Are Actual Infinities Possible?

[dmarb]

My view is:

It is obvious that actual infinities are rationally (metaphysically) impossible, in the sense of their capability of being empirically conceptualized. One can't conceive such an infinity in empirical terms. The only way one can try to conceptualize such is by attempting a measurement function that is potential in nature. Zeno demonstrated this long ago in order to discredit the credibility of phenomenal experiences, which accordingly are logically untenable. (See Achilles and the Tortoise and The Stadium). Zeno used the paradoxes to support his monist metaphysics. However, the arguments could, I think, be equally used to dump the reliability of rational metaphysics and cheer pluralistic realism.

W L Craig interprets Zeno's infinite divisions as potential and not actual. What he means is that one can go on, empirically, dividing a distance endlessly and never reach a metaphysical point of indivisibility, though in reality (experience), traversing distances is a daily affair - we do cross roads. He sticks to the empirical angle of interpreting the paradox. What I think Craig has done is to reiterate that actual infinities are not metaphysically possible, though the empirical concept of crossing roads, for instance, shows that an actual infinite distance was traversed in actual time (empirical sense, also infinitely divisible). In other words, when the rational function is applied to an empirical fact, a paradox ensues. It can also mean that the distance between two points is an objectively actual infinity of points, and the act of traversing is potential, meaning that the athlete cannot metaphysically traverse the distance, though he physically does it. The problem is there because a distance between points is an empirical concept while division is a rational category. The problem still remains.

However, it seems to me that strictly speaking, potentiality is an empirical category and not a rational one. Rationally speaking, the objective infinity of divisions is actual, though empirically absurd.

What do you think?

[Immanuel Can]

W L Craig interprets Zeno's infinite divisions as potential and not actual. What he means is that one can go on, empirically, dividing a distance endlessly and never reach a metaphysical point of indivisibility,...

This isn't my understanding of WLC's contention, though I'd be interested in seeing a quotation from him asserting it, if you have such.

In fact, his argument seems to me that there is NO "empirical" infinite at all...I think he uses the phrase "actual infinite." For "empirical" means "judged by experience," and one can't really "experience" a non-actual thing.

Zeno's paradox is an old one, and one that lasted a long time; but it has been solved. The simplest way of explaining that is that Zeno surreptitiously forces us to accept a discrete (i.e. a "separated steps", or what you term a "distance between points") model of motion in our thinking; whereas motion is actually a ray (an action that has a starting point, but then has continuous, non-discrete direction). Zeno's misrepresentation in the premises seems to compel his conclusion, but only because it's a misrepresentation of how motion works.

Since Zeno is not correct, there is no paradox in that we traverse roads. It's not a case of an "actual" or "empirical" infinite being practiced there. Rays do have specific commencement points, and are not past-time infinite, however long they may proceed into the future. Moreover, they are not composed of separated points on a line.

WLC's argument is especially potent when we consider past causal chains. For causal chains are discrete, and Zeno's paradox does apply to them. If it is necessary that X-1 happens before event X (in order to be the true cause of event X), and that X-2 must take place in order to become the cause of X-1, which then can be said to be the cause of X, then an infinite regress of causal attributions ensues. But infinite past regresses are actually impossible, as in causal attributions there would need have been a first event, or X-infinity. Thus, the whole causal chain could never commence at all.

Yet here we are. So how did the causal chain which produced us get started? I think that's his argument.

[surreptitious57]

Absolute nothing cannot persist so logically it means that temporal or spacial infinity must exist instead
Unfortunately this cannot be demonstrated at this point in time even if true so it is merely hypothetical

[Immanuel Can]

Absolute nothing cannot persist

Actually, that's ALL that we could expect to persist.

There is no reason why something has to exist at all. From nothing, nothing ought to have come.

Or, to put it in the words of one of the most august philosophical questions, "Why is there something, rather than nothing?"

This means that logically we ought to expect there to BE nothing. We ought not even to be here to ask the question, in fact. But here we are. So the question becomes, "How did that happen?"

[surreptitious57]

There is no reason why something has to exist at all

Actually there is because absolute nothing is far too fragile a state to carry on existing beyond an infinitesimal period of time
Quantum fluctuations come from nothing because of such fragility so there will always be something in whatever form it takes

[Immanuel Can]

There is no reason why something has to exist at all

Actually there is because absolute nothing is far too fragile a state

"Nothing," by very definition, cannot be "a fragile state." In the state of Nothing, there is literally nothing to cause anything to come about; and that looks quite permanent.

Quantum fluctuations come from nothing

Sorry to contradict, but they do not, actually.

If I understand the theory, quantum fluctuations are supposed to come from what's scientifically called, "the Quantum vacuum." But neither quantum particles nor vacuums are, by definition, "nothings," for even a vacuum is itself an existing state, and it's one which presupposes the lack of something. Thus quantum mechanics presupposes the existence of the prerequisite state for quantum fluctuations; and that, in itself, lacks explanation for existing.

From a genuine, complete state of Nothing, nothing follows.

[surreptitious57]

A true state of absolute nothing can not actually exist because it would be lacking in both property and dimension
However a state of nothing only defined by its dimension and nothing else can and does exist at the quantum level
In such states there is no energy or mass and it is within them that quantum fluctuations then come into existence

[Immanuel Can]

A true state of absolute nothing can not actually exist because it would be lacking in both property and dimension

This is a good observation. I agree about it lacking dimensions. It would have neither dimensions of time nor of space. But there is no inherent reason why time and space, let alone matter, properties, worlds and people "have to" exist.

So may I ask, what is the particular scientific law that declares there must be something rather than nothing? I am unaware of any such.

[Erk]

A true state of absolute nothing can not actually exist because it would be lacking in both property and dimension

So may I ask, what is the particular scientific law that declares there must be something rather than nothing? I am unaware of any such.

Based on the laws of Identity, Noncontradiction, and the Excluded Middle everything is what it is, it can't be what it is not, and it can't be anywhere in between.

Therefore, absolutely nothing is absolutely nothing. There is no thingness about it. It can't exist. It doesn't exist. Therefore, something does.

PS: In a previous post in this thread you stated that there is no reason why something should exist because from nothing one only gets nothing. That came from Parmenides and he wasn't saying that nothing does exist. It was part of him saying it doesn't and he went on to say that something does and described it as a perfect sphere.

[Immanuel Can]

A true state of absolute nothing can not actually exist because it would be lacking in both property and dimension

So may I ask, what is the particular scientific law that declares there must be something rather than nothing? I am unaware of any such.

Based on the laws of Identity, Noncontradiction, and the Excluded Middle everything is what it is, it can't be what it is not, and it can't be anywhere in between.

Well, two points: one, these are laws of logic, not of science. As such, they are not empirical, but rather analytic and operational. They refer to the consistencies of a closed system of conceptual operations (i.e. logic), and do not of themselves dictate what empirical information gets put through them. For that, we need the empirical world. Secondly, they are only of application once something already exists: they have no explanatory role in WHY anything exists or does not exist.

Now, they are certainly wonderful rules, and help us to perform rational operations with what already exists; they don't go to answering the question, though.

Therefore, absolutely nothing is absolutely nothing. There is no thingness about it. It can't exist. It doesn't exist. Therefore, something does.

Well, this is a non-sequitur, actually. The claim "Nothing exists" cannot be converted logically to "Therefore nothing doesn't exist," because that second premise treats "nothing" as if it were one of the set of "things." But "No-thing" is, by definition, no member(s) of that set; it indicates the total absence of any such members. It's a negation of any-thing, not a thing-in-itself.

And that's the point: from genuine nothing, nothing ever comes.

PS: In a previous post in this thread you stated that there is no reason why something should exist because from nothing one only gets nothing. That came from Parmenides...

Actually, I was not alluding to Parmenides at all, nor did I derive that claim from him. I would rather say that simple common sense will do.

If you ask someone what caused X, and he responds, "Nothing," then you can understand him to be confessing his own personal ignorance of the cause, perhaps; or you can understand him to believe in something far more wildly irrational and superstitious than magic -- perhaps he actually believes that somethings appear from nothing, meaning without any cause at all. Things just happen, he says. And that would be about as unscientific a claim as a person could possibly make, I'm sure you'd agree.

If we pressed him, we would expect that he would either say, "I don't know," or less plausibly, "I don't believe in any causal attributions." But the latter would be irrational, for sure: and if true, would stultify the idea of scientific or causal explanation entirely. If things "just happen," then ultimately, that is the total explanation for all phenomena in the universe, and for the universe itself. We can no longer even expect rationally to work in such a universe, because there, well, "Things just happen."

[Erk]

Well, two points: one, these are laws of logic, not of science ...

Yes, they are the three laws of logic or thought, and that's exactly what they should be since we're in the metaphysics section which just like mathematics is not based on empiricism, but based on the self-evidence of analytical thought.

The claim "Nothing exists" cannot be converted logically to "Therefore nothing doesn't exist," because that second premise treats "nothing" as if it were one of the set of "things." But "No-thing" is, by definition, no member(s) of that set; it indicates the total absence of any such members. It's a negation of any-thing, not a thing-in-itself.

Yes, I did say absolutely nothing (no-thing) doesn't exist.

If things "just happen," then ultimately, that is the total explanation for all phenomena in the universe, and for the universe itself. We can no longer even expect rationally to work in such a universe, because there, well, "Things just happen."

If you would allow it, we've been rational all along. We've also shown more than 'just happen.' We've shown reason. Absolute nothing can't exist for a reason and something absolute does exist for a reason. It's self-evident and needs no empirical proof.

[Immanuel Can]

Well, two points: one, these are laws of logic, not of science ...

Yes, they are the three laws of logic or thought, and that's exactly what they should be since we're in the metaphysics section...

Not at all, actually. We may be in the Metaphysics section, but that does not eliminate empirical questions, especially when a metaphysical position (such as the claim that the universe appeared both necessarily and from nothing) has been advanced. If there is no scientific law to back such a claim, then the Metaphysical position is really in trouble.

My request was for the scientific (empirical) law that would make it necessary for something to come out of nothing. Not only is no such law forthcoming so far, but the laws of logic (great as they are) have nothing to say about that question.

The claim "Nothing exists" cannot be converted logically to "Therefore nothing doesn't exist," because that second premise treats "nothing" as if it were one of the set of "things." But "No-thing" is, by definition, no member(s) of that set; it indicates the total absence of any such members. It's a negation of any-thing, not a thing-in-itself.

Yes, I did say absolutely nothing (no-thing) doesn't exist.

And I responded that that is a fallacy. it's a category error. The negation of the existence of anything (i.e. "nothing") cannot be treated as if it were itself a "thing": at least, not rationally. "Things" belong in the category of "material entities" or at least "dispositions of energy particles." "Nothing," by definition is the negation of ALL such things, not one of the things. It is not matter, not energy, but the complete absence of all such.

And complete absences do not produce effects.

[Dontaskme]

IC:
And I responded that that is a fallacy. it's a category error. The negation of the existence of anything (i.e. "nothing") cannot be treated as if it were itself a "thing": at least, not rationally

It’s not being treated as a “thing” ... Erk is stating there is no thing to negate itself. And that all there is is everything which is not a thing..any negator would not exist...because to negate would require a negator which cannot exist. It works both ways..it’s a two way mirror.



That’s how i interpreted Erk’s post anyway.

.

[Dontaskme]

We may be in the Metaphysics section, but that does not eliminate empirical questions, especially when a metaphysical position (such as the claim that the universe appeared both necessarily and from nothing) has been advanced. If there is no scientific law to back such a claim, then the Metaphysical position is really in trouble

The metaphysical position isn’t talking to the logical mind of scientific thought and reason, it’s pointing to a truth beyond the mind which is impenetrable to the mind of logic and reason.
It’s pointing to a place where questions don’t ever arise.

The universe cannot appear from nothing, because nothing cannot exist. Any claimer of such a claim does not exist.

[Immanuel Can]

IC:
And I responded that that is a fallacy. it's a category error. The negation of the existence of anything (i.e. "nothing") cannot be treated as if it were itself a "thing": at least, not rationally

It’s not being treated as a “thing” ...

Actually, it was...though not by me. But you'd have to go back and pick up the earlier posts of the thread to see that.

The proposition under discussion was the notion that "nothing" was an "unstable" property which could not endure, and must necessarily produce something -- like, say, the universe. (However, only states, not "nothings" can be referred to as "stable," or "unstable," which is what the former poster was asserting.) But to think that it can be unstable is to suppose that "nothing" is a property or state...a thing-in-itself, which it manifestly is not. It is merely the absence of any things. As such, it has no components, forces within it, and nothing that can render it "unstable." So the postulate is incorrect, and is the product of a category error.

Nothings are not themselves things. The term "unstable" makes no reference to the condition of absolute nothing.

So if we begin with absolute nothing...say at the beginning of the universe...then that is all we would ever have had. For there would be absolutely nothing to turn the nothing into something. And yet, here we are...in the midst of something. So something must have done that.

What was it?