Circular Time

Productivity Member Writing
41

I’m not sure what you mean by ‘refer to reality’ in this context; the whole point of pure mathematics is that it _doesnt_ refer to reality directly - it primarily studies abstractions and generalisations that are divorced from any particular existents in the world. The entirity of abstract algebra for instance has no ‘referent in reality’, since the objects of study are purely abstract entities such as rings and groups (which are themselves defined in terms of sets). Things like power sets are perfectly well defined in mathematics, and although they dont directly refer to any real world existent, neither do many other important mathematical concepts which I assume you accept. What do imaginary numbers ‘refer to in reality’? What about constuctions in non-euclidlean geometry (before Einstein)?

I’m also not sure precisely what role you want induction to play in mathematics. Induction obviously cant be used for things such as proofs, so I assume you mean it that it should have a role when it comes to forming mathematical abstractions?

They say that all mathematical concepts are sets, and that “any mathematical expression” can be used in the process of forming a set. This is circular, since mathematical expressions were what they were supposed to be defining in the first place (i.e., they need to define what “set” means without using the concept of “set” in the definition.))

No, sets are undefined. Every formal system needs to be built upon undefined terms, simpy because if you weren’t prepared to have undefined terms, then everything would be defined in terms of everything else and the system as a whole would be illogically circular. You’ve got to stop your definitions somewhere and take some terms to be primary and undefined, and in modern mathematics sets (rather than numbers) have been chosen to play this part. This isn’t a new thing; in classical euclidean geometry the basic elements such as ‘points’ and ‘lines’ were never defined.

42

I’m not sure what you mean by ‘refer to reality’ in this context; the whole point of pure mathematics is that it _doesnt_ refer to reality directly - it primarily studies abstractions and generalisations that are divorced from any particular existents in the world. The entirity of abstract algebra for instance has no ‘referent in reality’, since the objects of study are purely abstract entities such as rings and groups (which are themselves defined in terms of sets).

We have some very different premises here. According to Objectivism, an abstraction must be reducible to existents in order to be an abstraction. For example, the concept “furniture” is an abstraction. It is formed by noting similarities and differences amongst real-world objects and thereby does refer to reality. It is not divorced from reality.

Things like power sets are perfectly well defined in mathematics

The problem is that the field of mathematics has not been philosophically validated, just as the field of general epistemology was not validated until Ayn Rand developed Objectivist epistemology. Therefore, there are no concepts that are well defined in mathematics. “Well defined” has to mean “refer to reality.” No other meaning is sensible. Think of the “identification” part of “non-contradictory identification.” Non-contradictoryness, so to speak, is not enough. You have to have identification. That means you need to attach real-world meanings to all of your concepts, including mathematical ones.

No, sets are undefined. Every formal system needs to be built upon undefined terms, simpy because if you weren’t prepared to have undefined terms, then everything would be defined in terms of everything else and the system as a whole would be illogically circular.

I really recommend that you study Dr. Peikoff’s book, “Objectivism–The Philosophy of Ayn Rand.” You don’t need undefined terms in order to avoid circularity. What you need is a base of ostensively defined terms.

43

Is it strictly a scientific issue to insist that every existent possess a finite size and time? Or is that near the edges of what philosophy can say on the subject?

I don’t see why one should assume that either philosophy or science would come to that conclusion. (For the record, I’m the author of the essay being discussed here.) Via philosophy, we know that all existents of consciousness (e.g., emotions) do not possess any size at all. With regard to time, the ultimate constituents of the universe would have to be eternal, and thus would not be temporal or possess an age. The universe, being all that exists, similarly must be eternal: the universe (i.e., existence) has always existed, since nothing can exist before existence.

It seems rationalistic to claim, on one hand, that existence necessarily implies identity, but that the identity itself need need not consist of anything we really know for sure – maybe size, maybe time… but maybe something else entirely.

I don’t see why the universe as a whole has to be able to be ascribed measurable, quantifiable attributes for it to have identity. It’s not rationalistic to say that the universe has identity, since every piece of knowledge consists in knowing the identity of the universe (i.e., the universe), and I don’t see how such knowledge ever assumes that the universe as a whole has a measurable, quantifiable attribute. I’m not saying that the universe is this thing with an identity that we are ignorant of; I’m saying that the universe has identity, the objects of our knowledge consist in it, and the universe as a whole does not have size or age (and probably lacks every other measurable, quantifiable attribute as well, although this is more debatable and not explicitly argued for in my essay).

Can’t one say at least that size and time are necessary qualities of existents? Even if future knowledge should amend our contextual understanding of these concepts, the evidence for the existence of these qualities, at least, seems universal.

Again, many things possess a size and an age, but it’s simply not the case that everything does. So, my question is: why assume that the universe has either attribute? What would it mean to say that, for example, the universe has only existed for a specific time, and thus came into existence at one point? The universe can’t “come into existence”; it is existence.

The main question of my essay centers around the attributes of size and age, and one must have a specific argument to show that the universe possesses these attributes. The claim that such attributes are universal simply isn’t true, and does not address my positive arguments that operate in the context of knowledge that size and age are not universal attributes. One must examine the nature of the existent in question to see if it has a size or an age, rather than assume that such attributes must be present. With regard to the universe, I’m questioning a widespread (and very understandable) assumption that it does in fact have a size, so the mere fact that it is an assumption is not a sufficient objection.

Another question I have with the above quote is that it is used specifically in the essay to refer to the universe as a whole. As such, it is a confusing illustration, because the object of its point, is the only exception to the illustration…

It really isn’t. But even if it was, I did try to draw out my argument (in my essay) for why it is the case that the universe cannot possess a size or an age. I did not simply make a question-begging exception to a universal law of reality; I made an argument, based on the nature of size, time, and the universe, that the latter is incompatible with the other two. If it is objected that size and time are universal and thus must apply to the universe, then – if anything – it is this objection (rather than my argument) which begs the question.

One could probably well say that the universe is a sui generis “exception” in the following sense: as far as I can tell, it is only in the context of the universe as a whole that one has something which lacks a size, while still having parts that do possess a size. I think (although am not entirely sure) that this is a phenomenon unique to the universe. But, either way, uniqueness is not proof of falsehood.

If anyone has any further questions on and/or objections to my essay, I’d be more than happy to respond.

– Alex

44

With regard to time, the ultimate constituents of the universe would have to be eternal, and thus would not be temporal or possess an age.

Hi Alex.

How do you reach this conclusion?

This would rule out an alternative such as the idea that these little things may interact with each other in such a way as to create new ones or destroy old ones.

The universe, as a whole, may be eternal, but I don’t see why that must necessitate immortality for its ultimate constituents.

45

Hi Alex.

How do you reach this conclusion?

This would rule out an alternative such as the idea that these little things may interact with each other in such a way as to create new ones or destroy old ones. 

The universe, as a whole, may be eternal, but I don’t see why that must necessitate immortality for its ultimate constituents.

Create new ones? Out of what? It cannot be out of nothing. And neither can the constituents be “destroyed” (i.e., become nothing). Creation implies creation with something. If they are created and destroyed they are not fundamental.

46

It’s not rationalistic to say that the universe has identity, since every piece of knowledge consists in knowing the identity of the universe (i.e., the universe), and I don’t see how such knowledge ever assumes that the universe as a whole has a measurable, quantifiable attribute.

Don’t forget that the Axiom of Existence and the Axiom/Law of Identity both refer to the same basic fact of reality, but from a different perspective or philosophical context.

This would rule out an alternative such as the idea that these little things may interact with each other in such a way as to create new ones or destroy old ones.

One of the implications of the fact that existence exists is the fact that existence is eternal. Another implication/corollary is the fact that there has to be eternal ultimate constituents. If there was some small constituent of the type that could be created or destroyed, then it would have to be the manifestation of a composition of even smaller constituents, since there can be no such thing as spontaneous generation or spontaneous disintegration. There has to be a “bottom” or “ultimate” layer of constituents which are eternal, in order for existence to be eternal, i.e., in order for it to be true that “existence exists.”

47

I don’t see why the universe as a whole has to be able to be ascribed measurable, quantifiable attributes for it to have identity. It’s not rationalistic to say that the universe has identity, since every piece of knowledge consists in knowing the identity of the universe (i.e., the universe), and I don’t see how such knowledge ever assumes that the universe as a whole has a measurable, quantifiable attribute.

I agree with that. Assuming by “universe” we mean the sum total of all that exists," I am not even sure what it would mean for philosophy to attribute characteristics to the universe. Attributes are inherent characteristics of entities, and the universe is not an entity in the primary sense of that term. But, even if we extend the notion of “entity” to include the universe – to be a “thing” – we cannot point to it and abstract away its attributes by observation.

In ITOE (p. 273) Ayn Rand mentions that we can only ascibe to the universe those “fundamentals that we can grasp about existence.” She ascribes to the universe only “identity” and being “finite,” not as characterisitics of the universe but as being inherent in existence, per se. Identity is not an attribute, and, as far as being finite, I think that Alex’s essay clarifies the use of “finite” in a precise manner.

However, with that said, there is nothing that I know of within philosophy which would mandate against science identifying what could be considered to be attributes of the universe. What we can say philosophically cannot be contradicted scientifically, but that which philosophy remains silent on, becomes a strictly scientific question.

48

Time being circular would require that the universe eventually collapse and then start back out the same way it did the last time. All evidence points to the universe not ever collapsing.

49

Time being circular would require that the universe eventually collapse and then start back out the same way it did the last time.  All evidence points to the universe not ever collapsing.

I disagree. I don’t see how one implies the other at all. If you want me to criticize your argument, you’ll have to elaborate and let me know what your argument is.

50

Perhaps I am resurrecting a dead horse here, but for those who assert the universe has no beginning, how do you justify an infinite regress of causes?

conan

51

Perhaps I am resurrecting a dead horse here, but for those who assert the universe has no beginning, how do you justify an infinite regress of causes?

conan

There is no “infinite regress of causes” to justify. The universe is all that exists, and causality presupposes that which exists. The universe, meaning existence, does not require a cause, and it cannot have a beginning. Nor can it have an end. Time, and causality, are within the universe.

52

Stephen,

I agree that “time and causality are within the universe”, but you cannot justify a begining-less universe based on a presuppositon you hold. First, it is impossible to prove a universal negative. Secondly, what you really have is a circular argument because you are using the the thing you are trying to prove (the universe is all there is) as proof of the thing.

Wathces are started (caused) and they can be stopped. So perhaps it is reasonable to consider the possibilty that there may be an infinite reality that is not a natural one. Time and causality are definately of the natural universe, but that in no way justifies an infinite regress of causes.

conan

53

An infinite regress of causes is not a problem. Causality indeed presupposes that which exists.

That which exists, exists - and, it exists as _some_thing - and, what it exists as determines how it acts.

The idea that “event X is caused” under the traditional system implies that “event Y, which is caused, caused event X.” But under Objectivism, “event X is caused” means, simply, that “entity Y exists and caused event X.” So under Objectivism, causation does not imply infinite regress; all it implies is the entity that acts in accordance with its nature.

Causality therefore does not imply the universe must have had a beginning, and it does not imply that it must not have had one either.

54

I agree that “time and causality are within the universe”, but you cannot justify a begining-less universe based on a presuppositon you hold.

What presupposition? There is no alternative to existence. Existence is all that there is.

First, it is impossible to prove a universal negative.

What “universal negative” are you referring to?

Secondly, what you really have is a circular argument because you are using the the thing you are trying to prove (the universe is all there is) as proof of the thing.

It is difficult to follow your logic here. Existence per se is not subject to ‘proof.’ That existence exists is the starting point, the base of all that follows. There is no alternative.

Wathces are started (caused) and they can be stopped.

Yes, we make reference to the nature of entities that exist to explain the causal actions of those entities.

So perhaps it is reasonable to consider the possibilty that there may be an infinite reality that is not a natural one.

I have no idea what those words could actually mean, but “reasonable” is the last word I would use to describe them.

Time and causality are definately of the natural universe, but that in no way justifies an infinite regress of causes.

Isn’t that where we started? In response to your question, I said:

“There is no “infinite regress of causes” to justify. The universe is all that exists, and causality presupposes that which exists. The universe, meaning existence, does not require a cause, and it cannot have a beginning. Nor can it have an end. Time, and causality, are within the universe.”

55

I recently came across this article by a Catholic writer about the “First Cause” argument that critical readers may find valuable:

The First Cause Argument

(I love how, at the end, the author says that if the logic behind the First Cause argument becomes “too tricky” to follow, the thing to do is to return to to one’s emotions – to the feeling that the universe as a whole requires a cause.)

56

… Time and causality are definately of the natural universe, but that in no way justifies an infinite regress of causes.

If you assume a beginning or “first cause”, what was before?

You are forced to assume that something came from nothing which is a logical impossibility.

Throwing in a “creator” at this point, to “solve the problem”, only adds a totally arbitrary assumption into the argument and still leaves the question, then from whence did this creator come? If you say, well, it always existed, then why don’t you have a metaphysical problem with that notion while you do have it for the universe?

Fred Weiss

57

Thanks everyone for your replies and livly discusssion.

Causality therefore does not imply the universe must have had a beginning, and it does not imply that it must not have had one either.

Exactly the point. To declare that ones beliefs/presuppositions is evidence of itself is circular.

We can however, argue/debate the reasons why we hold the position we do. I believe Mr. Weiss asked what casued the first cause, but that is paradoxial. A first cause by definition would be uncaused and not require a cause because it is not an effect. In reguards to an infinite regress of causes, Dr. Norm Geisler addresses this fairly well with his “Existenial Argument” (a variation of the cosmological argument).

1.Things exist.

  1. It is possible for those things to not exist.

  2. Whatever has the possibility of non existence, yet exists, has been caused to exist.

  3. Something cannot bring itself into existence since it must exist to bring itself into existence which is illogical.

  4. There cannot be an infinite number of causes to bring something into existence.

Because an infinite regression of causes ultimately has no initial cause which means there is no cause of existence.

  1. Since the universe exists, it must have a cause.

  2. Therefore, there must be an uncaused cause of all things.

The uncaused cause must be God.

For the most part this argument hinges on point 5. I think this can best be understood by imaging a chian hanging before you with no visible begining. Because each link is dependant on the existence of another, one can reasonably assume that the chain must be attached somewhere down the line. It is reasonable to assume that there must be something that make the existence of the most recent link possible. This argument at least holds the possibility of justification.

conan

58

Conan:

What your argument boils down to is: Since everything in the universe requires a causal explanation, the universe itself must also require a cause.

“The universe” means the sum of everything that exists. Whatever exists, it is part of the universe. There can be nothing which exists “outside” of the universe: Not to exist in the universe, means not to exist.

(When I hear people explain that God is “outside” of the universe, I always think to myself: You have no idea how right you are!)

“There must be an uncaused cause of all things,” is a self-contradictory statement. If God exists, then He is subsumed under all things and cannot be their cause. If not – well, then He can’t be much of anything at all, now can He? :dough:

The answer to all of these confusions is the axiom: Existence exists.

59

Kevin,

Thanks for your reply.

“The universe” means the sum of everything that exists.

What you are really saying is that matter is all that exist, which is what you are trying to prove in the first place. As I stated in my last post “To declare that ones beliefs/presuppositions is evidence of itself is circular.” That does not mean you are wrong, only that your argument is invalid.

“There must be an uncaused cause of all things,” is a self-contradictory statement. If God exists, then He is subsumed under all things and cannot be their cause. If not – well, then He can’t be much of anything at all, now can He? :dough:

I am not sure what to make of this. It does not make much sense.

conan

60

Conan,

You hold the premise that any material thing that exists requires a creator, I gather. Why? What’s the rationale for that premise?

This confuses the metaphysically given with the created. The two categories are not equivalent. It also confuses creating things by way of using existing resources with creating things ex nihilo.

Also, if every material thing requires a creator, then why wouldn’t non-material existents require a creator?

By pointing out contradictions in your assertions, we are aiming to show that the assertion is not well formed and hence is not an assertion at all. That’s not the same thing as us assuming that which we are trying to prove. We merely point out that assertions must be sensible, i.e., meaningful, to be actual assertions.

“Creating something ex nihilo” really is just a string a words that do not come together to form a bona fide assertion. “Ex nihilo” by itself (“out of nothing”) in this context is meaningless. It is unfathomable.

If you say it is a void, but that God also exists, then it’s not really a void. God has to have some form of some kind. And there would be no reason to assume that everything requires a creator except the Creator. That would be just an arbitrary assumption.

If you say it’s just a theory for our consideration, then it’s an arbitrary theory that should be dismissed out of hand, since it is based on an arbitrary assumption.

Adrian