I think claiming belief and not knowledge is paradoxical. The claim to 'faith' is, to me, an indication of dishonesty or delusion. — AmadeusD

Well, I'm inclined to agree with you at least this far, that "I believe that p and that p is false" is a contradiction. "I believe that p and that p might be false" is not a flat-out contradiction, and could be described as paradoxical. "I believe that p and that p cannot be known, even though p is capable of truth and falsity." is extremely odd, but, for someone who believes on faith, comprehensible.
The resolution is a bit complication. When I say "I know that p", I am endorsing p as true. When I say "AmadeusD believes that p", I am reporting that AmadeusD endorses p as true. I am not asserting that p is true or false. When I say "AmadeusD knows that p" I am reporting that AmadeusD endorses p and endorsing p myself. When I say "AmadeusD thinks that p" I am reporting that AmadeusD endorses p; but I am endorsing p as false.
It's a bit of a side-issue, but it's the only way I can make sense of the "phenomena".

to me, delusion implies that someone has simply formed a conclusion without adequately assessing the relevant states of affairs. — AmadeusD

That seems a reasonable idea. Maybe a bit harsh - people can be misled even if they do their level best to check things out properly.

I think it would be productive for this thread if either you or anyone gives the most compelling case just why they cannot be both at the same time. Even if one doesn't personally agree with the argument. — ssu

Thanks for the invitation. I can try. But as long as people think that the search for free will is the search for an uncaused cause or a search for indeterminacy, I doubt that anyone will be interested.

The basics, which I confess I though were universally known are that actions performed by people require for their explanation purposes, values and reasons. Values cannot be recognized in standard scientific determinism, because of the fact/value distinction. Purposes require orientation to a future state, which clearly cannot be the cause of action (in the standard sense of cause). Reasons are easily confused with causes, but they justify actions by linking the aim, purpose, ambition, goal or target of action to what is to be done (this is sometimes referred to as the practical syllogism) which is a form of explanation that has no role in causal determinism.

All of this is at least over-simplified and is possibly wrong. But unless this agenda is discussed, we cannot even articulate the difference between what people do and what happens in the inanimate world, never mind decide whether one is compatible with the other.

Forgive me if I've seem short-tempered, but I've been looking for a chance to put this on the table for a long time.

There are a few reading groups here — Wittgenstein, Aristotle, Kant, Descartes. But you don't see them unless you look for them because they get quickly taken over by dumb nonsense such as this and this. — Lionino

I've been aware of some of them. I suppose I'll just have to experiment and see what happens.

Anyhow, any meaningful discussion to be had is covered 90% in the IEP/SEP page of the respective philosopher — Lionino

That suggests one could start a useful discussion from the relevant pages of the encyclopedias - and then read the book. Standing on the shoulders of the giants.

In my view both are very useful concepts. I will argue that you can have determinism and free will. Free will is a great concept to use as it easy describing various events and phenomena extremely well. Yet so is determinism too. — ssu

I agree with this. But there are some questions.
A popular way of having both is to argue that they are compatible. There's been a lot of discussion of that possibility, but I haven't seen anything that really resolves the differences between them. There's either freedom in the gaps or reduction of freedom to causality. Or have I missed something?
Another way of having both is simply to treat them say that they are different concepts (language-games), not in competition with each other. That would support the pragmatism that you seem to be suggesting, at the price of giving up on the question of truth.

And your statement (at least as you wrote it) was that none of them could be completed, which is even more It is wrong. — TonesInDeepFreeze

In the quotation in that message, I made no statement. I just asked a question.

I made no judgement on that — TonesInDeepFreeze

Thank you for the answer to my question. It is very helpful.

It is incorrect to infer that infinitely many tasks may be completed in finite time from the premise that there is no finite upper bound to how many task may be completed in finite time. I would put it this way: For for any finite number of tasks, there may be a completion of all the tasks. But that does not imply that there may be a completion of all of infinitely many tasks. — TonesInDeepFreeze

I would have thought that "for any finite number of tasks, there may be a completion of all the tasks" does not imply that there may be a completion of all of infinitely many tasks and does not imply that there may not be a completion of all of infinitely many tasks.

It is not the case that when we define an infinite sequence we must individually define each entry in the sequence — TonesInDeepFreeze

I agree with what you say. But, nonetheless, we have defined each entry in the sequence. Or is there an entry that is not defined? I can't think of one.
My indirect response is:- I'm sorry. I should have explained.
I was thinking about "there is no finite upper bound to how many task may be completed in finite time." It occurred to me that that depended on how long each task takes. (And that depends on what the task is.)
Clearly, if each task takes 1 second, there is a limit to the number of tasks that can be completed in 2 minutes. But how long does it take to add 1 to a given number? Does it take less time or more to add 1,000,000 to a given number? How long does it take to switch Thompson's lamp on or off? How long does it take to divide a given number by 2 or 10?
And then,the proof that sqrt(2) is irrational is also a proof that no rational number is sqrt(2)? Do I have to show separately and individually that each rational number is not sqrt(2)? I think not, but I have proved, of each rational number, that it is not sqrt(2). Is this one task, or many? How long does it take, either to prove that sqrt(2) is irrational or to prove, of a specific rational number, that is not sqrt(2)?

It is not the case that when we define an infinite sequence we must individually define each entry in the sequence. — TonesInDeepFreeze

Certainly. But there are some points I am not clear about.

Example:
Definition of sequence S:
The domain of S is the set of natural numbers.
For every natural number n, S(n) = n+1.
That's a finite definition (all definitions are finite) of an infinite sequence. — TonesInDeepFreeze

Yes, but how long did it take? Have you not defined each individual member of the sequence and all the members of the sequence? Which members of the sequence are not defined? How many tasks have I completed?

I like to keep the word 'series' for sums per convergences, and the word 'sequences' for sequences. — TonesInDeepFreeze

Thank you. I struggle with that difference. I'm not sure that everyone is consistent. What term do you use for a member of the sequence. People seem to by using "stage" or "term". Then there's the difficulty that "0, 1, 0, 1, ...." has, in one way, two members, each of which occurs repeatedly, So what do we call the first "0" as distinct from the second "0"?

Hence 2500 years of philosophers, mathematicians and scientists talking about it. — TonesInDeepFreeze

Yes. They're still talking about Epimenides the Cretan (and variants), as well. I can't deny they are both fascinating and annoying.

Metaphysical possibility is either equivalent to logical possibility or narrower than it (what a philosopher thinks the relationship between the two is depends, in part, on the philosopher's view of logic).

quoted by @Michael
Which means that metaphysics does not have an authoritative definition that we can all use for communication purposes, apart from the recognition that it involves logic.
For that reason, I prefer to stick to logical and physical possibility. There at least appears to be some consensus about the use of those terms, even though philosophers will, from time to time, quarrel about their definitions as well.

For the purpose of learning philosophy, time spent actually reading the classics is more productive than arguing with idiots in the hopes of the occasional informative post. — Lionino

Well, I think that the opportunity to discuss them with other people who have also read them helps a lot. That's my biggest problem. Perhaps I should try to start some reading groups.

But that does not imply that there may be a completion of all of infinitely many tasks. — TonesInDeepFreeze

S has a lower bound in S if and only if there is a member of S that is less than or equal to every member of S.
S has a lower bound if and only if there is an x such that x is less than or equal to every member of S. — TonesInDeepFreeze

The range of the sequence 1, 1/2, 1/4 ... has no lower bound in the range, but it has a lower bound (the greatest lower bound is 0). — TonesInDeepFreeze

Thank you for the clarification. I must admit, I was a bit puzzled by "bound". I'm used to "limit". This clarifies something that was puzzling me - how one could describe the relationship between the 0 and 1 to the steps of the series. This seems to work very well.

Again, even if there is no completion of all of infinitely many subtasks, it is not entailed that there is a finite upper bound to how many may be completed, so, a fortiori, it is not entailed that each of the subtasks is not completed. — TonesInDeepFreeze

Are you suggesting that it might be the case that all of infinitely many tasks can be completed? What would the last task be?
On the other hand, perhaps we should accept that when Achilles catches the tortoise or finishes the race, he has completed all of infinitely many tasks. That might need some explaining, though, wouldn't it?

If I'm not mistaken, Thompson recognizes physical possibility and logical possibility, which are at least fairly well understood, but he doesn't mention metaphysical possibility. That's not to say that the notion of metaphysical possibility should be ruled out, but only that it requires explication. — TonesInDeepFreeze

There is the possibility that he doesn't recognize metaphysical possibility. Not everyone does.

P1. If (A) the first task is performed at 11:00, the second at 11:30, the third at 11:45, and so on, then (B) infinitely many tasks have been completed by 12:00
P2. B is impossible
C1. Therefore, A is impossible — Michael

Here's a thought. When we define the series, we have defined each and every step in the series (or, if you prefer, each and every member of the relevant set.) Defining a step is a task. Suppose we do that at 10:55. So we completed infinitely many tasks, not only before 12:00, but before 11:00. So it is not impossible to complete infinitely many tasks before 12:00.
What's more, adding together the first step and the second step is a task. I can calculate the limit (sum) of the infinite series, well before 12:00.
Obviously, I haven't defined the last step, or the penultimate step, but that wasn't the challenge.
Or have I misunderstood the mathematics?

The distinction comes from language and purpose, and is not physical, which is the point of me posting all this. — noAxioms

Yes. I'm not disagreeing with you, for a change.

Or in a double spiral, resulting in a pair of very difficult to disentangle Slinkys. — noAxioms

:grin:

There is, of course, some variance in edge cases, but on the whole convention seems to correspond to the observable properties of things across different cultures. — Count Timothy von Icarus

Yes. Given that we are all human beings and therefore similar in many important ways (as well as different in other important ways, that is not surprising. That's why Wittgenstein grounds everything in human life and practices.

I would add that these problems become particularly acute, I would say insoluble, if one starts from the position that what we know/experience are "mental representations" or "ideas" rather than these being that through which we know. — Count Timothy von Icarus

Yes. I think we should think of them as lenses, rather than obstacles.

What I'm trying to say that there being a certain future simply doesn't limit in any way free will. — ssu

Yes, I hear you. One of the basic issues I have with determinism is understanding why people equate it with being forced to do things.

Strict materialism and physicalism simply leads people to make silly generalizations and to wrong conclusions. — ssu

Strict idealism, empiricism also lead to silly generalizations and wrong conclusions. I realise that we can't avoid generalizations, but I think we have to be pragmatic about them. There's a lot to be said for treating them as useful or not (so long as we assess that in context) or not, rather than true or not. But I wouldn't be dogmatic about that.

I meant metaphysics as things before physics, like the nature of existence (and universal principles) and as the study of mind-independent features of reality. — ssu

the branch of philosophy that deals with the first principles of things, including abstract concepts such as being, knowing, substance, cause, identity, time, and space. — Gnomon

... which demonstrates why metaphysics is so confusing. But I can see that there might be philosophy to be done with concepts; but then, I don't see how concepts can exist without language and I gather that some people regard a turn to linguistics as problematic. "Mind-independent features of reality" are more problematic, unless you just mean tables, trees and so forth. On the face of it, I would have thought that the empirical sciences are more likely to be useful than philosophy.

To Ludwig's gutters: The gutters are two separate objects if considered by a convention that identifies them as such. Them being physically attached to each other or not is irrelevant. Physics is utterly silent on the topic. There is no device that can be pointed to a 'thing' that will tell you the boundary of that thing, despite all the fictional devices that do exactly that. — noAxioms

I agree with you about this. But I have a pedantic desire to clarify the matter of the gutters. I mentioned them when I suggested that one could decide to cut a pipe into two halves either by cutting across its length, so you get two shorter pipes, or by cutting along its length, so you get two objects of the same length, but not complete circles so not pipes - I decided to call them gutters because they could be used as gutters. When I posited painting the pipe, I did not consider painting the gutters.

The choice is not an illusion: we are actually making the choice - we have to actually go through the mental process to reach that choice. — Relativist

I agree that when we come to a fork in the road and take one rather than another, we are, under normal circumstances, making a choice. Sometimes, when we make choices, we weigh the options, thinking of benefits and costs and so forth. But I don't agree that we always go through any particular mental process when we do so.

the branch of philosophy that deals with the first principles of things, including abstract concepts such as being, knowing, substance, cause, identity, time, and space. — Gnomon

This looks like a definition of philosophy, rather than a branch of philosophy.

Here's my problem:-

Do you see any relationship between physical freedom (mathematical value) and mental freedom*3 (metaphysical value)? :smile: — Gnomon

I don't understand the question. I could probably invent some sort of meaning for it, but I would have no idea whether that was in any way relevant.

But meta-physical (mental) choices are not subject to physical laws --- perhaps only the laws of Logic", it can be argued that he is making the argument that there's something else than the physical. — ssu

I don't understand what you are saying here.

Is there some other "language" in my posts that give you pause? I haven't been indoctrinated in the legalistic "linguistic turn" in philosophy (Wittgenstein, etc). So my language is generally vernacular & informal, and may sometimes run afoul of "legal" usage. — Gnomon

I suppose you are aware that "indoctrinated" and "legalistic" have presuppositions and overtones that anyone who had been indoctrinated into that legalistic turn would not accept? So why ask the question?

Are you uncomfortable with my use of "meta-physics" in reference to mental processes. Are Ideas subject to physical laws of gravity, or is there some other force that gives "weight" to opinions? — Gnomon

I don't understand what "meta-physical" means in that question. It doesn't conform in any obvious way with your definition.

We tend to use physical metaphors to describe psychological concepts, but are the analogies intended to be taken literally & physically? — Gnomon

Metaphors are not ever intended to be taken literally. I don't know what it would mean to take a metaphor physically. I don't know what it would be to take analogy literally or physically.

Are Ideas subject to physical laws of gravity, or is there some other force that gives "weight" to opinions? — Gnomon

Of course ideas are not subject to physical laws of gravity - they are not physical objects. If there is any force that gives weight to opinions, it is an appropriate kind of force, and then the concept of opinions having weight is no longer a metaphor.

How do physical limitations affect abstract ideas? — Gnomon

Good question. I've no idea what it means.

The physics books discussed things that change; the metaphysics books discussed things that don't change. — Gnomon

On this definition, if natural laws don't change, then they are not to be studied by physics. The definition must be incomplete.

There are different philosophical dialects, which enable different approaches to philosophy to articulate their ideas. I'm happy to spend some time and effort to decode what you say into something I can respond to, but I expect you to do the same for what I say.

Of course, if you deny the supposition of the puzzle, then it may be easy to dispense the puzzle. But one may wish not to take the easy way out but instead grapple with the puzzle under the suppositions it makes. — TonesInDeepFreeze

Sticking to the supposition of this puzzle creates confusion. The only possible solution is to look at it differently, not being hypnotized by 1/2, 1/4, ..... But I accept that it is your choice.

There are not two x/2, each one a separate object made by dividing x. — TonesInDeepFreeze

That's right. The difficulty is, I think, the assumption that "divide" means exactly the same thing in all contexts, taking the case of cutting something into pieces as the model. It obviously doesn't apply to numbers, or to space or time.

It is taking this hypothetical premise – that there is no smallest unit of space and time – that gives rise to such things as Zeno's Paradox, Bernadete's Paradox of the Gods, and Thomson's lamp. — Michael

No, it's confusing theory with practice, abstract with concrete and not understanding that infinity means endless (but not necessarily limited)

We use models about reality to get answers to certain questions. Many times, those models aren't declarations of our views on ontological questions. Yet often the models are interpreted as how we think what reality actually is. The difference between reality and a certain model of reality (that answers certain questions about it) is blurred. — ssu

I don't quite understand this. I could understand if you were talking about hypotheses. The journey from hypothesis (possibility) to theory (proven) is a long and tortuous one - blurred, if you like. But a model doesn't have a similar journey - unless there is a way in which a hypothesis can be a model or vice versa. Is that your point?

Above all, do we have to fall into the pit of metaphysical discussions that we have no way of solving (and hence no way to climb out from)? There's no ladder there to reason your way out from the pit. — ssu

That's how I feel about it. But people keep using the word.

It's false to draw conclusions from a materialist World view that then free will or making decisions doesn't happen / is meaningless. — ssu

Are you saying that any theory that is incompatible with freedom (free will) is false on that ground alone? That's a good start. But many people speak as if determinism was true and we have to bear the consequences, yet seem to believe that determinism is an empirical claim. Even when there's empirical evidence against it, they don't give up on it. I think it has to be classified along with hinge and grammatical propositions, perhaps as a research programme.

Metaphysical questions of what reality really is, don't give an answer to this and deterministic world models are quite useless models to use in this place. — ssu

There are ways of determining what is real and what is not. Those ways differ depending on the kind of thing you are talking about, but they exist. Asking what's Real, as if there could be a single-non-context-dependent answer, is the metaphysical way and goes nowhere.

Physical actions are indeed constrained by the limiting laws of physics. But meta-physical (mental) choices are not subject to physical laws --- perhaps only the laws of Logic. — Gnomon

One has to be careful about language here. What we can do is obviously constrained by our physical limitations. But what we can do is also enabled by our physical capabilities. The physical both constrains and enables what we do.
When I choose my sushi from what's on offer or a book from the shelf, is that a physical action, a mental action or a metaphysical action? (What's a metaphysical action?)
When you say that my mental choices are not subject to physical laws, you are using language that is at home and perfectly clear when we are talking about the law of the land. What it means when we are talking about physical laws is not at all clear. What would it be like to be not subject to physical laws? I don't think that any of the many non-conformist phenomema that have been identified, both in classical physics and in quantum physics, take us any nearer to understanding human action. Freedom of the gaps is no more helpful than God of the gaps was.

In a way, I would agree with you; human actions and choices are a distinct category from events taking place among inanimate objects, and perhaps that's what you mean when you say they are metaphysical. I think it is clearer to say that they and physical events are embedded in a distinct language games. The law of the land operates as part of the language-game of human actions; it doesn't operate at all in the language-game of physical events and their causes. If we speak of law it is a distinct kind of law, almost a metaphor, derived from the idea that God makes (and presumably enforces) the laws of nature. I don't think we need that idea any more; certainly, part of the point of the 17th century was to abandon that resource in natural science; making room for the new theories absolutely required that.

That's why I'm only advocating FreeWill in a Compatibilist sense. — Gnomon

I think we cannot get away with just saying that human freedom and laws of nature apply to different categories/language games. They obviously interact, and it is that interaction that we have to understand.

There is only an illusion of freedom. — Relativist

That's an interesting half-way house. But can deterministic theories explain how there can be an illusion of freedom?

I would say that painting a pipe two different colours is not a case of dividing the pipe. To use your terminology, you are distinguishing two halves without separating them. This does not qualify as "dividing". When I look at an object I can distinguish different parts of the object, and even draw lines on its surface, and all this is done without dividing the object. — Metaphysician Undercover

OK. So I guess measuring an object would count as "distinguishing different parts" of it even if the line that I draw does not correspond to any pre-existing difference or discontinuity in the object.

Why do you say that the two gutters are not distinct objects. — Metaphysician Undercover

Perhaps I wasn't clear. I never intended to say that. I thought this was crystal clear:-

You have two gutters (or that is what I call them). — Ludwig V

However, dividing an object in two always produces two new objects (as well as the waste material). — Metaphysician Undercover

It depends what you mean by "divide" and by "object".

However, dividing an object in two always produces two new objects (as well as the waste material). — Metaphysician Undercover

This is not exactly wrong, but requires that you recognize that "division" and/or "object" may change their meaning in some contexts. That's why I said:-

... if I paint half the pipe blue and half red, the halves do not become objects in their own right, but remain halves of the same pipe, even though they are of different colours. — Ludwig V

I said that the two painted halves do not become objects in their own right, meaning separate, distinct objects. You may argue that this is not dividing the pipe, or that each half becomes a distinct object. I don't mind what you choose. This shouldn't be too difficult for you, since you said earlier:-

And, divisibility is dependent on the type of thing to be divided. Therefore, when it comes to division one standard does not fit all things, and the principles of division must be specifically designed for the different type of things to be divided. — Metaphysician Undercover

But the fact of waste in any act of division nullifies the validity of the supertask. — Metaphysician Undercover

Oh, there's no doubt that no-one could actually cut the pipe into halves, and then divide one of the halves into halves ad infinitum. But painting the pipe shows that it depends what you mean by "divide" and/or "object". You could say that painting the pipe is a theoretical, not a practical division; that would be a bit at odds with ordinary language, but we are not speaking ordinary language here.

But maybe we could notice that we are not actually cutting the pipe, but imagining cutting the pipe. So perhaps we could imagine cutting the pipe without any waste?

"One half" in practise does not have the same meaning as "1/2" in theory. — Metaphysician Undercover

I hate to be difficult, and I'm not really disagreeing, just amplifying. But I would like to add that if the pipe is cut in half lengthways, neither half is a (newly individuated) pipe. You have two gutters (or that is what I call them). And that if I paint half the pipe blue and half red, the halves do not become objects in their own right, but remain halves of the same pipe, even though they are of different colours.

Everyone knows that tea is taken at at the tea time hour and that one is not to dawdle still drinking it, not even hypothetically, not even gedankenishly, past the tea time hour. — TonesInDeepFreeze

Yes. I discovered that after the tea-time hour, it turns into a grumpy tortoise.

too much public exercise of arithmetic would allow citizens to become too number savvy — TonesInDeepFreeze

Since then, however, it has been discovered that citizens will still get themselves into a hopeless muddle even if they practice all day. So the betting industry is safe.

We need only take it for granted that it does change at the rate stated in the puzzle. — TonesInDeepFreeze

The lamp puzzle doesn't require anything to occur in an infinitely small amount of time. — TonesInDeepFreeze

Yes. I was careless.

But I do understand Thomson's point that there cannot be infinitely many task steps executed in a finite duration. — TonesInDeepFreeze

But here's my problem. If I take one step, do I execute one task, or many? The argument of the paradox is that in order to take my step, I either must execute infinitely many tasks in a finite duration or fail to complete (or even begin) my step. I maintain that the issue is about how you choose to represent my step, and representing my step as composed of infinitely many segments is only one of many representations.

So it seems your analogy is between misuse of imaginary numbers and misuse of infinite numbers. — TonesInDeepFreeze

I think everyone agrees that there's misuse of something going on here. There's disagreement about what is being misused and how.

However, whatever you mean by 'complete', there are infinite series that have a sum. — TonesInDeepFreeze

I never meant to deny that.

I'm going to have a cup of tea. I shall divide it into parts 1/2, 1/4, 1/8 ... so it will last for as long as I want it to.

Only came to mind as I composed my reply to your earlier post. — Wayfarer

OK. Thinking on one's feet is allowed.

He says that there's no finite upper limit to the number of tasks that can be completed in finite time, but that not infinitely many can be completed in finite time — TonesInDeepFreeze

I've been thinking about this. My comment on this was wrong. Of course, one cannot complete infinitely many tasks in a finite time. "Complete" does not apply to infinite series, by definition.
On the other hand, what counts as one task. If one takes three steps, one completes three tasks. But that distance can be analysed in many different ways, so it could be represented as one task, or many.

I'm not talking about physical possibility. But even then, if space and time are infinitely divisible then motion is a physically possible supertask. — Michael

It depends on how you choose to analyse it.

No, I think (as did he) that it successfully shows that supertasks are not possible. — Michael

Yes, that's what I thought. I think the concept of a valid paradox is a bit confusing.

Yes. If space and/or time being infinitely divisible entails that supertasks are possible, and if supertasks being possible entails a contradiction, then it is proven that space and/or time are not infinitely divisible. — Michael

But space or time being infinitely divisible does not entail that supertasks are possible.

In this case the mistake is in the application of transfinite numbers. — Michael

That's the first I've heard of any use of transfinite numbers in this thread. I don't think they are relevant - more, I very much hope they are not relevant.

He says that there's no finite upper limit to the number of tasks that can be completed in finite time, but that not infinitely many can be completed in finite time. — TonesInDeepFreeze

How is that possible? Infinite means without limit.
Surely, the number of tasks you can complete in a given time depends on how long they take. If you want to perform an infinite number of tasks in a limited time, just define a task that takes the appropriate amount of time. in the puzzle, each task takes less time to perform, without limit. The trouble with Thompson's lamp is that no switch can function in an infinitely small time.

I am a tough customer when it comes to giving up my natural prerogative to add 1 to any number. — TonesInDeepFreeze

I'm sure it could count as a human right. But can we also stand up for the right to form the inverse of any natural number? (For clarity, forming 1/2 from 2, 1/3 from 3 and so on. (I'm not sure whether 0 or 1 need to be included here.)

Why do you say this? Doesn't science proceed through the falsification of theories? — Metaphysician Undercover

Yes. The trouble is that the inapplicability of convergent series in certain situations does not, for my money invalid them in all situations.

I don't deny that calculus is extremely useful, but that usefulness may be misleading relative to the goal of truth. — Metaphysician Undercover

Well, it would be interesting to know what your criterion of truth is in mathematics, if a calculation procedure is effective and useful.

This is the way I understand boundaries between two pieces of private property. — Metaphysician Undercover

I agree with everything you say.

If the discussion is about points in ordinary real 2-space or real 3-space then points are distinguished by being a different ordered tuple.
In 2-space, the point <x y> differs from the point <z v> iff (x not= z or y not= v).
In 3-space, the point <x y t> differs from the point <z v s) iff (x not= z or y not= v or t not= s).
If a particular line, say the ordinary horizontal axis, then <0 x> differs from <0 z> iff x not=z. — TonesInDeepFreeze

Thank you. That's very clear.

There is no smallest number, but if paradoxes like Zeno's and Thomson's are valid then there is a smallest unit of space and/or time. — Michael

I'm puzzled. I thought you thought that Thompson's paradox was flawed and therefore invalid - as Thompson did, didn't he?

I understand the view that there is no smallest number but that there are smallest distances and durations. But I am asking about the views of others too. — TonesInDeepFreeze

That seems to be the result of some recent research. But I don't think it applies to mathematics as such, and perhaps one ought to wait and see whether anything else emerges from research.

And, well, I think you can guess the problem lies (as we have been talking about a limitation on mathematic modelling). — ssu

And secondly, the result here isn't generally accepted or public knowledge. Just look at the references, videos or writings about LD. The usual idea is that since we have quantum physics, LD isn't happening because the physics isn't all Newtonian. But that's it. — ssu

Well, perhaps I'm ahead of the curve, for a change.

let's just call it "Philosophy". — Gnomon

I'll buy that. I'm sure we can get along and maybe occasionally agree to disagree. Most topics in philosophy seem to have only contested definitions, so there's nothing new here.

[/quote]

On the contrary, I think classical philosophy has always demanded something of that approach. I’m thinking for example of Pierre Hadot’s ‘Philosophy as a Way of Life’. — Wayfarer

It would have been helpful if you had mention Hadot in the first place. Philosophy as a way of life is a recognizable topic within philosophy. I've never been convinced by any proposals I've seen. So I fall back on Socrates. As you point out, for him the search was the philosophical way. I think that many of us do that. Some people give up, but it is hard to know whether that's because they have found their answers or because they have despaired of finding any. Some people don't seem to be bothered by the question at all.

According to Hadot, one became an ancient Platonist, Aristotelian, or Stoic in a manner more comparable to the twenty-first century understanding of religious conversion, — IEP

Well, light-bulb moments do occur in secular contexts. The term metanoiais quite rare, but seems to be used in quite ordinary contexts, and ancient Greece didn't discuss religious conversion in this sense, so far as I'm aware. However, metanoia isn't mentioned in any Ancient Greek philosophical work, or so Liddell & Scott tell me. I can't help feeling that both Plato and Aristotle would have insisted on rational persuasion as the only sound basis for philosophy. It is mentioned in Acts and Hebrews, but I assume that's the religious meaning.

The difficulty is, that to even attempt to name or indicate something beyond the contingent or constructed, brings it within the scope of a ‘community of discourse’ which is once again one of social construction and language. — Wayfarer

Well, you can't expect to name or indicate something without a social context and a language. I think language does quite well in dealing with the world. I doubt it would survive if it did not.

But I recall an instruction I read once, that the student (‘prokopta’, or ‘preceptor’) can become aware of certain kinds of evidential experience in their quality of life as a consequence of right realisation, although for obvious reasons that is not necessarily something ascertainable in the third person. — Wayfarer

H'm. I doubt that would stand up to even the mildest philosophical scrutiny and suspect that it would carry with it great moral dangers. But if it makes them happy and they do no harm, who's to complain?

It follows from wanting to adopt degrees of belief (which Manuel did), except for hinge propositions such as logical laws and such (the existence of God is no such proposition non-presups would agree). — Lionino

Well, I'm not fond of degrees of belief. But there are certainly ways we can qualify our commitment to what we believe. I don't think it is impossible to accept a logical law hesitantly or doubtfully. I read somewhere that Van Til's presupposition is not that God exists, but that the Bible is true.

ThEn you can't discard the pOsSiBiLity of a green donkey behind Jupiter! — Lionino

Yes, I can. There is no evidence that it is possible that there's a green donkey behind Jupiter.

The debate happens when people concede to theists the definition of 'atheist' "explicitly stating the non-existence of God", instead of the normal "not believing because there is no reason to believe": — Lionino

I think that some religious people will be quite happy to engage in debate with you on the basis that you need reasons to believe. But I suppose that does mean accepting the burden of proof. I would be absurd for an atheist to accept the burden of proof, because proving that something doesn't exist is much, much harder than proving that it does.

It isn’t robust relativism that leads to skepticism, but Idealism and empiricism, by not realizing that the practices of meaning we find ourselves enmeshed within are already real and true, already of the world, absent of any need to valid them on the basis of conformity to anything outside of these already world-enmeshed practices , ‘beyond the contingent’. — Joshs

I'm more or less with you on this, though I'm doubtful about what "beyond the contingent" means. But why do you classify that as relativism?

Our understanding doesn’t evolve by more and more closely approximating some foundational content but by using our past world-engaged practices to construct more intricately relational forms of understanding. — Joshs

Yes, I think that's about right. Foundationalism seem to provide endless questions, rather than a secure foundation.

No matter what the device says, we are free to choose the other option. — Ruckavicka above

Yes. That's why we could only ever conclude from the LD that prediction is not control and though the D may be said to determine, at least sometimes, in the sense of "discover", it cannot be said to determine in the sense of "control".

The effects of feedback of predictions on future action is very well known in economics, isn't it? Though perhaps it is the self-fulfilling prophecy that is more to be feared. That said, I do think that feedback loops in general are very important in understand how the body works, so they will contribute substantially to our understanding how we are able to do what we want - without being incompatible with determinism. That's the only way to go, in my opinion.

The limitation is essential part of logic, yet it's not understood as to be so. — ssu

I'm not quite sure what you mean. But I think that the important logical part of this is that the future is unlike the past in the sense that a prediction is not really true or false, but fulfilled or not. Compare G. Ryle "Dilemmas" Lecture II 'It Was To Be'. But I'm not aware that it has been discussed in the context of the symmetry of past and future in science.

Your pitch in is welcome, indeed. But you must have expected to encounter disagreement - you've been involved here for quite a while.

The difficult point about religious doctrines, in particular, is that they generally demand certainly qualities of character. — Wayfarer

I'm happy to agree that religious beliefs, on the whole, are not empirical - although Christ's Resurrection is often claimed (isn't it?) to be a historical (empirical) fact. But the idea that believing them requires certain qualities of character looks like an empirical claim to me.
I don't have any proper empirical evidence, but anecdotally, I've found all sorts of people hold religious beliefs and not all of them are particularly virtuous in any conventional sense. Scandals occur in amongst religious believers as well, you know.

Your quotation doesn't seem to deal with religious doctrines specifically, but with truth in general. There is a good deal of philosophical discussion of epistemological virtues and there is much to be said for that idea. However, I'm not aware of any specific arguments that everybody needs a radical transformation of character in order to know anything.

I'm not aware of purity as a moral virtue. Could you define it?

I do hope that isn't a version of the old argument that atheists are wicked. I thought we had got way beyond that.

As best i can bring myself to adopt a label, its emotivism. — AmadeusD

I always resist labels. They are supposed to be shorthand for complex views, but in practice they enable people to pigeon-hole where they have arguments prepared. It saves thought, which is almost always a bad thing. The objective/subjective distinction is another example of the same kind.

There is nothing coherent about claiming a belief and not knowledge unless you also claim the thing cannot be known — AmadeusD

That seems paradoxical. But if one believes on faith, especially in the case of religious belief, one may well believe that what one believes cannot be known, on the assumption that knowledge requires evidence and proof.

I think that "believe" has special connotations that get neglected in philosophical discussion, and perhaps in ordinary discourse as well. It can be used to declare trust or confidence in something. This is particularly prominent in religious discourse. If one believes on faith, it is not really appropriate to claim knowledge (because, perhaps, one also acknowledges that rational proof is not available).

But this is incompatible with the widespread idea that belief implies one is not certain (and knowledge implies one is certain). I'm happy to assert that that is not the case, but I doubt if anyone will pay any attention.

But I would say that a belief must be capable of being true and most people think that religious doctrines are true or false.

And when you just talk about limitations to modelling and forecasting, the debate can avoid drifting to metaphysical questions. — ssu

Well, I prefer it because it is so much easier to understand what is being said. But people seem to believe in it, and I can't work out why. The encyclopedias are not much help.

This is a good point. Free will is quite a loaded term, especially when you juxtapose free will with determinism. I think that's one of the problems here. — ssu

Quite so. But nobody seems to be interested in teasing out the complexities. It's all Freedom (capital F) and never free (attention to context and cases.) What are the differences between addiction and preference? Can people who do something in a temper plead provocation? Can a sincerely held, but completely unjustified, belief excuse a crime? (I thought the person I killed was an alien invader). And so on. Endless real questions.

You can use that term, — jgill

Do you mean "bijection"?

only if you are more specific about "points on a line" — jgill

Do you mean how they are to be identified?

Do you consider philosophy to be an ideal "language game" of no importance in the "real" world? — Gnomon

That's a difficult question to answer. Language-games are not well-defined entities. They are mostly useful as heuristics the "battle against the bewitchment of our intelligence by means of our language." Some of those bewitchments are very important. How effective philosophy is in neutralizing them is hard to discern. I don't justify philosophy any more than I justify science or art. All of them are worthwhile for their own sake, though one always hopes to be fighting on the side of the angels.

I was using physical indeterminacy as a parallel analogy to the philosophical question of Freedom vs Determinism. — Gnomon

Do you see any relationship between physical freedom (mathematical value) and mental freedom*3 (metaphysical value)? :smile: — Gnomon

Not really. I think that freedom is contextually defined, except where it is inapplicable. In each context, one needs to understand what counts as a constraint or compulsion, and that can be different.
If determinism is true, freedom and constraint or compulsion are inapplicable, at least in physics and similar sciences. On the other hand, there are ordinary language uses of "free" that do give a sense to saying that insensate objects are free or constrained, but philosophy seems unwilling to recognize them.
I try not to mention metaphysics, since I don't know what it means. :smile:

Some scientists inferred that the mind of the scientist could play the role of a Cause in the experiment. — Gnomon

Well, if you are really desperate, it's worth considering. I'm surprised the parapsychologists haven't got in there years ago. It's really a wild west out there.

Indeterminacy is a mathematical concept ; whereas Freedom is a human feeling, derived from lack of obstacles to Willpower*2. — Gnomon

If indeterminacy is a mathematical concept, then so is determinism. At last, we'll get an answer. Oh, wait, mathematicians don't agree about anything, either.
Being able to do what you want to do is not a bad definition of freedom. But then, are those choices necessarily free? It seems that sometimes they are not, so it's not enough. There's something about needing to be in good physical and mental health, living in a healthy society if one is to be free.
Willpower is very problematic concept for me; it is metaphysically loaded and poorly defined, even though there are ordinary language uses that are unobjectionable. It is awkward that if someone is trying very hard to achieve something, we say that they are determined to do it.

Perhaps the brain does not operate in a "classical" way. — Gnomon

Now there's something to agree with, so long as it isn't taken to have metaphysical implications.

I think there is a real problem about understanding how physics relates to human action, and the blanket free or determined is very unhelpful. At this stage and for our purposes, it is the detailed analysis of cases that will help us most.

No. If "the points on a line" correspond to integers or rational numbers, yes. Way too vague. — jgill

Fair enough. Should I be talking about a bijection between the non-dimensional points on a line and the set of integers?

Language play. — jgill

You had me going there. :smile:
So if I had said "And when we describe the principle of distinction between non-dimensional points on a line, we find that our counting with natural numbers is endless", you would have agreed?

Real numbers are uncountable. — jgill

I see. Why can't I count with natural numbers?

So one could argue that free will (or interaction) is a limit to making models, extrapolation or forecasting, but it doesn't refute determinism. — ssu

No, I think that our limits to modelling, extrapolation and forecasting do not show anything about free or constrained choices, because actions are a different category or language-game from events. For a start, they are explained by references to purposes and values, which have no place in theories of physics, etc. BTW, I think that the concept of free will is hopelessly loaded with metaphysical assumptions, and it would be much better to talk about freedom, free choices or free actions.

Determinism is not absolute. So, why assume human choices are forbidden by the gapless Chain of Cause & Effect? — Gnomon

Any events that are not determined by cause and effect are indeterminate. Freedom (or at least the philosophical version of it) is a language-game distinct from physics, etc.

Personally, I don't think human Life, or Culture, is incompatible with scientific explanation. — Gnomon

Nor do I. On the contrary, I think that scientific explanation is a part of human life of culture.

Does ordinary life require a whole different way of thinking in the same sense that we need to think of large numbers of air molecules as thermodynamics, because we simply can't perceive such a gargantuan number, much less calculate all the interactions that will take place between all of them within the space they occupy? — Patterner

I don't know about "in the same sense", because the cases are very different. But along the same lines, yes.

Is everything in this reality deterministic, — Patterner

I don't think that the idea that everything in this reality is deterministic is an empirical hypothesis. It is a completely different kind of proposition. Think of it as a research programme that defines what questions can be asked about phenomena and when they have been answered. Does that help?

But the necessity for Observer choices --- in experimental set-up, and interpretation of evidence --- resulted in "a whole different way of thinking". — Gnomon

H'm. I probably don't know enough to evaluate that. But I would have thought that observer choices in setting up experiments and interpreting evidence have always played an essential role in science. Though it is true that scientists have mostly assumed that it is possible to observe phenomena without affecting them, and that only becomes inescapably false at the sub-atomic level.

We cannot logical deduce or find out answers to metaphysical questions. If we could, they wouldn't be metaphysical. — ssu

I like that. Can we stop talking about it now?

Isn't that surface itself an edge, a discontinuity? And isn't it true, that what you see (sense) is actually a discontinuity, and you think it to be a continuous surface? I suppose, that you might think that within the confines of the edge, there is continuity, but look closer, and you'll see colour changes, texture changes, and other deformities which indicate discontinuity within the surface. — Metaphysician Undercover

H'm. I thought you would throw the results of sub-atomic physics at me - that apparently solid object is mostly empty space. But you are right. You are also right that the surface of an object is a discontinuity - a border - between the object and the rest of the world. But my point is that you cannot peel the surface of an object off, in the way that you can peel a skin off it. We can distinguish between a surface, with all its irregularities, and the object, but we cannot separate them.

Is this directed at me, or Michael? I maintain that a sensor is a material object consisting of components. The proposition of a non-physical sensor is incoherent. — Metaphysician Undercover

I'm sorry. I get confused sometimes about who said what. I'm glad we agree on that.

Aren't you making a category mistake here? If separation is in the world, and distinguishing is in the head, then your examples up/down etc., are examples of distinctions, not separations. It is a category mistake to talk about these as "inseparable" by the terms of your definitions, separable and inseparable would apply to the category of things in the world, while distinguishable and indistinguishable apply to what's in the head. — Metaphysician Undercover

You are right. I should have put the point differently - something along the lines you used.

What I meant by "actually", is what can be carried out in practise. Your example is theory. Anything is infinitely divisible in theory. You see an object and theorize that it can be endlessly divided. But practise proves the theory to be wrong. — Metaphysician Undercover

So we are closer than we seem to be. The difference between theory and practice is well enough known. It is unusual to say that difference proves theory to be wrong. I would be happy to say, I think, that Zeno's application of the theoretical possibility of convergent series to time and space and the application in Thompson's lamp is a mistake. But calculus does have uses in applied mathematics, doesn't it? I imagine that physics will come up with some interesting ideas about time and space; at the moment it all seems to be speculation, so I'm suspending judgement about that.

The only thing which makes them not the same is a dimensional separation, the idea that they are supposed to be at different locations in the world. — Metaphysician Undercover

Non-dimensional points which have a dimensional separation? H'm. But then a boundary (between your property and your neighbour's) doesn't occupy any space, even though it has a location in the world and will consist of non-dimensional points.

There can be no counting to begin with. — jgill

I'm surprised. Could you explain why?

The continuum of mathematics is not consistent with any sense evidence. — Metaphysician Undercover

That's odd. The surfaces of the objects around me look as if they are continuous.

By the way, nobody is worrying about the fact that we cannot picture an infinitely divisible continuum.
— Ludwig V
Speak for yourself. — Metaphysician Undercover

You said:-

So mathematics uses a technique where terms are defined, and the sense image is not necessary. For instance, a nondimensional point, infinite divisibility, etc.. — Metaphysician Undercover

If spacetime is continuous and infinitely divisible, as is assumed, then an infinite number of two dimensional sensors can fit within finite space. — Michael

Only if space is infinitely divisible and they are not physical sensors. And you say in the quote below that a sensor is a material object.

That is not necessarily the case. A sensor is a material object, space and time are not material objects. There is no necessity that the limitations of a material object are the same as the limitations of space and time. In the end, it's all conceptual, and the problem is in making the conception of an object consistent with the conceptions of space and time. — Metaphysician Undercover

Well, do you know of anything that's actually infinitely divisible? — Metaphysician Undercover

What do you mean by "actually"? Take any natural number. It can be divided by any smaller natural number. The result can be divided by that same number again. Without limit.

What do you mean? What is this difference between distinguishing and separating? — Metaphysician Undercover

Whenever concepts are defined in relation to each other, they can be distinguished but not separated. Distinguishing is in the head, separation is in the world. Examples of inseparable distinctions are "up" and "down", "north" and "south" (etc.), "convex" and "concave", "clockwise" and "anti-clockwise", "surface" and "object" (in cases such as tables and chairs).

Our senses and our abilities are of course limits to us, but that actually is quite a different thing. — ssu

Yes, they limit us, but the also, at the same time, they give us opportunities.

"The "strongest" system where everything is provable is with sytem where 0=1". — ssu

"From a contradiction, anything you like follows." Calling that strength is a bit counter-intuitive. But I'm not going to argue.

And before he or she thinks that you are attacking the whole idea of determinism, it should be told that the issue in the limitations of modelling that determinism, not the determinism itself! — ssu

So you are saying that the world is deterministic, even though our models will never demonstrate that?

That you did make choices isn't relevant for the determinist model: your choosing to throw the pillow is just given. — ssu

Yes. Physics doesn't have the conceptual apparatus to describe or even acknowledge choices. Ordinary life requires a whole different way of thinking.

But you hopefully understand that it's different to model this when it hasn't happened, especially you know about the model before you have thrown it. — ssu

Yes. Past and future are different, even if physics can't acknowledge the fact.

I would not call that "imagining". Like the "round square" it's simply a case of saying without imagining. An author can say that the space ship moves from here to there in a time which implies faster than the speed of light, but to imagine faster than the speed of light motion requires imagining a material body moving that fast. That body moving that fast, could not be seen, and therefore cannot be imagined. — Metaphysician Undercover

OK. That seems clear enough for now. I won't argue about words.

The problem though is that .... the (unimaginable) mathematical conception of an infinitely divisible continuum is not consistent with the empirical data. — Metaphysician Undercover

What empirical data do you have in mind?

The problem is exactly what Michael has been insisting on, the assumption that space and time are continuous. This supports the principle of infinite divisibility. — Metaphysician Undercover

The problem arises when people believe that the infinite convergent series is the necessary outcome of the problem of infinite divisibility instead of seeing it as one possible representation. — Metaphysician Undercover

You seem to be saying in the first quotation that the assumption that space and time are continuous gives rise to the problem of infinite divisibility and in the second that the problem of infinite divisibility gives rise to the problem of infinite convergent series. I must be misunderstanding you. Can you clarify?
But I agree with you that the convergent infinite series is a possible representation of certain situations. (I would call it an analysis, but I don't think the difference matters much for our purposes.) All I'm saying is that it doesn't give rise to any real problems unless you confuse that representation with the cutting up of a physical object.

Why therefore, do you conclude that we can do something more with the space than we can do with the cheese? — Metaphysician Undercover

Because the cheese is a physical object and the space is not an object and not physical. You seem to be saying the same thing here:-

The problem though is that space and time are conceptions abstracted from empirical observation, how material things exist and move, and the (unimaginable) mathematical conception of an infinitely divisible continuum — Metaphysician Undercover

By the way, nobody is worrying about the fact that we cannot picture an infinitely divisible continuum.

When we describe this principle of separation we also provide ourselves with the basis for division. — Metaphysician Undercover

And when we describe the principle of distinction between non-dimensional points on a line, we find that our counting is endless. The surprise is entirely due to mistaking non-dimensional points for a physical object - thinking that we can separate them, rather than distinguish them.