Yes, I do believe that actually infinite quantities exist. For example, I believe that at every point in time an infinite number of events occur. This is an example of actual (or completed) infinity because it's the kind of infinity that does not last forever. Also, I believe that every finite period of time is infinitely divisible which means that it consists of an infinite number of moments. This too is an example of actual infinity.

On paradoxes, for example, Zeno’s paradoxes, there is a very simple solution if you take the view that the actually infinite is impossible:

- Assume time is continuous
- Examine any system over a fixed time period
- Then the system goes through an actually infinite number of states in a finite period
- Actually infinite is impossible so reductio ad absurdum time is discrete
- Time is discrete so Archilles only has to cover a finite number of steps to reach the tortoise — Devans99

The system does not go through an actually infinite number of states in a FINITE period of time. That period of time is INFINITE but we SAY that it is finite because we are only aware of a finite portion of it.

↪Magnus Anderson What defines an event? You have made event sound as though everything came to a stop between periods of “duration”.

Time, as I see it, is a method of measuring motion. Motion does not cease.

“Events” are really just points of a duration which impress more so upon memory. — raza

Motion is one of those frequently abused terms. Motion simply means change in position. No concept of position, no concept of motion. It's a high-level concept.

Time is more fundamental than motion. Time is simply one of the properties of objects of experience. Time does not imply motion. Just because there is time does not mean there is motion. You need change, i.e. difference between points in time, in order to speak of motion. And not any kind of change but change in position.

This seems to imply that time could be constructed from events of zero duration, which is about as sensible as space being composed of points of zero extension. I fail to see the logic in either assertion. — prothero

What does it mean to say that a point has no size? Does it mean that it has zero size i.e. that it does not exist? Or does it perhaps mean that it has no specific size?

Or is an individual occasion like the present moment, of zero duration, therefore not actually existent?

"No duration" does not mean non-existent. Time can be defined as the number of events between two events. Events themselves have no duration. (Not necessarily related to Whitehead. Personally, I would stay away from Whitehead and most of the so-called process philosophers since they do nothing but introduce noise.)

You can easily "fix" induction by turning it into a deductive argument such as follows:

1. All observed As are Bs
2. The future mimics the past
3. Therefore, all As in the future will also be Bs

Note that this is still a form of induction. I am saying it is not induction to make Banno and others, such as Janus and that autistic boy who calls himself chester-something, happy. When they use words in a formally precise manner, i.e. when their words align with the manner they are defined by Google, Wikipedia and other established sources, they are happy. Nothing makes them happier than using words in a formally precise manner. So let them have their happiness, let us concede that the above argument is not a form of inductive argument but a form of deductive argument. We lose nothing by doing so, that's for certain. But despite our best efforts, despite our concession, the above argument won't make Banno happy. He will argue, desperately, that the second premise is wrong and that the entire argument falls apart because of it. The premise is wrong, he will claim, because there are moments in our past that were not doing their best to mimic the moments in our past that preceded them. Apparently, not every point in time mimics the set of points in time that preceded it. This, my friends, is supposedly an argument against the second premise. Of course, Banno is full of shit because Banno, like pretty much every single human being on planet Earth, routinely makes decisions by taking this premise for granted. Otherwise, Banno would never be able to eat his breakfast and make love to his girlfriend. He wouldn't be able to so much as compose a forum post. Nothing can function without induction. So an attack on induction is an attack on intelligence itself. What we have here is a form of schizm. Banno says one thing but does another thing. He says induction is wrong but his actions say it's not wrong. So what exactly is wrong? Is it induction? or is it something with Banno?

The future does not have to mimic the past all the time. It is enough that it mimics the past most of the time. Exceptions do not disprove the rule.

Yep. It implies that induction is invalid. — Banno

Not the answer that I was expecting. But it does justify every single post I wrote in response to your claim. For I was right: you do think that the fact that induction is deductively invalid (i.e. not truth-preserving) means that there is something wrong with it.

I was expecting you are going to say something along the lines that induction does not adequately represent the manner in which we naturally reason. For reasoning is, as you claim, something that cannot be captured by words, something that forever transcends them. To which I would have responded with something along the lines that every model of reality is grounded in a subset of reality and is therefore always a good candidate for being a simplification of the said reality. So there should be nothing strange when we discover that our models are not perfectly accurate; for in most instances, they were not even expected to be perfect.

We had agreed that induction was (deductively) invalid. You didn't see that as an issue. — Banno

What's the relevance of stating the obvious fact that induction is not a deductively valid method?

What's the relevance of stating that induction is not truth preserving?

What's the relevance of stating that the following argument . . .

1. All observed As are Bs
2. Therefore, all As are Bs

. . .is such that its premise can be true and its conclusion still be false?

Noone disagrees with that.
Noone disagreed with that.

The subject has been the relevance of making such a statement.
Does it imply that there is something wrong with induction?
What does it imply?
Does it imply anything at all?

It's not a method; its not algorithmic. It's just seeing the pattern. — Banno

What you're saying, probably without realizing it, is that pattern recognition is an entirely random process.

But for fun, do you believe the tower is 324m tall yourself? Just tell me yes or no! And how.

And when during the day is it so exactly 324m tall? Are we now talking about the hot Eiffel tower that is 15cm taller in the heat of the midday sun, or the one that is 15cm shorter when night falls and its cools down?

Do we in fact now have two Eiffel towers. Or a vast ensemble - one for every nanometre of variation.

Oh goodness, how do we measure the height as it expands/contracts unevenly as the sun hits only one side. It can bend 18cm away from the sun. So which is its true height now - the actual distance to the ground or the full distance if it were standing up straight?

Of course, Banno the tourist guide doesn't need to care. He just reads his facts off Wiki. But Banno the scientist might want to rely on some more careful process of inquiry. A hand-waving approach always makes for poor philosophy. — apokrisis

Apo's having a field day with Banno. Made me giggle.

Gender to me is similar to state of a system, like gas, liquid, solid in water. — bahman

The state of a system is simply the set of values its variables are assuming. If the system has two variables such as height and gender then its state would be something like "190cm, male" or "170cm, female". Gender need not be a state. The same applies to consciousness.

Because the state of system is a function of the properties of its parts. — bahman

There is a correlation between height and gender. The taller the person, the more likely the person is a man. And vice versa. That's an example of a very simple system. You have two variables that are related to each other in a specific way. One of the variables is quantitative (height) the other is qualitative (gender.) So how is it possible for a quality such as male/female to arise from quantity?

I believe that there could be a correlation between different variables depending on state of system. I however don't recall any physical example. Correlation is the result of interaction. It however cannot leads to consciousness. — bahman

The question is: why is it impossible for the brain to be conscious if atoms and molecules are not conscious?

↪Magnus Anderson I cannot teach you how to conceptualize a problem. Unfortunately, there is no training for such a skill I'm any educational courses other that art. So you either have to train yourself through hard work or be at the mercy of others to tell you the answers for the rest of your life. I can only suggest that you try to conceptualize the problem in your mind. — Rich

Alright, so you do not want to define what it means for life to be starting and stopping which means the discussion is over and it's your choice. No problem.

Brain cannot become conscious if atoms and molecules are not conscious. — bahman

So there can be no correlation between variables unless variables are of the same type?

You are just START/STOP which is the nature of the Paradox and my very first question to you. Do you believe feel like your life is coming stopping and going? This is rhetorical. I don't need an answer. — Rich

You need to define what it means for life to be starting and stopping.

↪Magnus Anderson How something can be at rest all the time and moving? Hmm. I'll try it out later today and see if I can teleport myself somehow. — Rich

The arrow is resting AT every instant but it is not resting BETWEEN instants.

Even the idea that the arrow is resting at every instant is strange. Rest is something that takes place BETWEEN instants.

Well apparently you are fine with this so nothing is going to convince you otherwise. For me, it is strange and doesn't coincide with every day experience. — Rich

Maybe you should try to explain why you find it counter-intutive?

If a moment is without duration, exactly how many moments does it take to make one second? The stuff that the clock is measuring. That science it's measuring. — Rich

There can be any number of moments within a second. Bergson claims that time is indivisible. I claim that time is not only divisible but also infinitely divisible.

If you understand the paradox, then you understand why moments and spatiality yields it. — Rich

I understand the paradox. The paradox is a word game. In other words, there is no paradox. If an object is at rest at every point in time, it does not follow that it is not moving. The solution to the "paradox" is to understand what the word "motion" means.

Well then you have an expected paradox. It is an outgrowth of your ontology which brings us right back to my first question, if you think you are moments then do you feel each moment starting and stopping. — Rich

You will have to define what it means for a moment to "start and stop". Moments do not start and stop, they simply follow one after another. For a moment to start and stop, it must have a duration. But moments are durationless by definition.

If the moments are continuous there are no moments. That was Bergson's point. This is what Zeno's paradoxes are all about. When you do away with points (the arrow never stands still) the paradoxes vanish. Whenever there are paradoxes there are problems with the ontology. Moments are the problem. Spacialization of time creates these paradoxes. — Rich

Right. Bergson thought that Zeno's paradox of the arrow demonstrates that time is not made out of points. But I don't agree. Zeno's argument is just a word game. Motion is a difference in position between two points in time. That's what the word means. The fact that we can say the object is at rest at every point in time does not mean its position is not different at different points in time.

I believe meditation is a technique for focusing ones mind, no? I suppose it could be considered a denial that unfocused use of the mind delivers the truth, or perhaps there is the denial of the ascetic who runs away to live on a mountaintop. There's good and bad denial right. Denial of a lie could be pretty important. — Perplexed

Meditation is a tool that we use to reduce mental stimulation. So yes, by eliminating distracting impulses, it can help us focus. It's a very useful too but in the case of those who consider themselves mystics it is a tool used to simplify their process of thinking to a degree that is quite astonishing.

Are you sure it is not just the conception of time as only a succession of moments that he is opposed to? As this is a very simplistic and linear way of describing it. — Perplexed

No, he says that such a conception falsifies the reality of time.

Time is exactly as you are experiencing it. Is time starting and stopping for you as a succession of moments? Mine is continuous. — Rich

What does it mean for time to be "starting and stopping"? The point is that my past is a succession of moments. You have one moment coming after another moment.

Bergson opposes spacialization of time. If you don't understand what I just said, you have to either think about it or read about it. — Rich

Or you can simply explain it to me so that I can be enlightened.

"Spatialized time" is precisely the kind of time that I am talking about i.e. the kind that can be thought of as a succession of moments. For Bergson, everything that is divisible is considered "spatial".

↪Magnus Anderson What you are describing is not mysticism but denial. i.e. hiding from valid distinctions. The trouble is that a great deal of discrimination takes place without us being aware. — Perplexed

That's right. What I am describing is denial. The thing is that mysticism in general is about denial. That's simply what it is. Why is it that meditation is the holy grail of mysticism? Is it not because meditation is a form of denial? It is a return to a more primitive way of thinking that is known as intuition.

It seems to me that Bergson takes a phenomenological approach to time so he would be interested in discussing distinctions as they appear rather then by comparative measurements of different observers via the objectification of space-time. — Perplexed

Bergson is opposed to any conception of time as a succession of moments.

Observation. This guy thinks that time is something other than a sequence of moments. When you ask him what this "something other" is, he tells you that it is something that cannot be described using words.

I think that Bergson, like every other mystic, is against awareness. He hates it. He wants to go back to being blind because he finds reality to be too painful. Normally, people want to be aware and that means they want to discriminate; they want to see separate and distinct elements where previously only a unity was seen. But when reality becomes too painful, the opposite process becomes fashionable.

You are not saying anything relevant.

I was responding to Banno.

Here's the first paragraph form the Shorter Rutledge Encyclopedia of Philosophy, inductive inference.

According to a long tradition, an inductive inference is an inference from a premise of the form "all observed A are B" to a conclusion of the form "All A are B". Such inferences are not deductively valid, that is, even if the premise is true it is possible that the conclusion is false, since unobserved A's may differ from observed ones.

Now, does anyone here think that this is wrong? Surely at least we have agreement on this. — Banno

Basically, the encyclopedia is saying that inductive arguments have the following form:

1. All observed As are Bs
2. Therefore, all As are Bs

You must be smarter than this encyclopedia because it says nothing about the conclusion being "merely" probable. Right?

I generalized this to:

1. Some As are Bs
2. Therefore, all As are Bs

The premise is no longer restricted to observations.

Now I have to ask: what exactly is your point?

You problem is that you just don't know what you are talking about.
If you don't find out, people are just going to laugh at you. — charleton

Tsk. You're being a fool.

Rubbish.
This is just poor logic. A broken deduction, pretending to be something. Nothing to do with induction at all.


An inductive argument is more like X happens after Y all the time. So maybe X is caused by Y.
Post hoc ergo propter hoc is only fallacious if it is wrong. — charleton

You're being pedantic. It's what people to do in order to feel superior (when they are actually not.) See Banno for example.

Here's an amendment to my argument:

1. Some Ps are Qs (e.g. all of the observed ones)
2. Therefore, all Ps are Qs (in my opinion, so yeah, maybe I'm wrong, it's not certain)

Basically, what we have here is people who do not think ob their own but parrot. So when someone comes along and does not repeat the popular narrative word-by-word he's subjected to pathetic pedantry.

↪bahman The only experience that I have had that is fully emergent is a new idea or epiphany. This would represent growth of the mind. — Rich

Depending on how you define the concept of emergence, you can say that pretty much any event is emergent. This is to emphasize that the concept of emergence must be clearly defined.

What is emergent if not that which cannot be predicted by some specific model of reality? Emergence is a relation between an event and a model of reality. There is no emergence outside of this relation. You cannot say that an event is unpredictable on its own, in the sense that it cannot be predicted by any kind of model reality, because it is possible to predict any kind of event through sheer luck. You can predict the entire universe through luck. Instead, what you can say is that an event cannot be predicted by particular model of reality. If your model of reality says that all people are bald then your model of reality cannot predict people who are not bald. That's the same exact way in which ideas can be emergent -- by not being predictable by some particular model of reality.

"Emergence" is a complicated topic (in part because there is no common view of what it is). — SophistiCat

The word "emergent" simply means "arising unexpectedly". It refers to an observation that contradicts our model of reality. It refers to an observation that is unpredictable in the sense that it cannot be predicted with our model of reality. If your model of reality says that every swan is white then a black swan would be considered emergent because your model cannot predict it. Very simple. Unfortunately, some people are confused and so they want to make everything unnecessarily complicated and that under the guise of profound complexity.

Constraint is, as I understand it, simply a limit to what is possible. The opposite of it is freedom.
— Magnus Anderson

Yep. Simple really.

The world we live in, in other words, is stable enough to make induction good at making predictions. This makes perfect sense.
— Magnus Anderson

Yep. You got it again. — apokrisis

Alright. That might be the case. But I think that you're saying a bit more than that. I am not sure. Your insistence that you're not interested in narrow subjects such as logic, epistemology, conceptual analysis, etc suggests to me that your interest lies in devising a theory of everything i.e. a theory that explains how everything in the universe works. And I belive that's what you mean when you talk about metaphysics. Metaphysics = a theory of how everything works. You also talk about how your metaphysics is not reductionistic but instead holistic. How do we interpret this? I interpret it to mean that you are in fact a monist. A dialectical monist. Yin-yang philosophy. You want to unite the opposites. Uncontrolled interaction is not enough. There must be a central force, some kind of God, controlling the antagonism. Hence your focus on trichotomies, triadic conceptual structures. Very reminiscent of Aristotle's theory of golden mean. You have a center and two extremes. Left, middle and right. So in the case of order~chaos dichotomy, you want to subsume the two to a third category which is basically that of order (which explains why you make a distinction between constraints and patterns or regularities which you say are merely observable.) So you're acknowledging the dualism and then reducing it to monism under the guise of trialism. There is chaos but this chaos is subsumed to order. I think that Perice said something along the lines that there is no absolute certainty but that there is absolute truth. That would make him a very clever absolutist in my book. But is he? I am not sure. Further investigation required.

↪Magnus Anderson

No I can't comprehend your eccentric account of the rules of reason. — Janus

I don't think that's eccentric. I think that what they teach you in school is eccentric. The rules of reasoning, or inference, is a very intuitive idea.

You know what a mathematical function is, right? It's a relation between two sets where every element from the first set is associated with exactly one element from the second set. Now, I think that this is too strict. Instead of thinking in terms of mathematical functions, I tend to think in terms of partial functions, since these are more relaxed; or better yet, in terms of relations. But even these are kind of strict . . . The basic idea is that you have two sets which may or may not be related to each other. It's sort of like a system except we're not talking about variables, parameters, etc. Well, we can, if you want; we can say we have two variables or two parameters but no more and no less than that. That's what every logical argument fundamentally is. Can we agree on that? We have a set of premises on one side and a set of conclusions on the other side. And we also have connections, or associations, between the two sets (which may also be absent; again, we love general concepts because they give us more freedom.) We need some basic rules to limit what kind of premises and what kind of conclusions are permitted. Once these are set, we need to determine what kind of associations are permitted and/or expected. This is where "the rules of reasoning" kick in. This is what determines whether any given argument is valid or not. No notion of consistency whatsoever. Just associations and rules that determine what kind of associations are legal and what kinds are not. You can't just associate any kind of premise with any kind of conclusion, right? Reasoning is a process that works according to a set of rules. So if you note that "All men are mortal" and that "John is mortal" you cannot conclude that "John is a man". You can't associate these two premises with that conclusion. It's against the rules.

↪Magnus Anderson

I would have to first understand what you mean (and you haven't explained it in any way that makes it all clear to me) before I could agree or argue against it. So, best leave it, I guess. :s — Janus

You don't understand what it means for a logical argument to abide by the rules of reasoning?

"Truth-preservation" is really just consistency, which means not having premises which contradict one another or the conclusion. The validity of deductive arguments is independent of the truth of premises, maybe that's where you're becoming confused; I don't know. — Janus

Maybe I'm not the one who's getting confused ;) I understand very well what truth-preservation is. My point is that it's a concept that is 1) narrow, 2) complicated and 3) deceptive. Don't tell me it's not complicated. It is. There is a much simpler and a much better way to define logical validity. Validity in general, outside of logic, means "the state of being legally acceptable". We can define logical validity in the same exact way, as the state of being legally acceptable. This means that a logical argument is one that abides by the rules of reasoning (whatever they are.) This is broad enough to cover all the different types of validity (not only truth-preservation), it is not unnecessarily complicated and it is not deceptive. It fits every single need perfectly. If we need specific concepts, we can use those too, but we don't have to rely on them all the time. They are, in many situations, inappropriate. Again, that's how I define the concept of validity and that's how I think validity should be defined. It's not how most people think. You don't have to accept it if you don't want to though you can argue against it.

I understand the problem. NOTHING, defined as nonexistence, is difficult to grasp. We're in the habit of or are confined to understanding in terms of attributes/properties which, by far, are positive in nature. What I mean is we need some attributes that are attached to a concept or object and only then do we even begin to understand them. However, unlike most objects (mental/physical) NOTHING is defined in the negative. In fact it is the ultimate negative - the absence of everything. In a way we could say "There's NOTHING to understand." — TheMadFool

Negative concepts are defined in relation to one's expectations. The word "nothing" means nothing other than "absence of that which was expected". It must not be taken literally. If I open a box and find "nothing" in it what this means is that what I found in it is not one of those things I was expecting to find. In the same way, non-existence means nothing other than "the kind of existence I was not expecting". That's all it means. I don't think this is difficult to grasp.

This probably doesn't make sense give what I've said above but I have commented on how math can make sense of NOTHING by equating it to zero. — TheMadFool

Zero means "no number of objects of expected type". I say "there are zero apples in front of me" to mean that whatever I see in front of me (e.g. one computer monitor) is not a number of apples equal to or greater than one.

I think "nothing", the word, is quite different from other words. Other words have physical/mental referents but "nothing", by definition, lacks any referent. — TheMadFool

"Nothing" refers to that which contradicts our expectations. "There is nothing on the screen" means the screen does not contain what we define to be "something". For example, I might be expecting to see a picture, a video, a text . . . but none of these are present; therefore, nothing is on the screen.

Any thing can exist only once — Daniel

This depends on how you define the concept that is represented by the word "thing". If it's too specific, the object will exist for a very short period of time (i.e. once.) If it's too generic, the object will exist for a very long period of time (e.g. forever.) Depending on how you define your words, you can say that everything exists only once or that everything exists for all times.

which happens when it becomes; after becoming, it cannot be anymore, for it is subject to change, and necessarily "becomes" something else. Before becoming, it certainly is not the thing that it will be. So, it is as if something exists (potentially) up to the point it becomes an actuality; after that, it "becomes" literally nothing, for the memory of it is totally different to the thing itself. — Daniel

Your concept of "thing" goes through three stages: potentiality, actuality and death. Again, this is a matter of definition. It's not an empirical matter.

I am going to return to something @apokrisis said in response to me on page 8.

Constraints generate regular patterns in a probabilistic fashion. So that is how science understands physical systems. And it is how we would speak of nature if we take a systems view where we grant generality a reality as a species of cause.

So again, it is simply a reflection that I am arguing from a consistent metaphysical basis. It is how reality would be understood if you believe in an Aristotelean four causes analysis of substantial being. — apokrisis

I am struggling to understand what you mean when you say "constraint". The way I understand it, and the only way I can sensibly interpret it, is that the word "constraint" means nothing other than pattern, regularity, law, order, etc. However, as it appears, that's not what you mean by the word. Instead, you mean something . . . else. What this else is I don't know. I think it has something to do with "downward causation". Which is another obscure term that is often thrown around. Perhaps I should start a new thread dedicated to this concept? Just to see if someone else can elucidate it for me. Or maybe someone here can help me with it?

Constraint is, as I understand it, simply a limit to what is possible. The opposite of it is freedom. It is that which allows us to discriminate between those possibilities that are more likely and those that are less likely. It's a very simple concept. But your exposition is generally quite obscure and complicated (as is that of Charles Sanders Peirce.) This suggests to me that we might not be on the same page.

You say that "history builds constraints on free possibility". The only sensible manner in which I can interpret this statement is in the sense that the world we live in is relatively constant. The universe is flux, i.e. it is constantly changing, but it is doing so at a rate that is sufficiently low to make induction successful in most cases. The world we live in, in other words, is stable enough to make induction good at making predictions. This makes perfect sense. But the fact that you do not express yourself in such simple terms suggests to me that your point is a different one. In fact, it suggests to me that you find this type of process philosophy, the one championed by Heraclitus and Nietzsche, deficient in certain regards.

That's not what I think. Just because the premises are true, or can be true, does not mean the argument is valid. "True xor true = true" is not valid even though its premises and conclusion are all logically true and equal to true.