Which reminds me of Russell's joke that while every individual human being has a mother, it is a fallacy to supose that therefore the human species has a mother...

The mother of the race is a limit, not an item in the sequence...

But Mitochondrial Eve ruined the joke. — Banno

The limit to a type is completely different from the cause of an individual. So what Russell shows is that switching from individuals to types is nothing but a category mistake. To avoid the category mistake we must remain with individuals, and not switch to "the race" as you do.

Taking the stated analogy, the point which the cosmological argument makes, is that if every individual human being has a mother, then there is necessarily a mother which is prior to every human being, and therefore not a human being.

So, in the terms of the cosmological argument, if every material thing has a cause, then there is a cause which is prior to every material thing, therefore not material, i.e. immaterial.

To redefine "cause" with the intent to remove temporal priority is simply avoidance, just like redefining "change" to remove temporality is avoidance. Finding clever ways to avoid the truth of what an argument demonstrates is not philosophy it's denial.

Its nice to see someone tackle the actual argument. First, let me point out what the definition of a first cause is. Its a cause that has no prior explanation for its existence. In other words,

"It simply is, there's no prior explanation for its being" Yes. — jgill

So then your conclusion is the same as mine. Its not the simplification of the formula for infinite regress that the OP is noting, its just noting the set of all steps can be considered to represent it. You illustrated that for me. The question is then asked, "What caused there to be an infinite regress of causality?" The answer is, "There is no prior explanation, it simply is." Meaning that without us knowing whether there is a set of infinite causal regression, or a set of finite causal regression, we will reach a point of finite causal regression. Even a set of infinite regression, cannot avoid ultimately arriving at finite regression.

Essentially, "What caused it to be finite/infinitely regressive?" has no answer but the fact of its own existence. Now, maybe my vocabulary could be better. Maybe what I'm explaining could be described another way. It is really this phrase, "It simply is, there is no prior explanation for its being." that is ultimately true in any causal relationship. Do we call that a first cause? An uncaused cause? What do you think?

Fixed-point iteration, i.e. F(z) = z, is the mathematical description of circular causation, which can be considered a non-finite conception of causality that is symmetrical and has no initial-cause, thus also eliminating the causal arrow. — sime

No, that actually proves a first cause. "What caused a circular causation to exist instead of another type of causation?" As you noted it "Has no initial-cause", thus there is no prior explanation for its existence. Meaning, its a first cause as defined in the OP.

the truth of what an argument demonstrates — Metaphysician Undercover

And what exactly does this mean? At limits for limits, nothing. Consider it proved that either there is an infinite supply of mothers, or there must be a first motherless mother. The matter settled; we just don't know which. But now do a fast rewind of the history of life on earth. Clearly it's not infinite. Equally clearly there is no first mother. The lesson - the moral of the story - being that when thinking about limits you have to take care with your conclusions. Truth and demonstration are only truth and demonstration within the contexts that make them so, and that can break down at limits.

. Consider it proved that either there is an infinite supply of mothers, or there must be a first motherless mother. The matter settled; we just don't know which. — tim wood

The type of mother in question here is explicitly the mother of a human being. So the infinite supply you suggest as a possibility, would imply that human beings have always existed. Science has determined otherwise, so we really do know which.

The conclusion I stated remains sound, there is a mother which is prior to all human mothers. Likewise, science has determined that there is not an infinite regress of material things, so the conclusion that there is an immaterial cause which is prior to all material existence, remains sound as well.

So the mother both of and prior to all human mothers is not human, or not material? Imho it's better to acknowledge that language and logic, like their brother arithmetic, have their limitations, beyond which, it seems to me, it is better to concede ignorance and remain grounded than to float away on nonsense.

Um, science has determined that there is not an infinite regress of material things? Kindly refer me to that determination. My own intuition, fwiw, is that pushed out to the edges and the limits, the world is just not that simple.

It's true that the colour changes over distance, whether you discern it or not. — Banno

To be taken seriously, show your reasoning. For instance, in what theory or truth that you wish to uphold is truth not partly dependent on one or more observer’s discernment of what is real (i.e., actual or else ontically occurrent).

And here we are off into realism against antirealism, and the thread goes on... — Banno

Are you now labeling yourself an “antirealist”? If not, that ought to address this issue.

May I ask, Javra, where the insistence that change requires time comes from? Why is it important to preserve this idea? this by way of trying to understand why folk seem so adamant about something that to me seems obviously wrong. Thanks. — Banno

It’s a matter of semantics: To me, the term “change” can only denote and connote “to become something else”, “to replace one thing for another”, “to make into something else” and related phrasings and synonyms. All these entail the occurrence of one or more processes. With “a process” being understood as a series or else sequence of events, hence entailing that some event occurs before some other event that occurs after the previous one. And this, thereby, entails time.

Since this to you "seems obviously wrong", what semantic for the term "change" do you hold in mind wherein change is, or else can be, fully independent of process(es)?

(To answer this by pointing to static images or to mathematics is fully counterproductive due to the very disagreement between us.)

For instance, in what theory or truth that you wish to uphold is truth not partly dependent on one or more observer’s discernment of what is real (i.e., actual or else ontically occurrent). — javra

I think I've presented enough stuff on truth over the years not to need to do so again here. T-sentences and deflation.

Are you now labeling yourself an “antirealist”? — javra

No. But if you insist that in order to be true a statement must be believed (or some other intentional attitude) then you appear to be committing yourself to rejecting bivalent logic in this context and hence to antirealism.

Anyway, thanks for your response. I'll take your insistence that change requires time as axiomatic, then.

But I don't see how you could then understand $\frac{\delta x}{\delta y}$.

Cheers.

Funny reply, but OK.

So the mother both of and prior to all human mothers is not human, or not material? — tim wood

I just cannot see how you could possibly come to this conclusion from what i said.

Um, science has determined that there is not an infinite regress of material things? — tim wood

There is a first material thing, it's called "the universe", and it came into being at the Big Bang. Therefore no infinite regress of material things. What was prior to the Big Bang cannot be said to be material, because matter is dependent on the spatial temporal conditions of our universe.

I'll take your insistence that change requires time as axiomatic, then. — Banno

Ahh, now you're catching on, but not quite right. If it was mathematical, we might call it axiomatic. But this is philosophy so we call it "self-evident". There is a difference between the two, the former being mere stipulation, and the latter being supported by empirical evidence.

yeah, I was a bit distracted.

Perhaps if I describe what I think is happening.

There is a metaphysical view that holds that causation and time are inextricably linked. It's in effect a bit of grammar, such that folk hold that "change" (that word) ought only be used for sequences of events over time.

But when we look around we find changes that do not require time. We have at hand three examples: the image that changes form white to yellow, Hook's law, and $\frac{\delta x}{\delta y}$.

Now those who hold to the metaphysical view will deny that these are instances of change, and offer reasons for not accepting them.

Such folk are introducing ad hoc excuses not to see that their metaphysical view is false.

But anyway, may I ask again, if there is no change apart from time, how do you understand $\frac{\delta x}{\delta y}$? You must, I presume, claim that it is not a change?

There is a difference between the two, the former being mere stipulation, and the latter being supported by empirical evidence. — Metaphysician Undercover

:100: I would only add: "supported by experience, of which empirical evidence is one form of" (this in the modern sense of "empirical").

Such folk are introducing ad hoc excuses not to see that their metaphysical view is false.

But anyway, may I ask again, if there is no change apart from time, how do you understand δxδy? You must, I presume, claim that it is not a change? — Banno

Your former expressed, very slanted (if not utterly incorrect) biases should be addressed by this answer:

In short, you are (most likely unconsciously) reifying the sign "δx/δy" into the meaning it conveys for you and everyone here that can comprehend it in like manners:

There is no change whatsoever in "δx/δy" as sign, just as there is no change whatsoever that occurs in a static image for as long as it remains static. And both will require certain processes of mind to be interpreted in any meaningful way. (If not interpreted in any meaningful way, the argument can well be presented that they might not even be cognized as objects of awareness to begin with. But I won't here argue for this tangential.)

Processes of mind are processes (to state a triviality). Hence, time is requisite to them.

Any possible changes that the sign "δx/δy" can evoke - in one's mind, if this needs to be added - will then occur in processes of mind that, for instance, use the abstraction of variables (in this case, "x" and "y") to abstractly understand that when one variable changes (which requires time in before and after the given change) the other variable will also change (requiring the same abstracted frame of time) in manners established by the given sign as equation. This (mental) understanding of change is not itself static but dynamic; it is not a state of mind but a process of mind.

In what conceivable metaphysics is the sign "δx/δy" changing as one looks at it without in any way shifting one's focus of vision? Else, in what conceivable metaphysics can processes of mind occur in the absence of duration (which is always a temporal extension, or else temporal length, between two events)?

-----

To be blunt, your quoted biased conclusions so far look to me to amount to a pile of BS, to put it kindly - to not get into the psychobabble of "projections". As a recommendation that you are of course free to not take: it might be better to engage in discussions and debates on a philosophy form without insulting your interlocutors' intelligence or character by presupposing them to be far more idiotic than you yourself happen to be. Hey, no one here or anywhere is omniscient and hence perfectly intelligent, so I say this as one relative idiot among other non-omniscient beings that are thereby fallible.

I'm not asking about the symbols "$\frac{\delta x}{\delta y}$", but about the mathematics, or better, if we take x and y as displacement, the change in displacement of x with respect to y. An example might be the change in height of a hill with regard to distance from the peak.

Yes, the sign does not change. But the value of y may well change with a change in x, yet without t.

I don't think you have followed this, but perhaps we'd best leave it there.

Yes, the sign does not change. But the value of y may well change with a change in x, yet without t.

I don't think you have followed this, but perhaps we'd best leave it there. — Banno

For my part, no, I see you not having followed the very points I just made.

In what way can "y may well change with a change in x" in which there does not occur a before and after the addressed change?

If you agree there is no conceivable way, then in what way can there be a differentiation between "before and after" without time occurring?

In what way can "y may well change with a change in x" in which there does not occur a before and after the addressed change? — javra

The example I gave was the height of a hill with regard to distance from the peak. The height changes over distance, not over time.

I don't know how to make this any clearer.

The example I gave was the height of a hill with regard to distance from the peak. The height changes over distance, not over time.

I don't know how to make this any clearer. — Banno

You're gonna have to be inventive and/or cogent.

Is the hill itself changing (say due to some volcanic eruption)? I presume not. Does the hill's measurement require processes of mind? I presume it does.

There is no such thing as "change over distance" when the temporarily of mental processes that start at the hill's peak (an event) and move toward the hill's base (another event) are removed from the analysis.

There is no change over distance period, but always change over time.

At some point it becomes worthless to continue such discussion.

The example I gave was the height of a hill with regard to distance from the peak. The height changes over distance, not over time. — Banno

At some point it becomes worthless to continue such discussion. — Banno

agreed in full

The example I gave was the height of a hill with regard to distance from the peak. The height changes over distance, not over time. — Banno

The distance from the peak does not change without a change in location, and this requires time. What you can say, that the distance to the peak (height) differs according to location is a simple statement of difference, not change. You seem to be confusing difference with change.

As javra indicates "The height changes over distance, not over time" is not even intelligible.

Again, given your views on instantaneous velocity and $0.\dot 9 = 1$, you'll have to forgive me for setting aside your opinion on issues mathematical and physical.

Pardon the intrusion into a less than delightful conversation. First, take the calculus out of the picture by considering ratios of distances, $\frac{\Delta y}{\Delta x}$. If the measure of y depends upon a measure of x, then for a small measure of the latter, like looking at the space of one inch on a ruler, there will be a small measure of the corresponding y. Time does not enter into the discussion. The measures simply are. One inch on the x-axis may correspond to two inches on the y-axis.

Now, if you throw in a quantum-like perspective ( a favorite tactic on this forum), the time it takes to look at each measurement counts. And you have complicated something very simple. Good show.

On the other hand to introduce time set $\frac{\Delta y}{\Delta x}=\frac{\Delta y/\Delta t}{\Delta x/\Delta t}$. Now we consider the passage of time in determining these distances.

An example might be the change in height of a hill with regard to distance from the peak. — Banno

The distance from the hill as one walks towards it grows smaller, and the line of sight distance to the peak also diminishes, but the height of the hill remains constant. The angle of line of sight grows also.

Your intervention is welcome - I wasn't much enjoying myself. Yes, $\Delta x$ is clearer than $\delta x$.

A formatting question - sometimes I get a line feed before the math expression, other times, not - I don't see any obvious reason why. Any suggestion?

The distance from the hill as one walks towards it grows smaller, and the line of sight distance to the peak also diminishes, but the height of the hill remains constant. The angle of line of sight grows also. — jgill

Oh, I was thinking of the height, say above sea level, decreasing as one moves away from the peak - not the apparent height of the hill. Interesting take.

No, that actually proves a first cause. "What caused a circular causation to exist instead of another type of causation?" As you noted it "Has no initial-cause", thus there is no prior explanation for its existence. Meaning, its a first cause as defined in the OP. — Philosophim

One can interpret circular causality as saying that there is no initial cause, or as saying that what is considered "initial" is subjective or relative to the observer. The important thing, is that causal circularity implies that every causal relation is symmetric and of the form A <--> B. or equivalently, that the causal order A --> B --> C comes equipped with a dual order in the opposite direction, C --> B --> A.

However, circularity isn't a requirement for symmetric causal relations. E.g the interpretation of QM known as "Super-determinism" is in effect committed to symmetric causal relations as a consequence of denying the existence of counterfactual measurements, without committing to temporal circularity.

Also, a presentist might interpret the present as being the perpetual "first" cause , in spite of also admitting that present events are caused by "past" events when speaking in the vulgar. To resolve this apparent contradiction requires distinguishing causality from temporality, including the topologies in each case that might conceivably be different.

The measures simply are. — jgill

That's a mistaken idea. Measurements need to be made, and measurement is an act which requires time. The simple fact that any measurement requires time is a fundamental premise of Einstein's special relativity, which produces the concept of the relativity of simultaneity.

Yes, you can remove the temporality from measurement, and work with measurements which "simply are", but that is to assume a static world which you are working with. This is adequate for many applications, things in the same frame of reference, static relative to each other. Even the locations which are used to produce the "rest frame" are taken to be static locations which "simply are", as indicated by "rest frame". The assumed "rest" provides the premise required to remove temporality.

But as an ontological principle, the "static world" assumption, the assumed "rest" which is required to remove the temporal aspect as you describe, is a false premise, therefore producing unsound logic for any ontological purpose.

This is a very good demonstration of why Banno has much difficulty understanding metaphysics. Banno seems to think that axioms of mathematics which have been proven very useful in a wide range of physical applications can automatically be given an even wider range of application, a metaphysical application, without first undergoing the critical analysis of a metaphysician. Not recognizing that metaphysics is a broader field than physics, and that some axioms which are very useful to physics will turn out to be inapplicable in the wider field of metaphysics, and therefore very misleading if applied by a pseudo-metaphysician, is a fundamental misunderstanding of the field of metaphysics. That is a failure to recognize the difference between a trained metaphysician and a pseudo-metaphysician.

Oh, I was thinking of the height, say above sea level, decreasing as one moves away from the peak - not the apparent height of the hill. Interesting take. — Banno

This is very clear evidence that your claim is simply unintelligible. No one can even figure out what the hell you are saying, and to make yourself understood you need to add the temporal aspect ("decreasing as one moves away from the peak"), which you are insisting can be removed. That's hypocrisy plain and simple, and hypocrisy demonstrates with actions the exact opposite of what one is arguing in words.

One can interpret circular causality as saying that there is no initial cause, or as saying that what is considered "initial" is subjective or relative to the observer. — sime

No, whether there is an observer or not, there is still no reason, no prior existence why there is an infinite regress of causality. People seem to confuse the idea that you are needed for reality to exist. You are not. You are needed for reality to be interpreted. There still exists the thing in iteself that can be interpreted.

The important thing, is that causal circularity implies that every causal relation is symmetric and of the form A <--> B. or equivalently, that the causal order A --> B --> C comes equipped with a dual order in the opposite direction, C --> B --> A. — sime

This is one type of regressively infinite causality. There is also just flat regressive with no circularity. Understanding how the regressive causality works doesn't change the conclusion.

Also, a presentist might interpret the present as being the perpetual "first" cause , in spite of also admitting that present events are caused by "past" events when speaking in the vulgar. — sime

It depends on your measurement slice. Lets say I take a measurement slice to be as long as the universe has existed. While a fairly useless measurement slice for any other practical purpose other than this, we could do it. What prior existence caused the universe to have occurred? Whether its seconds, minutes, hours, or really, REALLY big, we're still left with the same conclusion when we complete the full set of prior causality. There is no prior reason that caused the set to exist, it simply is.

The point of the OP is to show you that no matter how causality regresses, you are left with the conclusion that there is no prior reason for existence period. Why does circular causality exist? Infinitely regressive causality? Finite causality? At some point you understand that it simply exists. There is no reason it should, or should not be. It is the first cause.

, Again, given that you have been unable to distinguish A=A from A⊃☐A, you'll have to also forgive me for setting aside your opinion on issues metaphysical.

A formatting question - sometimes I get a line feed before the math expression, other times, not - I don't see any obvious reason why. Any suggestion? — Banno

I use MathType, set to Wikipedia format, then change < to [ and > to ] at either end. It usually works but sometimes not, and I have no idea why.

The measures simply are. — jgill

That's a mistaken idea. Measurements need to be made, and measurement is an act which requires time. — Metaphysician Undercover

Does an inch exist on a ruler without someone looking at it?

the causal order A --> B --> C comes equipped with a dual order in the opposite direction, C --> B --> A. — sime

A-->B-->C-->A => C-->A-->B ?

It is really this phrase, "It simply is, there is no prior explanation for its being." that is ultimately true in any causal relationship. Do we call that a first cause? An uncaused cause? What do you think? — Philosophim

Mathematically, I would not. If an infinite composition exists it is the limit of a process that requires at each step a variable upon which that segment is defined.

${{F}_{n}}={{f}_{1}}\circ {{f}_{2}}\circ \cdots \circ {{f}_{n}}$ versus

${{F}_{n}}(z)={{f}_{1}}\circ {{f}_{2}}\circ \cdots \circ {{f}_{n}}(z)$

As n increases without bound one can look at the entire structure as a mathematical entity that has the value $\alpha =\underset{n\to \infty }{\mathop{\lim }}\,{{F}_{n}}(z),z\in S$

Now, outside the bounds of the theorem I have been discussing, alpha may not exist and the entire structure may oscillate or go to infinity, or whatever. Then the causation chain exists as a mathematical enterprise but cannot be associated with a particular value. It simply is. (My attempt at philosophy) :cool:

As n increases without bound one can look at the entire structure as a mathematical entity that has the value α=limn→∞Fn(z),z∈S — jgill

Yes, the point is not to analyze the regressiveness itself, its to look at the entire structure then ask what prior causation existed that caused it to be that structure.

Then the causation chain exists as a mathematical enterprise but cannot be associated with a particular value. It simply is. (My attempt at philosophy) :cool: — jgill

Yes, the value in question is irrelevant. The point is that no matter the the value, it simply is and thus 'a first cause'.

I use MathType, set to Wikipedia format, then change < to [ and > to ] at either end. It usually works but sometimes not, and I have no idea why. — jgill

Thanks. I don't use math often enough to have an app for it, so I type it manually or steal it from somewhere else - which is why I had a $\delta x$ where a $\Delta x$ would have been preferred.

Does an inch exist on a ruler without someone looking at it? — jgill

Long ago, one of the regulars here insisted that Mount Everest did not have a height until it was measured. The prognosis was advanced pragmatism, unfortunately incurable.

Then the causation chain exists as a mathematical enterprise but cannot be associated with a particular value. It simply is. (My attempt at philosophy) :cool: — jgill

I think this is pretty much it. My temptation, given an OLP background, is to see causation as primarily a way of talking about stuff. So things happen in the word, the window breaks, the rock flys, the child throws, but what counts as "A caused B" very much depends on what one is talking about - did the rock cause the broken window, or was it the child? It depends on what you are talking about, and what you are doing. Meaning as use, again.

Does an inch exist on a ruler without someone looking at it? — jgill

An inch no more exists without anyone contemplating it than does any word (such as the word “money”) exist without anyone contemplating it. In other words, it doesn’t. It is 100% a socially constructed and established unit of measurement - whose actuality as such is fully contingent on that cohort of minds (and their individual process of thought) which accept it as commonly established construct. Same is true of a centimeter, and so forth.

Long ago, one of the regulars here insisted that Mount Everest did not have a height until it was measured. — Banno

And I bet they still maintain this bit of advanced philosophical thought.