How can this premise in the Cosmological Argument be true?

[Tomdstone]

Is there something to which “time” refers?

The movement of the earth about the sun. A full revolution will take one year of time.

 

[Tomdstone]

To be fair, I think Aquinas would allow that an infinite regress could be possible, but that it couldn’t sufficiently explain its own existence…

We do look for explanations; that is true. But would that necessarily imply that the explanation does exist? Similarly, we look for causes, but does that necessarily imply that the cause exists? In other words, are the principles of sufficient reason and of causality, unproven assumptions which need to be questioned, just as there was a need to question the parallel axiom of Euclidean geometry?

 

[polytropos]

How can we know that the causes we see are second causes, and not simply N+1th causes?

The distinction between first and second causes does not have to do with numerical order in a linear series. Calling them instead primary and secondary would make this clearer. (Aquinas’s stick example is also misleading on this count.) The claim is that primary and secondary causes differ in kind. A secondary cause is basically defined as sort of cause we observe in the world, ie. something which receives actuality from something else the potency of which is being actualized; a secondary cause is a cause which itself requires a cause. (He only calls them “secondary causes” because he intends to conclude that there is a primary cause, which is categorically different. Nothing rides on the name, but that is probably what gives the argument the appearance of begging the question.)

I’m having trouble understanding one of the premises in the argument, however. In particular, the premise “this cannot go on to infinity” is puzzling to me. I do not see how that premise can be true. Why cannot an infinite chain of causes exist?

Aquinas isn’t arguing against actual infinities, full stop. He says:

In efficient causes it is impossible to proceed to infinity “per se”–thus, there cannot be an infinite number of causes that are “per se” required for a certain effect; for instance, that a stone be moved by a stick, the stick by the hand, and so on to infinity. But it is not impossible to proceed to infinity “accidentally” as regards efficient causes; for instance, if all the causes thus infinitely multiplied should have the order of only one cause, their multiplication being accidental, as an artificer acts by means of many hammers accidentally, because one after the other may be broken. It is accidental, therefore, that one particular hammer acts after the action of another; and likewise it is accidental to this particular man as generator to be generated by another man; for he generates as a man, and not as the son of another man. For all men generating hold one grade in efficient causes–viz. the grade of a particular generator. Hence it is not impossible for a man to be generated by man to infinity; but such a thing would be impossible if the generation of this man depended upon this man, and on an elementary body, and on the sun, and so on to infinity.

It seems that he is begging the question: “if no first cause exists, then no second causes exist, and we know second causes exist. Then a first cause must exist.”

The dependency of each member on the other members (that each member acts by virtue of the power of some other member) is the salient point. If there is an infinite series* of secondary causes (ie. causes that depend on each other in such a way), then there is no explanation for any member of the series, since the activity of each is by virtue of others, which are by virtue of others, etc.

• Note the series here does not have to be linear. It can branch and circle back on itself.

Time does not really matter here. Though simultaneity is not exactly what makes a cause “per se,” in general they will coincide, and temporally distinct causes and effects will be “per accidens”.

I don’t think any set of numbers would provide a counterexample to Aquinas’s argument here. There may be an attenuated sense in which 5 “depends” on 1, 2, 3, and 4, but the numbers clearly are not “per se” causes of each other. (There are, of course, arguments against taking mathematical infinities as actual infinities, but numbers are really irrelevant to Aquinas’s cosmological argument apart from any such considerations.)

So basically Aquinas argues, as you say, in this way:

(1) If there is no primary cause, then there are no secondary causes.
(2) But there are secondary causes.
(3) So there is a primary cause.

This formulation suppresses a lot of the support that Aquinas gives for (1) in numerous places. But it doesn’t beg the question: it’s modus tollens. He would argue that (1) can be derived from an analysis of what secondary causes are, the sort of dependency they have on each other. If there are any secondary causes, there must be some primary cause that does not depend on another. (Another reason people sometimes feel like the argument begs the question is that (2) is really obvious, so the argument really rides on (1). But that doesn’t really matter if Aquinas supports (1).)

 

[Tomdstone]

The distinction between first and second causes does not have to do with numerical order in a linear series. Calling them instead primary and secondary would make this clearer. (Aquinas’s stick example is also misleading on this count.) The claim is that primary and secondary causes differ in kind. A secondary cause is basically defined as sort of cause we observe in the world, ie. something which receives actuality from something else the potency of which is being actualized; a secondary cause is a cause which itself requires a cause. (He only calls them “secondary causes” because he intends to conclude that there is a primary cause, which is categorically different. Nothing rides on the name, but that is probably what gives the argument the appearance of begging the question.)

Aquinas isn’t arguing against actual infinities, full stop. He says:

The dependency of each member on the other members (that each member acts by virtue of the power of some other member) is the salient point. If there is an infinite series* of secondary causes (ie. causes that depend on each other in such a way), then there is no explanation for any member of the series, since the activity of each is by virtue of others, which are by virtue of others, etc.

• Note the series here does not have to be linear. It can branch and circle back on itself.

So basically Aquinas argues, as you say, in this way:

(1) If there is no primary cause, then there are no secondary causes.
(2) But there are secondary causes.
(3) So there is a primary cause.

This formulation suppresses a lot of the support that Aquinas gives for (1) in numerous places. But it clearly doesn’t beg the question: it’s modus tollens. He would argue that (1) can be derived from an analysis of what secondary causes are, the sort of dependency they have on each other. If there are any secondary causes, there must be some primary cause that does not depend on another.

How would quantum field theory fit into this, where you have virtual particles and anti-particles popping into existence? and causality is replaced by indeterminism?

 

[Prodigal_Son]

Not true. Here is a list of the integers, but it has no first object:
{…,-3,-2,-1,0,1,2,3…}.

That is not a listing of numbers. A listing is an event that takes place. What you’re giving me is not an event, but a schema. Even if you call it a “list”, it is not something that involves listing. How could you *start *a list in the middle? There is always a first number listed.

 

[Prodigal_Son]

I remember reading a book by Sean Carroll which suggests that we owe our perception of time to entropy. The interesting thing about entropy is that (insert the usual disclaimer about only applying to closed systems here) it can only increase. Thus I can tell when a building’s been deserted for a while because it has fallen into disrepair, which is a state of higher entropy.

Imagine if we lived in a universe with only conservative forces such that every event is perfectly reversible. The universe may be like billiard balls colliding on a frictionless table where the collisions are perfectly elastic, for example. I could record some footage of such a situation, play the video in reverse, and no one could tell the difference. Entropy, friction, and nonconservative forces are how you distinguish past from future.

So basically all we need to have a conception of time is to find an observable quantity that only increases or decreases.

This is all quite abstruse speculation. Do you intend to have your speculation defend the premise that time lacks a beginning?

I’m not saying that time has a beginning, but your apparent argument against it surely relies on extremely controversial premises – namely, Mr. Carroll’s speculation about the nature of time.

 

[polytropos]

How would quantum field theory fit into this, where you have virtual particles and anti-particles popping into existence? and causality is replaced by indeterminism?

You and I have been over this before. If one has independent reasons for believing the principle of causality, then quantum field theory is only a counterexample if there does not exist any interpretation of quantum mechanics on which causality is preserved. But there are such interpretations. One example is a “monadistic” interpretation whereby every particle is uniquely and internally predetermined to behave the way it does behave. Another would allow faster-than-light speeds and backwards causation. (As I pointed out in our previous exchange, these ridiculous, untestable theories are proposed because they are consistent, not because I think they are true.)

That said, I also think that there can be indeterministic or stochastic physical processes that are consistent with the Thomist principle of causality. What the Thomist really cares about is not the actualization of the potency to exist for any contingent object while it exists. Whether it had a physically determined origin is not actually relevant to that question. (For this reason, I tend to favor a slightly different cosmological argument, since it addresses this issue more directly.)

 

[polytropos]

That said, I also think that there can be indeterministic or stochastic physical processes that are consistent with the Thomist principle of causality.

Thomists actually believe that indeterminism is true, for they reject compatibilist free will.

 

[Tomdstone]

That is not a listing of numbers.

That’s an opinion. A list can be thought of as a register of items and the set given above qualifies under that definition.

 

[Oreoracle]

This is all quite abstruse speculation. Do you intend to have your speculation defend the premise that time lacks a beginning?

I’m not saying that time has a beginning, but your apparent argument against it surely relies on extremely controversial premises – namely, Mr. Carroll’s speculation about the nature of time.

I’m not saying time lacks a beginning. I am saying that I don’t think the question can be answered “by reason alone”, because time is, a priori, just a construct to help us order events. If time had always been conceived as an index for listing, there would be no dispute. Any system that used time merely for ordering would be incoherent, or at least internally inconsistent. As I’ve said, you may disagree with certain conceptions of physics, but they are at least logically consistent. Thus they have to be disproven empirically, not deductively.

 

[Prodigal_Son]

I’m not saying time lacks a beginning. I am saying that I don’t think the question can be answered “by reason alone”, because time is, a priori, just a construct to help us order events. If time had always been conceived as an index for listing, there would be no dispute. Any system that used time merely for ordering would be incoherent, or at least internally inconsistent. As I’ve said, you may disagree with certain conceptions of physics, but they are at least logically consistent. Thus they have to be disproven empirically, not deductively.

I’m fine with admitting that, while Aquinas’s premise makes sense, it cannot be proven from other more obvious axioms.

 

[oldcelt]

I’m fine with admitting that, while Aquinas’s premise makes sense, it cannot be proven from other more obvious axioms.

Maybe god only created the universe…no sentient beings. It’s worth consideration at least.

 

[john_doran]

I hate to be “that guy” but I have to disagree here. If you develop, say, the theory of integers axiomatically, the negative numbers arise as a consequence of the axioms of order and the axiom of additive inverses (opposites). So from this perspective, -1 exists because 1 does, -2 exists because 2 does, and so forth. Furthermore, 2 exists because 1+1 has to be well-defined, so both -1 and -2 exist because 1 exists.

on no mathematical theory do any of the numbers of a set actually cause any of the others to exist. what you are describing is not a set of existential relations (e.g. as between fathers and sons), but rather logical relations.

the cosmological argument is an argument about what must be true about concrete objects that exist in existential relations; not about the (many) logical relations that may exist between abstract objects.

Oreoracle:

Now we don’t actually talk about contingencies in math, but only logical implication. So I think our main disagreement is the assumption that modality and contingencies have to come into play at all. Spacetime is conceived as a 4-dimensional abstract space. Saying that the past has to exist for the future’s sake is like saying that a region in another space, say a 2D plane, has to exist for the sake of the rest of the plane. It really isn’t immediately obvious what you mean, let alone that the assertion is true.

i believe that our main disagreement (if there is one) concerns an (i.e. your) elision of existential and logical relations, and concrete and abstract objects: spacetime as it exists in our universe is not an abstract space, but a contingent concrete space, and the objects that inhabit that space are themselves all contingent concrete objects. and all of them require a (causal) explanation of their existential relations. this includes the existential and causal relations of the parts of spacetime to one another: witness the horizon problem of current cosmological theory.

a 4 dimensional manifold taken as the subject of mathematical inquiry and manipulation, on the other hand, is an abstract object that exists necessarily, no part of which stands in any causal relation to any other part (or any other abstract object).

so. while (4 dimensional?) spacetime requires a causal explanation for its (contingent) existence, 4 dimensional manifolds (arguably) do not.

 

[Tomdstone]

on no mathematical theory do any of the numbers of a set actually cause any of the others to exist. what you are describing is not a set of existential relations (e.g. as between fathers and sons), but rather logical relations.

the cosmological argument is an argument about what must be true about concrete objects that exist in existential relations; not about the (many) logical relations that may exist between abstract objects.

i believe that our main disagreement (if there is one) concerns an (i.e. your) elision of existential and logical relations, and concrete and abstract objects: spacetime as it exists in our universe is not an abstract space, but a contingent concrete space, and the objects that inhabit that space are themselves all contingent concrete objects. and all of them require a (causal) explanation of their existential relations. this includes the existential and causal relations of the parts of spacetime to one another: witness the horizon problem of current cosmological theory.

a 4 dimensional manifold taken as the subject of mathematical inquiry and manipulation, on the other hand, is an abstract object that exists necessarily, no part of which stands in any causal relation to any other part (or any other abstract object).

so. while (4 dimensional?) spacetime requires a causal explanation for its (contingent) existence, 4 dimensional manifolds (arguably) do not.

What is your definition of cause?

 

[john_doran]

What is your definition of cause?

the form of causation to which i’m referring is efficient causation (in thomistic terms): that which is the proximate cause of a specific effect.

 

[Tomdstone]

the form of causation to which i’m referring is efficient causation (in thomistic terms): that which is the proximate cause of a specific effect.

You are using the same word cause to define cause. Can anyone give a definition of cause?

 

[ccmnxc]

You are using the same word cause to define cause. Can anyone give a definition of cause?

I am not John Doran, but I would guess some think akin to “something that actualizes another’s potential” to use more Thomistic terminology.

 

[Tomdstone]

I am not John Doran, but I would guess some think akin to “something that actualizes another’s potential” to use more Thomistic terminology.

Sounds something like a catalyst.

 

[john_doran]

You are using the same word cause to define cause. Can anyone give a definition of cause?

well, i could use one or more synonyms, such as “generate”, “produce”, “bring about”, “create”, etc., but, in the current context, i’m not sure that those terms provide any greater clarity.

what is it about “cause” (or my definition of it) that you find opaque?

 

[Peter_Plato]

What is your definition of cause?

The sufficient (though not necessary) and (usually) observable condition(s) to bring about a manifest physical occurrence or event.

This does not exclude the possibility that other causes may bring about the same physical effect, but that if particular conditions exist, then the physical effect (as far as we can tell) comes about in the observable universe.