflate final cause with efficient cause to create a new concept which you call "essential cause". This is not Aristotelian. The efficient cause of the house is the action of the builder, the act of building. The cause of the builder building, what you call "the passion" of the builder, is the final cause. Why is the builder building? Because the builder desires a house. This is just like Aristotle's example. Why is the man walking? He is walking because he desires health. The final cause of the builder's activity of building is the desire for a house, just like the final cause of the walker's activity of walking is the desire for health. That is the nature of "intention" which is how we understand "final cause".

When final causation is given it's proper position, instead of conflating it with efficient causation, the temporal succession is evident. The desire to build (intention, final cause) is temporally prior to the activity of building, which is the efficient cause of the house.

As there is only one event, no intervention is possible, and this kind of causality (the actualization of a potential by the concurrent action of an agent) has intrinsic necessity. Since potentials are not yet operational, they cannot actualize themselves. So, something else that is already operational (actual) must work to actualize any potential. That is one of the most fundamental insights of Aristotle's metaphysics. — Dfpolis

And this is not quite correct either. The action of the agent is volitional therefore there is no intrinsic necessity to that act. Yes, in hindsight the final cause (will) of the agent is necessary, just like the efficient cause is necessary, in hind sight. But, we cannot distinguish one from the other in the way that you propose, as one being essential, and the other accidental. They are both essential conditions of the house, as are the material and the formal cause as well.

However, I agree that you are correct to say that something else, which in this case is the intentional act of the agent, (final cause), is necessary as the act which actualizes a potential, causing what we know as activity. And, I agree that this was a great achievement by Aristotle. But I do not like your characterization of this cause of activity, as "essential efficient causation". Since efficient causation is activity itself, then characterizing the cause of this activity as a further efficient causation, would just create an infinite regress of efficient causation. That's what the idea "concurrent action" as simultaneous cause and effect induces, an infinite regress of action.

Aristotle put an end to that infinite regress with "final cause". So conventional interpretation, as well as Scholastic interpretation, understands the cause of the builder's activity of building as final cause, the will to have a house. Likewise, God's activity of creating is caused by the final cause known as God's Will. Why did God create the earth? He saw that it was good.

Since God is unchanging, and time is the measure of change according to before and after, God is timeless. — Dfpolis

This is not valid logic. Time is stated as the measure of change, it is not stated as change itself, or even derived from change. Since time is the measure of change it must transcend all change. That which transcends change cannot be timeless, or time itself would be timeless. Therefore even if God is unchanging, this does not mean that God is timeless.

So, there is no separation of plan and execution in God. Thus, God's will for a being to exist creates the being. As would be the case when the builder stops building, if God were to stop willing the being of a creature, the effect (the existence of the creature) would cease. Thus, creation is not a launch and forget process, but an on-going activity. — Dfpolis

I agree with this, in a way. But the classical Christian conception of God is as a trinity, so we can still consider a separation, in principle, between plan and execution, in God. Augustine compared the trinity of God to the trinity of the human intellect, which consists of memory, reason (understanding), and will. If the plan exists in memory, then there is a separation in principle, between the plan and the execution. It may be the case that the act of God is inseparable from God's Will, but this would mean that God is changing in accordance with His Will. Therefore we could not say that God is unchanging.

Because God is the end of the line of concurrent explanation (essential causality). Since He is the end of the line there is nothing prior to actualize any potential He may have. So, God can have no potential. That means that God is pure act = fully actualized being. Change is the actualization of a potential insofar as it is still in potency. Since God has no unactualized potential, He cannot change. Since he cannot change, there is no before and after in God => God is timeless. — Dfpolis

This is where your interpretation becomes problematic. The end of the line of efficient causation is known under Aristotelian principles as final cause. The terms "end" as what is intended, and "final" in final causation are not merely coincidence. We agree that God can have no potential, and is pure act, but this does not mean that he does not change. That "change is the actualization of a potential", is your condition, produced from your interpretation, which appears to be a little bit faulty.

According to Aristotle change is the result of causation, and causes are of four principle types. One of these types is final cause, and we find examples in acts of free will. That the will is free implies that it causes a type of change which is not dependent on potential.

sign game of perfect information — sime

See that phrase, "perfect information"? That's why I say formalism attempts to do the impossible. In other words, it assumes an ideal which cannot be obtained, therefore it's assumption is necessarily false.

So I think your problem is actually with Platonic myths that have become psychologically wedded to innocent formal definitions, and in particular the formal definitions of limits and total functions that are ubiquitously misinterpreted in both popular and scientific culture as denoting a non-finite amount of information, E.g as when the physicist Lawrence Krauss misleads the public with nonsense about the physical implications of Hilbert Hotels. — sime

I view formalism as a form of Platonism. It's a Platonist game in which the participants deny their true character, that of being Platonist. Notice "perfect information" is the foundational feature of Platonist idealism. That perfection is the only thing which supports the eternality of Platonic ideals. So formalism and Platonism are really just the same thing, even though the formalists will claim otherwise.

But I don't think I have, because before that you refused to even acknowledge my proof that 2 + 2 = 4 from the Peano axioms. — fishfry

I have no problem acknowledging that 2+2=4. I have a problem with people who claim that "2+2" symbolizes the same thing that "4" does. And so, I refused to accept your claim to have proven that "2+2" signifies the very same thing as "4" does. Simply put, if the right side of an equation does not signify something distinct from the left side, mathematics would be completely useless.

You can say that I have a problem with formalism, because I do. Like claiming that accepting certain axioms qualifies as having counted infinite numbers, formalism claims to do the impossible. That is, to remove all content from a logical application, to have a logical system which is purely formal. If such a thing was possible we'd have a logical system which is absolutely useless, applicable to nothing whatsoever. Attempts at formalism end up disguising content as form, producing a smoke and mirrors system of sophistry, which is riddled with errors, due to the inherent unintelligibility of the content, which then permeates through the entire system, undetected because its existence is denied.

Logical equivalence does not imply "the same as". I have no problem with the axiom of extensionality. I have a problem with people who conflate the axiom of extensionality with the law of identity, to interpret that axiom as saying two equal things are the same thing.

God's intention to create whatever he creates, which is in the order of primary (metaphysical) causality, and not temporally prior because God is unchanging and so timeless. — Dfpolis

Hi Df. Can you clarify this idea for me? How can you conceive of a form of causality which does not involve temporal priority? Suppose God's intention to create (God's Will) is a cause of what He creates. How can this intention to create be a cause of the creation, and yet not be temporally prior to God's creation?

If we compare God's Will with the human will, we see that the human will is temporally prior, and acts as a cause. However, we understand the human will as "free", therefore not caused to act the way that it does. The idea that the human will is an uncaused cause does not imply that the human will is unchanging and timeless. How do you get to the point of concluding that God is unchanging and timeless?

What I am asking is how are you relating "intention" to "unchanging" and "timeless"? You appear to be saying that if God is unchanging and timeless, then God's Will cannot be temporally prior to God's creation. Since we know a lot about the nature of intention, from human intention, and that intention is temporally prior, isn't it logical to conclude therefore that God, who acts intentionally, is not unchanging and timeless?

And isn't this the conclusion of Christian theologists like Aquinas, as well? They conclude that God is a "Form", pure act. And to say that something which is "pure act" is unchanging and timeless, would be contradictory. Therefore we ought to conclude that this notion of God, as "unchanging and so timeless", is incorrect.

and when one analyses it, it is a confused mixture of physical possibility and logical possibility, each of which are coherent on their own. — Ludwig V

I don't think infinite divisibility is a logical possibility, that's the point I'm making. Infinite division is logically impossible.

A finite thing certainly cannot be divided an infinite number of times, if by "divided" you mean "physically divided", subject to clarification of what you mean by a finite thing. — Ludwig V

I mean to "divide" in any sense of the word. The qualification of "physical" is irrelevant. Division is an action, an operation, and we are talking about the possibility of dividing something an infinite number of times. Do you think that this is logically possible? It's like counting, which is another activity. Do you think it's possible to count infinite numbers?

t the same time, it is possible to divide it into halves, quarters, etc. (how many fractions are there?) and into feet, inches, etc. and into metres, etc, and according to an indefinite number of other units of measurement. — Ludwig V

You may say that it is possible to divided indefinitely, but that does not mean that infinite divisibility is possible. Take pi for example. You can get a computer to produce the decimal extension for pi, "indefinitely", but you never succeed in reaching an infinite extension. Divisibility is the very same principle. Some mathematical principles allow one to divide indefinitely, but you never reach infinite division. That is because infinite division, therefore infinite divisibility, is logically impossible.

Yet it cannot be physically divided at all (because it is an abstract thing), yet it can be divided by a familiar mathematical operation, and that operation can be applied to it an infinite number of times. (No, I'm not talking about space or time.) — Ludwig V

No, the mathematical operation of division cannot be applied to an infinite number of times, for the reason explained above. If the action is completed it is not infinite, and if it continues indefinitely, at any stage in its progression, it is not infinite either. Quite simply, there will always be more dividing to do before an infinite number of times is achieved, and if you stop it is not achieved either. Therefore it is very clear that such an activity (infinite division) is logically impossible. In general, an infinite activity, or operation, is logically impossible.

I've learned that there's been a minor revival of interest in Aristotle's biology, due to the inescapable teleological features of, well, all living things. — Wayfarer

This is very true, and I believe it's a key point toward understanding Aristotle's metaphysics. The teleological aspect of biology necessitates that there is a sort of "form" which is temporally prior to the material existence of a living body, as the cause of its being an organized body. This implies an immaterial form which the Greeks knew as the soul.

The second point, I believe is to understand the distinction between the immaterial "form" which is prior in existence to a material body, as cause of that body being the unique body which it is, and the "form" as we know it, in the sense of the formula of our understanding. This produces a duality of "form" in Aristotle, as one sense is proper to final cause, and the other is proper to formal cause. The revival of Aristotelian principles which you refer to, as displayed in this forum by participants like @Dfpolis and @apokrisis, commonly does not reflect this distinction, and it is common to find a conflation of these two distinct senses of "form".

We have disagreed over Gerson in the past. As a devoted student of Plotinus, I cannot fault his view of Plato since Gerson follows Plotinus' reading.

But I object to Gerson's picture of Aristotle as an anti-naturalist. It elides Plotinus' criticism of Aristotle.

Gerson's version of materialism ignores the limits of the universal that Aristotle discusses in the Metaphysics, which my quote above is taken from. — Paine

The difference between Neo-Platonist interpretations of Plato, and Aristotelian interpretations of Plato, I have described to Wayfarer in the past. The problem with Pythagorean idealism which Plato exposed, is that the theory of participation, which is the theory that supports the reality of these separate Ideas, makes these Ideas passive, and does not allow that the independent Ideas are active in the real world. Today this is known as the problem of interaction. Plato introduced "the good", as a principle of action.

What Aristotle did was define "form" as the active aspect of reality, and then he showed the need for independent active "Forms" as causal in the sense of teleologically causal, final cause, to account for the reality of the role of "the good" in the world, demonstrated by the free will.

The Neo-Platonists, as demonstrated by Plotinus, did not follow this principle, and adhered more to Pythagorean participation, but turned participation around to be emanation. However, the first principle "the One" is pure potential, passive, and so this cannot account for the act, the cause of emanation. In this way the Neo-Platonist metaphysics hits a dead end, the first principle is purely potential, and not actual. That contradicts Aristotle's cosmological argument. Christian theologist like Augustine and Aquinas, turn to the active "Form" of Aristotle, to account for the reality of the free will, and of God in general, as the first cause.

Supertasks play on the difference between the physically possible and the logically possible to create an illusion. — Ludwig V

What I've explained though, is that infinite divisibility is really incoherent due to self-contradiction. So the supertask is not even logically possible. It just appears to be, when not subjected to critical analysis.

So the matter of doing something an infinite number of times never comes about, because the conclusion of an infinite number of times is only produced from the premise of infinite divisibility. If we remove that premise, and just start talking about doing something an infinite number of times, it's obvious that there is no end to such a task. It's only the contradictory notion, that a finite thing can be divided an infinite number of times, which produces the paradox.

From past experience I understand that @fishfry is very slow to accept the reality that some principles employed by mathematicians are incoherent.

That's some sentence — tim wood

180 in the usual form...absolutely incomprehensible.

Essentially, mathematical analysis will fail to persuade unless one is already a true believer of supertasks. — sime

That about sums it up.

Of course you did. I'm sorry. But in any case you've just accepted that mathematical objects aren't true objects. So what's the problem? — Ludwig V

The problem is the incoherency. Maybe, if there was no incoherency inherent within mathematical objects, they could be true objects.

So we just have a case of Domains of Magisterial Authority, and no need to fight about it. — Ludwig V

There's still the issue of incoherency, and the work of the metaphysician is to seek and destroy that sort of evil. Therefore, the fight is on.

Our only remaining issue is whether the problem of Achilles and the tortoise and Thompson's lamp is a mathematical problem or a metaphysical problem. — Ludwig V

It's both, and that's the reason for the fight.

Or maybe it's just a question of understanding two solutions to the same problem. They clearly won't be incompatible. — Ludwig V

When one uses incoherent principles, and the other does not allow incoherency, then they will not be compatible.

Your beer will never be finished. — Ludwig V

Where do i get one of these metaphysical beers?

I think, by the way, that you would have a tough job to convince mathematicians that there is an incoherency in the concept of the infinite. — Ludwig V

I clearly explained though, it isn't "infinite" which is incoherent, it is "infinite divisibility" which is. "Infinite divisibility" is a specific application of the term "infinite" which is incoherent. It is incoherent because the concept of "infinite" is incompatible with, inconsistent with, or contradicts, what is implied by the concept "divisible". Therefore the two together as "infinite divisibility" is self-contradicting.

Mathematicians have made "infinite" into a new term, which really has very little resemblance to its metaphysical roots. This is very evident in set theory. There is no consistency between "infinite" in mathematics and "infinite" in metaphysics. Because of this, mathematicians are incapable of understanding metaphysical "infinite". There is no word for it, as that word is used for something else in mathematics, so the concept escapes their grasp. This leaves mathematics, and mathematicians in general, as fundamentally incapable of dealing with the metaphysical problems involved with the concept "infinite".

.... apart from a geometrical straight or curved line. I grant you that that is a concept of an abstract, ideal object. I grant you also that such division does not necessarily affect the unity of the object in any way. — Ludwig V

Assuming lines to be infinitely divisible is problematic, just like assuming time or space to be infinitely divisible is problematic. As much as we like to claim that such a divisibility is "logically possible", it's really not. Such an assumption produces an unintelligibility similar to infinite regress, which is an incoherency, therefore illogical.

So when I choose a red coat to wear to-day, how do I manage that? The colour that I am aware of is divisible in the sense that there are many colours and shades of colours. These correspond only roughly to the wavelengths of light. — Ludwig V

I don't follow you. Why would you need to know something about divisibility to choose a colour?

So how can we be sure that anything can be measured in terms of metres, if metres cannot be divided so that they exactly measure the length we are measuring? — Ludwig V

Again, I do not follow. Metres can be divided. We have centimetres and millimetres. But when we measure, at some point an approximation is made, a rounding off.

An afterthought. Do I understand rightly that your analysis of wholes and parts applies to physical objects, and not to mathematical ones? — Ludwig V

I don't think that this is relevant. I believe the analysis applies to all objects. But there is a problem with supposed "mathematical objects", and this is that we assume them to be infinitely divisible. And this assumption creates incoherency. This incoherency renders the supposed objects as not true objects.

Yes, but it is not difficult to abandon the (pseudo-physical) lamp for a purely abstract version, which does not have the same problems. — Ludwig V

The point I've been arguing since the beginning of the thread, is that if we abandon the empirical, and adhere strictly to the prescribed, purely abstract version, then nothing indicates that 60 seconds will pass. You see in both the op, and the lamp example, 'there will be a condition at 60 seconds' is an unwarranted conclusion simply added on, and not derived from the initial premises. The initial premises, being the described activity do not allow that 60 seconds will pass. This conclusion, 'there will be a condition at 60 seconds' is pulled from empirical evidence, and is completely inconsistent with the prescribed purely abstract version.

We need infinite divisibility for the same sort of reason that we need infinite numbers. The infinite numbers guarantee that we can count anything. Infinite divisibility guarantees that we can measure anything (that is measurable at all). Limitations on either are physical. — Ludwig V

No we don't need infinite divisibility, for the same sort of reason that we need infinite numbers, for the reasons I described. Any thing which is to be divided has its divisibility determined by the sort of thing that it is. And each type of thing is divisible in different ways. And, the way that the thing is divisible must be determined prior to division, or else we attempt to do the impossible. There is nothing that is divisible infinitely, therefore this ideal needs to be excluded as necessarily an attempt to do the impossible.

This is not the same as infinite numbers. The countability of a multitude cannot be determined beforehand, as the divisibility of a thing must be determined beforehand. So, we need infinite numbers because we do not know how large the multitude will be until we count, but we do not need infinite divisibility because it is impossible to divide something prior to knowing its divisibility, and the possibility of infinite divisibility is already excluded as actually impossible.

That is a fundamental feature of the difference between a unity and a multitude. If a unity is composed of a number of parts, then the number of parts is necessarily finite. To have infinite parts would violate the finitude of the boundaries implied by the concept "unity". But the concept of "multitude" has no such implied boundaries, principles of limitations. Therefore a "unity" is always limited in its divisibility, limited by the principles which make it a unity rather than just a multitude (I cannot say "multitude of parts" because "part" implies a whole), and a multitude is not necessarily a whole, so its countability is not necessarily limited.

I think you are being misled by the temptation to take the divisibility of "medium-sized dry goods" as the paradigm of divisibility. — Ludwig V

No, I am talking about the divisibility of anything, in an absolute sense. There is no such thing as a unity which has absolutely zero limitations on its divisibility. That is a fundamental feature of what it mean to be a unity.

The colour of something isn't divisible at all. — Ludwig V

Colour is very much divisible. It is a collection of distinct wavelengths, and I believe it is divided by the harmonic principles of the Fourier transform.

There is no doubt that it is easy to do that. But it seems that people disagree about whether the scenario makes sense or is incoherent and even if they do agree, they still disagree about why. — Ludwig V

It's easy to see why it's incoherent. Start out with the concept of infinite. We can easily see why it is beneficial to allow for numbers to be infinite. This allows that there is no limit to our capacity to count any quantity, or to measure any size of thing, because we can always have a large number. In the case of division though, we may assume that infinite divisibility would allow us to divide anything anyway, but this is really incoherent. That is because division implies, or requires logically, that there is something, an object of some sort, to be divided, and its divisibility will always be dependent on the sort of thing that it is. An object, or thing is a unity of some type, and as such there is always limits to its divisibility, whatever unifies also determines divisibility.

To propose a thing which is infinitely divisible is an incoherent proposition, because as a thing, it is already necessarily limited in its divisibility. This is the issue of the proposition of a finite object being infinitely divisible. That is incoherent because the finiteness of the object limits its divisibility. In whatever way it is finite, its divisibility is limited accordingly.

I agree that this isn't really about anything empirical, but it sort of seems to be. — Ludwig V

This is the trick of the whole thing. It really is about empirical things. These empirical things are space and time, each of these is known through experience. Then we take these empirical things and pretend that they are absolutely abstract, purely ideal, and stipulate ideal principles like infinite divisibility. Then, someone creates a scenario, like the lamp or the op, which utilizes this purely ideal feature of infinite divisibility. Now we do not properly separate the purely ideal from the empirical, in our minds, so that "empirical time" interferes, and we say that 60 seconds must pass, it has to because experience tells us that it will. But that is allowing "time" to be an empirical thing.

In fact, one could simulate the on/off lamp so that at a certain rate you would see what appears to be a constant light. — jgill

The problem though, is that in the prescribed scenario there is no such thing as "a certain rate". The rate is not constant, but rapidly increasing. The only constant is the rate of increase. That rate of increase is what I say is incomprehensible and incoherent.

That's true, but seems to be a purely physical limitation. It raises the question whether that means it is really on or off, or a some sort of in-between state. Fluorescent lights flicker on and off all the time (at least if they are running on AC, and we just say they are on. And it is true that for practical purposes there is no relevant difference between that light and sunlight or candle-light. — Ludwig V

Jgill talked about how the lamp would "appear", and this implies a sense observation, and empirical judgement. The point I made is that the description describes something far beyond our capacity to sense, so it is incoherent to talk about how this described thing would "appear".

Something flashing on and off at a constant rate is not comparable, because the description is of a rapidly increasing rate. And the rate increases so rapidly that the prescribed rate becomes incoherent even to the mind, as well as the senses. This is just an example of how easy it is to say something, or even describe a fictional scenario, which appears to make sense, but is actually incoherent.

Do you mean "evolved" in terms of man's ability to use language overall, or in terms of how individual languages evolve? — Count Timothy von Icarus

I would say both, as the one seems to just be a more specific example of the other, which is more general.

I agree with what you're saying to some degree, but it's also the case that various metaphysical traditions: Platonism, atomism, Aristotleanism, etc. are all significantly older than any of the languages people on this forum are likely to speak as their native language. So there has been plenty of time to "work out the kinks," if it was easy to do so. — Count Timothy von Icarus

I don't see the point. The evolutionary force of change, brought about by the common usage of billions of people is much stronger than the force of a few metaphysicians. This makes it impossible for metaphysicians to "work out the kinks", because the kinks are being created at a rate much faster than anyone could have a hope of working them out.

Furthermore, the evidence of history shows, that controls over language use are not well received by the common people, and attempts at this will backfire. Look at the Catholic Church's attempt to control heresy, by controlling language use, The Inquisition.

Probably more relevant to the linguistic turn's hopes is that, for over a millennia, philosophers and theologians actually did use a dead language whose function was primarily to discuss these sorts of issues (outside of the liturgy obviously). — Count Timothy von Icarus

I don't see where you derive this idea. There was never a language whose primary function was to discuss theology and metaphysics. Latin's primary use was never simply theology and metaphysics. Now its use in religion is simply ceremonial, symbolic. In its late stage of actual usage, it was the language of all science and higher education. It had that role because the institutions of educational material were constructed with that language. Such institutions maintain tradition and are late to be affected by evolutionary change.

. You have a thousand year stretch of philosophers using a language that had been denuded of its "everyday" implications, supported by vast and elaborate lexicon of technical terminology worked out within that time period. — Count Timothy von Icarus

This is not at all true. It implies that higher education has no "everyday" implications. That of course is false, as higher education is a major driving force of evolutionary change. Changes at the higher levels of education trickle down to the less well educated, and the word usage gets altered on the way, because of the difference in understanding.

Yet this clearly didn't resolve all the issues vis-á-vis metaphysical questions—questions that appear to be at least as old as the written word itself, and which will seemingly always fascinate us. — Count Timothy von Icarus

Of course all the metaphysical questions have not been resolved. If that were the case, knowledge would be absolutely complete. The problems of quantum physics, wave-particle duality, entanglement, etc., and the problems of cosmology, dark energy, dark matter, etc., demonstrate that knowledge is far from complete, and many metaphysical questions remain unsolved.

I don't understand what you are arguing. Language does not resolve metaphysical problems, it is simply a tool used by the human beings who work to do this. When human beings are uninspired toward addressing such problems, directing their attention in other ways instead, and using language toward those other endeavours, it is incorrect to blame the failure of solving those metaphysical problems on the language. Clearly, when human beings have no interest in solving metaphysical problems, the failure of solving these problems is not to be blamed on the available tools.

Human beings are quite innovative, and are very capable of formulating, adapting, and shaping tools to suit there purposes. So if the human population was inclined toward solving specific metaphysical problems, they would adapted the tools necessary for this task, as they have done in science. The reality is that very few are inclined in this way, so the tools do not get produced.

The Latin era sort of seems like a gigantic natural experiment to see if the problems of philosophy can be fixed by moving away from everyday language. There is an irony in the fact that the medieval period is often singled as an exemplar period "bad philosophy" vis-á-vis the linguistic turn given the language philosophy was done in at the time. — Count Timothy von Icarus

You've got this backward. You are not looking at the proper chronological order, looking backward from now instead of from the ancient times toward now. What is the case is that "everyday language" moved away from Latin, not vise versa. There was, historically, a very close relationship between everyday language and Latin, and even further back in time, Latin was everyday language for many. However, as the written language, replacing Greek, Latin always held a place of authority, being "the memory" of the people. When people started questioning the authority (and this was deemed heresy), and those acting in the position of having authority responded with enforcement rather than allowing freedom, then everyday language rapidly moved away from Latin.

Is there another way to study and critique metaphysical and epistemological issues, or is language indispensable for the task? — Janus

I don't think there is any other way. But the issue is as I mentioned above. Language changes and evolves according to usage, and the usage is determined by the aims (intentions) of the users. Primary usage is the billions of mundane communicative everyday expressions. Secondary usage is business, legal and political. Tertiary is higher education. Metaphysics and epistemology are far down on the list of importance. Therefore language in its natural form, is fundamentally not well suited for these purposes.

Since natural language is not well suited to these purposes, yet language is the tool which must be used, then we can conclude that a special form of language needs to be designed for this purpose. And, there is nothing absurd about designing a special form of language for a specific purpose, mathematics is an example of such a specialized form of language. It's formulated for the endeavours of empirical science. Also we commonly create languages for purposes, in computer science.

But it seems just as plausible that language evolved in such a way as to be vague and confusing precisely because it's being generated by people facing a world full of vague and confusing metaphysical and epistemological conundrums. — Count Timothy von Icarus

Language evolved to be efficient for the purpose of mundane communication, that's why it's vague and ambiguous. We learn the minimum number of words required to make ourselves understood in a maximum number of different circumstances. Accordingly, it's not well suited for metaphysical and epistemological problems, and it's confusing when applied in this way.

This is more of a meta-thread on HOW PEOPLE debate Wittgenstein.. — schopenhauer1

You could look to @Banno as an example. Banno has argued an interpretation of Wittgenstein, supporting that interpretation with an appeal to authority, Wikipedia. Later, in a completely different context, Banno bragged, I wrote that Wikipedia page. Hahaha, good one, Banno.

And, I might add, that I don't think such shenanigans are exclusive to Banno, or discussions of Wittgenstein in general.

No, it isn't the same as being stopped. Being stopped is an everyday occurrence. Infinite speed, is, as you say, unintelligible. If that's what underpins the supertasks, it makes sense of the narratives - apart from the fact that it doesn't answer the question whether the lamp is on or off. — Ludwig V

I think that if the lamp is going on and off at an infinite rate, then it's not correct to say that it would be on at any particular time, or off at any particular time, because it is going on and off at a rate faster than our ability to determine a particular time.

If one watches the lamp in a dark room, at some point it will appear to be on continuously. — jgill

We're talking about a time duration which is far beyond the distinctions which could be made by the human eye. This would be what is occurring in a tiny fraction of a second. It doesn't make any sense to talk about how the lamp would appear in this time.

If I recite the first number after 30 seconds, the second after 15 seconds, and so on, then I have recited them all and so stopped after 60 seconds, even though there is no largest number for me to stop on. — Michael

I have to disagree. What you describe is a rate of acceleration which would produce an infinite speed. The rate at which you recite the numbers becomes infinite before 60 seconds passes. And, despite the fact that infinite speed is in some sense unintelligible, it is clearly not at all the same as being stopped.

If (2) is true then we can stop without stopping on some finite number. — Michael

How do you make this conclusion?

Not in those words. "Does not allow for a minute to pass", like somehow the way a thing is described has any effect at all on the actual thing. — noAxioms

Let me remind you, the "thing" being described here, in the op is a fictitious scenario. It is one hundred percent dependent on the description, just like a counterfactual. We might say that "the factual situation" is that a minute will pass, but the counterfactual described by the op does not allow for a minute to pass. You seem to be unable to provide the required separation between these two, thinking that the factual and the counterfactual may coexist in the same possible world.

Anyway, I see nothing in any of the supertask descriptions that in any way inhibits the passage of time (all assuming that time is something that passes of course). — noAxioms

Right, as I said there is nothing in the op to inhibit the passing of time, in fact the passing of time is an essential part, it is a constant. However, the premises of the op restrict the passing of time such that 60 seconds will not pass.

Ah, it slows, but never to zero. That's the difference between my wording and yours. Equally bunk of course. It isn't even meaningful to talk about the rate of time flow since there are no units for it. The OP makes zero mention of any alteration of the rate of flow of time. — noAxioms

There is nothing in the op to indicate that the passing of time slows. That is an incorrect interpretation. As you say, it isn't meaningful to talk about the rate of time in this scenario. What happens is that the speed of the person descending the staircase increases. And, as the speed increases, there is no limit to the acceleration indicated. The velocity is allowed to increase without limit. Even if we considered "infinite velocity" is a limited (which is of course contradictory), and assume that limit could be reached, this would still not imply "no time is passing". It would only make the spatial-temporal relationship unintelligible due to that contradiction.

This is actually very similar to the perspective of special relativity theory, which uses the speed of light as the limit, rather than infinite speed. This avoids contradiction but ti still renders the spatial-temporal relationship as unintelligible at the speed of light. From the perspective of the thing moving that fast, it appears like no time is passing, yet time is still passing. It's just a twisted way of making the passage of time relative to the moving thing for the sake of the theory. But there is no relativity theory stated in the op, nor any other frame of reference, so there is nothing to indicate a stopping, or even a slowing of time. The frame of reference which you keep referring to, in which 60 seconds passes, is excluded as incompatible with the described acceleration. The described acceleration is purely fictional though, like a counterfactual.

Socrates (as presented by Plato) considered himself wiser than anyone else because he knew he didn't know anything, which doesn't seem to leave much room for anyone else (at least in Athens) to be a philosopher. However, his dialogues with sophists do not show Socrates treating them disrespectfully and this is something of a puzzle. The orthodox interpretation regards Socrates' respect as ironic. Maybe it is. But maybe Plato's practice was a bit less dismissive than all this implies. — Ludwig V

I believe Socrates (as portrayed by Plato) had great respect for the sophists. They displayed power and influence, and this piqued his interest. In Plato's dialogues, Socrates holds lengthy discussions with some sophists, and this would not be possible without the appropriate respect. On the other hand, I also believe that since the sophists presented themselves in a conceited way, as filled with a sort of complete or perfect knowledge, this produced a challenge in Socrates, to demonstrate their faults and weaknesses. Because Socrates had some degree of success in this personal challenge, Plato developed a level of disdain for them.

Prior to Socrates I believe that sophists were generally well respected, and this is evidenced by the power of their rhetoric. Socrates revealed the subjectivity of rhetoric, leaving the character of the sophists who employed it, exposed. The principal sophists who were exposed in this way, were the the politicians of Athens. But Socrates carried on toward exposing those in the even higher level, more exclusive schools of logic (I don't agree with you that there was no concept of "logic" at this time) like the Pythagoreans and Eleatics, and this allowed Plato to class them as sophists. This is where Zeno fits in. And Socrates is portrayed by Plato as having great respect and curiosity for the lofty principles held by these prestigious schools. Nevertheless, despite great respect for the individuals, he sees that there must be flaws in the principles, and therefore proceeds with his personal challenge of engaging the individuals to defend, and ultimately reveal those faults.

I think that the important point is the use of valid reasoning with unsound premises. This is how Aristotle attacked Zeno's paradoxes. But Aristotle didn't have a good understanding of the nature of knowledge, and the effects of faulty premises. He claimed that logic leads us from premises of greater certainty, to conclusions of lesser certainty, when in reality the opposite is true. Uncertainty in the premises is what introduces uncertainty into the conclusions. And the problem is that many premises are intuitive notions simply taken for granted, such as in the Achilles, the premise that the faster must first reach the place where the slower is, prior to passing. In reality, the faster passes the slower without ever sharing the same place.

The Aristotelian view of knowledge is still common place. You'll see that many here at TPF argue that there are fundamental principles, 'bedrock propositions' or something like that, which are beyond doubt, and support the whole structure of knowledge. In reality, those fundamental principles are the least certain because they are taken for granted, lying at the base of conscious thinking, bordering on subconscious knowledge. Those highly fallible intuitions are the ones most needing the skeptic's doubt, but it takes someone like Zeno to demonstrate this.

Says the proponent that time stops. — noAxioms

Huh? I said that time stops? I don't think so. I said that in the scenario of the op, 60 seconds will never pass. But clearly time does not stop. In that scenario, time keeps passing in smaller and smaller increments, such that there is never enough to reach 60 seconds, but time never stops. The claim that 60 seconds must pass or else time will stop, is derived from different premises which are inconsistent with the described scenario.

I suspect Zeno believed his premise to be false... — noAxioms

That's what I was arguing as well, but Ludwig produced references to show that this might not be the case.

No evidence of your interpretation here. — Ludwig V

A few quotes with no real context, does little. Anyway, it's off topic, and really sort of pointless to argue a subject like this. You have your opinion based on how you understand Plato, and I have mine. Due to the reality of ambiguity, i don't think there is a correct opinion here.

Fair enough, but to go on, as Plato does, to accuse the sophists of deliberate deception or wilful blindness is completely unjustified (except when, as in the Protagoras,(?) Gorgias (?) someone boasts about doing so – though it doesn’t follow that everyone that Plato accuses of rhetoric and sophistry did so boast.). — Ludwig V

The problem is that "sophist" was a word with a very wide range of application at that time. In the most general sense, you'll see Aristotle use it to refer to someone who uses logic to prove the absurd. Zeno might be a sophist in this sense. But also "sophist" referred to people like Protagoras and Gorgias, for their use of rhetoric. And "sophist" also referred to those who had schools and charged money to teach virtue. So there was a range of meaning, but "rhetoric" seems to be the essential aspect, and this is a mode of persuasion which is not necessarily logical. Accordingly, "sophist" has bad connotations, but as Plato demonstrates in "The Sophist", it's very difficult to distinguish a philosopher from a sophist. It appears like either the sophist is a type of philosopher, or a philosopher is a type of sophist.

But accepting that connection is a long way from accepting that he had any doubts about the validity of his conclusions. — Ludwig V

The issue is not the validity of the conclusions, it's the soundness. Take the Achilles for example, with two principle premises. First, to overtake the slower, the faster has to get to where the slower was. Second, in that time, the slower will move further ahead. So the faster does not overtake the slower, and this may repeat if the faster is still trying. It appears valid to me, so if we want to refute it we need to look at the premises, as Aristotle did. But when we try to understand how the premises are wrong, then there is disagreement amongst us, because we really can't demonstrate exactly what the premises ought to be replaced with.

,

That there is no first number to recite is the very reason that it is logically impossible to begin reciting them in reverse and it astonishes me that not only can't you accept this but you twist it around and claim that it not having a first number is the reason that it can begin without a first number. — Michael

NoAxioms has a habit of making astonishing claims, then instead of recognizing the incorrectness, arguing some twisted principles. Like above, noAxioms insisted Zeno did not conclude that the faster runner could not overtake the slower, then refused to recognize my references, insisting they were in some way improper.

They're clearly being confused by maths. They think that because a geometric series of time intervals can have a finite sum and because this geometric series has the same cardinality as the natural numbers then it is possible to recite the natural numbers in finite time. Their conclusion is a non sequitur, and this is obvious when we consider the case of reciting the natural numbers (or any infinite sequence) in reverse. — Michael

This is the problem with mathematical axioms in general. As fishfry said, I can't really count the natural numbers, but I can state an axiom that the natural numbers are countable, and this counts as me having counted the natural numbers. So mathematicians really need to be careful to distinguish between the fantasy world they create with their axioms, and the true nature of what is "logically possible". Just because it can be stated as an axiom does not mean that it is logically possible. And when the axiom claims that something which is by definition impossible (to count all the natural numbers), is possible, then there is contradiction, therefore incoherency, inherent within that axiom. But would a mathematician accept the reality of an axiom which is self-contradicting?

There is a far more fundamental problem, and they're just ignoring it. — Michael

The problem is the age-old incompatibility between being and becoming. Logic, and this includes mathematics, applies naturally to "what is", "being". But "becoming" has aspects which appear to escape logic, what lies between this and that, one and two, etc., and therefore it seems to be illogical. If we apply the logic of being, to the reality of becoming, we find paradoxes as Zeno demonstrated.

This implies that "becoming" requires a different form of logic. That's what Aristotle laid out with his definitions of "potential", and "matter", as the aspects of reality which violate the law of excluded middle. In modern times, much progress has been made with modal logic, and probabilities. But the truth is that these aspects of reality, those which are understood through probability, remain fundamentally illogical, and the so-called "knowledge" which is derived creates an illusion of understanding.

I'm not sure it is possible to articulate what people who have not thought about the question think the answer to it is. — Ludwig V

It's simple, talk to people, ask them. Then you'll see that it's more than just a matter of thinking about the question, it is a matter of making the effort to educate oneself. Metaphysics is not apprehended as a valuable subject.

I don't think we have anything near the evidence required to divine Zeno's motives. We don't even have his articulation of the argument. — Ludwig V

Well, there is a lot of information available from Plato. In works like "The Sophist" and "The Parmenides", he takes a very critical look at the motives of some of the Eleatics, Zeno in particular. Specifically, in "The Sophist" he attempts the very difficult task of developing a distinction between philosophy and sophistry, even the sophist is engaged in philosophy.

But you don't know that he recognised what is so very clear to you, that the argument was ridiculous, or that he had "apprehended the faults in that ontology", though I admit that if he had understood what you understand, he might well have been poking fun at it. Still, other people since then have poked plenty of fun at it. But that's not a substitute for understanding the argument. — Ludwig V

It's very clear from the discussion at the time, Plato and Aristotle, that Zeno knew he was using logic to produce absurd conclusions. There should be no doubt in your mind about that. He did not pretend to believe what he had proven, that motion is impossible, that the faster runner could never overtake the slower, etc..

I think that's perfect. It's the conjunction of mathematics and - what can I say? - the everyday world.
What's difficult is the decision which is to give way - mathematics or the everyday world. Zeno was perfectly clear, but some people seem to disagree with him. — Ludwig V

The difficult thing is that many human beings are like naive realists, and they think that our sense perceptions of "the everyday world" are a direct copy of the way an independent world would be. From this perspective, we cannot look toward the everyday world to be what needs to give way. But from a more philosophical perspective, we know that sense perception doesn't really show us the way the world is.

So to be prudent, I'd say both sides need to allow give and take. This may be like the ancient division between Parmenides with being and not being, and Heraclitus with becoming. Plato described how the two seemed to be fundamentally incompatible, and Aristotle provided principles whereby they both could coexist as different aspects of reality.

That suggests that we do know roughly how things move. I don't think that's what at stake in Zeno's thinking. His conclusion was that all motion is illusory. The only alternative for him was stasis. But I guess we can do better now. — Ludwig V

That was Zeno's conclusion, from his paradoxes, that motion is impossible. But I do not think that this was what he was sincerely trying to prove. Clearly he could observe motion, and he would know that this would be considered a ridiculous proof. So I think his arguments were designed to show that there is incompatibility between motion as observed, and motion according to the principles of logic applied to it. Zeno came from the Eleatic school, so the first principle was "being", stasis, but what he was demonstrating was that this principle was insufficient to understand reality. That's why Socrates and Plato took interest in the sophistry of the Eleatics. The Eleatics could employ logic to prove absurd things, and this showed the gap between the "becoming" of the physical world, and the "being" of the Eleatics and Pythagorean idealism. So I think that Zeno, even though he came from the Eleatic school, was apprehending the faults in that ontology, and was sort of poking fun at it.

That's apparently what somebody else reported about what Aristotle reported. I've seen it conveyed about 20 different ways. — noAxioms

I quoted that directly from Aristotle's Physics. I gave the page and lines, 239b, 14-17. Further, Aristotle compares it to the arrow paradox, and says "the 'Achilles' goes further in that it affirms that even the quickest runner in legendary tradition must fail in his pursuit of the slower"

This particular wording says 'never' and 'always', temporal terms implying that even when more than a minute has passed, (we're assuming a minute here), Achilles will still lag the tortoise. — noAxioms

The time length is irrelevant. The pursuer will "always" lag the pursued, for the reasons indicated. The pursuer must reach the point where the pursued was, and in the time that it takes to do that, the pursued will move further ahead.

The logic as worded here is invalid for that reason since the argument doesn't demonstrate any such thing. — noAxioms

The logic is invalid for what reason? There is no specic time periods mentioned.

. I've seen more valid ways of wording it (from Aristotle himself), in which case it simply becomes unsound. — noAxioms

I gave you Aristotle's wording. He rejects the arrow argument which demonstrates that motion is impossible, by saying that time does not consist of instants. So that is an attack on the premises of that paradox. He then says that the solution to the 'Achilles' "must be the same". But he doesn't show how time not consisting of instants would solve the Achilles paradox. The matter of instants appears irrelevant here, and the problem seems to be with the assumed nature of space, rather than time.

I just didn't like the fact that the quote didn't match the site linked. — noAxioms

I can assure you, the quotes are taken directly from the referenced sites. I just went back to check. Click the links and you will see.

You mean because they allow the convergent infinite series?
Mathematically? Physically? (I'm inclined to think you mean physically, because of your reference to fundamental particles.) — Ludwig V

I meant, that they can mislead us when we apply the principles to the activities of the physical world. That's what Zeno's paradoxes show.

Is the direct spatial route not available because it contains a convergent regress?
What path does Achilles take? (I assume he is not a fundamental particle.) — Ludwig V

What is evident, is that we do not know how things move, and the exact "path" through space, that things take, whether they are big planets, stars and galaxies, small fundamental particles, or anything in between.

I know the story. You seem to have reworded it for your purposes, since the quote you give does not come from that site, but the site also seems to be conveying the story in its own words, not as reported by Aristotle. — noAxioms

Here's what Aristotle reported:

The second is the so-called 'Achilles', and it amounts to this, that in a race the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. — Aristotle Physics 239b 14-17

How is this different from what I said? I gave a full explanation, as did the site I quoted. Aristotle just said "it amounts to this...", providing a shortened version, probably because the specifics were well known at that time.

Yes, and without justification, or at least without explicitly stating the additional premise that makes the conclusion valid. — noAxioms

I'm still waiting for you to explain how the conclusion is not justified, and why you think there is a requirement of an additional premise.

So are you going to conclude, with Zeno, that motion is impossible? or that Zeno is analyzing the situation in a misleading way? — Ludwig V

Yes, Zeno is analyzing in a misleading way, but only because the axioms of continuity and infinite divisibility are themselves misleading. So Zeno simply demonstrates how standard conventions are actually misleading us.

And here we are. a couple of millennia later, still being misled by the same conventions. This is because we have not yet determined the natural points of divisibility. And so, fundamental particles take every possible path when they move from A to B, because the direct spatial route does not allow them to get ahead of the tortoise.

Anyway, I deny that Zeno in any way suggests that the overtaking will never take place. He just says that another step always follows any given step. — noAxioms

According to this reasoning, Achilles will never catch the tortoise, says Zeno. — Internet Encyclopedia of Philosophy

https://iep.utm.edu/zenos-paradoxes/

The paradox is like this. Both Achilles and the tortoise are moving, but the tortoise has a head start. So at t1 Achilles is at location A and the tortoise is at location B. At t2, Achilles reaches location B, but the tortoise has moved to location C. At t3, Achilles reaches location C, but the tortoise has moved to location D. As this procedure will carry on without end, Zeno concludes that the faster runner cannot overtake the slower.

Zeno Paradox 1: Achilles and the Tortoise
Achilles is a lightening fast runner, while the tortoise is very slow. And yet, when the tortoise gets a head start, it seems Achilles can never overtake the tortoise in a race. For Achilles will first have to run to the tortoise's starting point; meanwhile, the tortoise will have moved ahead. So Achilles must run to the tortoise's new location; meanwhile the tortoise will have moved ahead again. And it seems that Achilles will always be stuck in this situation.

https://personal.lse.ac.uk/robert49/ebooks/philsciadventures/lecture24.html