This is regarding the puff of smoke or the plate of spaghetti. And that's why I mention Cinderella's coach. Nobody ever complains about that. Why is the lamp constrained to be off or on, when it's a fictitious lamp in the first place? — fishfry

I think the problem is precisely that there is nothing to constrain the lamp and we want to find something. In theory, we could stipulate either - or Cinderella's coach. But we mostly think in the context of "If it were real, then..." Fiction doesn't work unless you are willing to do that. It's about whether you choose to play the game and how to apply the rules of the game.

The terminal state of the lamp is not defined, so it may be on or off. What on earth is wrong about that? — fishfry

This seems to be more in tune with common sense, for what it's worth. The question is, why? I think it is because of the dressing up of the abstract structure. We assume the lamp has existed before the sequence and will continue to exist after it. So the fact that the sequence does not define it does not close the question and we want to move from the possible to the actual. But it is not clear how to do that - and we don't want to simply stipulate it. Perhaps that's because defining the limit of the convergent sequence as 1 - or 0, which have a role in defining the sequence in the first place, invites us to think in the context of the natural numbers (or actual lamps), whereas defining ω as the limit of the natural numbers does not.

Strictly speaking the actions taken when the rules are transcended are not consistent with the rules, because these actions transcend the rules. The rules may allow for such acts, acts outside the system of rules, but the particular acts taken cannot be said to be consistent with the rules because they are outside the system. — Metaphysician Undercover

I hope you meant that actions taken outside the system are neither consistent nor inconsistent with the rules. Could we not express this by saying that the rules don't apply, or that it is not clear how to apply the rules, in the new context?

Changing from a finite number of button pushes to an infinite number of button pushes doesn't let you avoid this common sense reasoning. — Michael

No, but it might be the case that common sense reasoning doesn't apply or is misleading in the context of infinity.

There is only us pushing the button an infinite number of times, where pushing it when the lamp is off turns it on and pushing it when the lamp is on turns it off. — Michael

You can think about us doing that, but you can't limit our thinking to that context. That's where the problems start.

What is the causal consequence of us having done this (and only this)? — Michael

Us doing this is not an empirical possibility, so there can't be any causal consequences. But I think you mean to ask what outcome there can be if we think only in that context. Sadly, that context doesn't give us an answer - except possibly that the state of the lamp is both on and off or neither on nor off.

I drive down the road and come to a fork. One day I turn left. Then next day I drive down the same road and turn right.? What logical inconsistency do you see to there being multiple possible outcomes to a process that are inconsistent with each other, but each consistent with the rules of the game? — fishfry

Possible outcomes can indeed be inconsistent with each other. But if they are inconsistent with each other, they can't both be actual at the same time. You can't drive down the road and turn left and right at the same time.

Benecerraf explicitly says: "... Certainly, the lamp must be on or off at t1
(provided that it hasn't gone up in a metaphysical puff of smoke in the interval) ..."
In other words he is making the the point that for all we know, the lamp is not even constrained to be either on or off at the terminal state. And why should it be so constrained? — fishfry

There is more to this than meets the eye, I think. Benecerraf's quotation is somewhat hedged. And "for all we know" hints at unexpressed complexities, I'm interested in all that. See below.

Yes, but are the philosophers who want to make synthetic necessity among them?
— Ludwig V
I don't get it. There is something missing in this phrase. — Lionino

I was commenting on

Some philosophers make away with both the a posteriori / a priori and analytic/synthetic distinctions, — Lionino

I'll try again. "Is it the case that all the philosophers who want to make away with those distinctions the same as those who want to define synthetic necessary truths"



I looked again at Benecerraf's article and found what I was looking for. His position is much more nuanced than I thought. Selective quotation is not ideal, but my summary would likely be worse. So here goes:-

A "swindle" has taken place, and we have been the victims. Somehow, all was going along swimmingly, and suddenly we find ourselves drowning in contradiction with no idea of how we got there. We are told that the concept of a super-task is to blame, but we are not told what about it has such dire consequences. We are sufficiently sophisticated mathematically to know that the concept of infinity is not at fault (or if it is, a lot more than the future of super-tasks is at stake). — Benacerraf on Supertasks - The Journal of Philosophy, 1962, p. 781

I suspect that, by and large, it is principally compound expressions that suffer the fate I attribute to 'completed infinite sequence of tasks' ..... What seems most notable about such compounds is the fact that one component (e.g., 'infinite sequence') draws the conditions connected with its applicability from an area so disparate from that associated with the other components that the criteria normally employed fail to apply. We have what appears to be a conceptual mismatch. Sequences of tasks do not exhibit the characteristics of sequences that lend themselves to proofs of infinity. And since there seems to be an
upper bound on our ability to discriminate (intervals, say) and none on how finely we cut the task, it appears that we should never be in a position to claim that a super-task had been performed. But even if this is true, it only takes account of one kind of super-task, and, as I argue above, it hardly establishes that even this kind constitutes a logical impossibility. — Benacerraf on Supertasks - The Journal of Philosophy, 1962, p. 783/4

To look at the matter diachronically and therefore, I think, a little more soundly, we can see our present situation as akin to that of speakers of English long before electronic computers of the degree of complexity presently commonplace when confronted with the question of thinking robots (or, for that matter, just plain thoughtless robots, I suspect). They were as unthinkable as thinking stones. Now they are much less so. I am not sure that even then they constituted a logical contradiction. However, I would not resist as violently an account which implied that the expression 'thinking robot' had changed in meaning to some degree in the interim. Viewed as I suggest we view them, questions of meaning are very much questions of degree-in the sense that although relative to one statement of meaning there may be a more or less sharp boundary established, no statement of meaning (viewing things synchronically now) is uniquely correct. Other hypotheses, and therefore other lines may be just as reasonable in the light of the evidence. The statement of the meaning of a word is a hypothesis designed to explain a welter of linguistic facts-and it is a commonplace that where hypotheses are in question many are always possible. — Benacerraf on Supertasks - The Journal of Philosophy, 1962, p. 784

Therefore, I see two obstacles in the way of showing that supertasks are logically impossible. The first is that relevant conditions associated with the words and the syntactic structure involved must be found to have been deviated from; and it must be argued that these conditions are sufficiently central to be included in any reasonable account of the meaning of the expression. The second is simply my empirical conjecture that there are no such conditions: that in fact the concept of super-task is of the kind I have been describing above, one suffering from the infirmity of mismatched conditions. — Benacerraf on Supertasks - The Journal of Philosophy, 1962, p. 784

The bolded sentence expresses my preferred diagnosis. (Which, by the way, is channelling Ryle. I think Benecerraf must have know that - look at the date of the article.) In the light of the various further supertasks that have been developed, a conclusive refutation seems as unlikely for the supertask problems as it is for the Gettier problems. But this is a good candidate.

We just need to say that the infinite sum is the limit of the sequence of finite sums. — TonesInDeepFreeze

Thank you.

What rule of the problem constrains the terminal state of the lamp? — fishfry

None. I'm afraid I'm indulging in double-think in this discussion. I can't make sense of the imaginary lamp. Either it is just a picturesque way of dressing up the abstract structure of the mathematics or it is a physical hypothesis. Some time ago I asked @michael why he didn't just run his computer program. He replied that a computer couldn't execute in the programme in less than some minute fraction of a second, so it wouldn't give an answer. Which was the answer I expected. The computer program was just another way of dressing up the mathematical structure. So I translate all talk of the lamp into abstract structure in which "0, 1, 0, 1, ..." is aligned with "1, 1/2, 1/4, ...".

In other words he (sc. Benacerraf) is making the the point that for all we know, the lamp is not even constrained to be either on or off at the terminal state. And why should it be so constrained? — fishfry

I agree. But I have some other problems about this. I'll have to come back to this later. Sorry.

I’m not sure we’re understanding ‘hermeneutic circle’ the same way. — Joshs

No, we are not. But there are not dissimilar arguments in other quarters about the relationship of Language and Reality, which come to very different conclusions. Perhaps I should not have stuck my nose in. On the other hand, I shall have to look at Gadamer more closely. Thanks.

First, there is etymological analysis, looking at old texts to determine how some term came to mean what it does. But second, there is looking into the actual physical referents of words to see what they are. — Count Timothy von Icarus

Yes. We can discern in both practices what Derrida I believe calls the "wandering signifier". It doesn't half complicate philosophical analysis. We can also discern that "scientific" is not monolithic. We should not presuppose a single "scientific" method.

If they undergo as much change as the terms for water , then isn’t a phrase like actual physical referent linguistically self-referential, belonging to the hermeneutic circle along with our changing terms for water, rather than sitting outside of it? — Joshs

Yes. Terms like "actual physical referent" or "materialism" are increasingly difficult to use in philosophical discussion. That's one reason for doubting how useful the concept of a hermeneutic circle is. Language constantly seems to refer beyond itself, and our practices do not find it difficult to use those terms. Isn't that as good as it gets for defining an outside?

But it's not only science that creates complications. Our changing practices can do so all by themselves. Consider the history of "cash". "Cash" used to mean physical chunks of metal. Then it came to mean physical chunks of metal stamped by authority to certify their physical composition. Then it came to mean physical chunks of metal stamped by authority. Then bank notes..... Nowadays, I discern it coming to mean a credit balance to which I have instant access. It all makes the economy run quicker and more smoothly. Whatever next?

That was Marx's point on Feuerbach: "philosophers have only interpreted the world in various ways; the point is to change it!" - — Count Timothy von Icarus

That's right, of course. The question now is whether one can change the world from one's arm-chair. There's a lot of reason to say that one can. Of course, that might depend on what one regards as meaningful or real change. And yet, one needs a phrase to refer to idle speculation.

Don't get me wrong. My last question was a question because I don't think that "ordinary language" is the answer. As a matter of fact, I think that the philosophical practice of ordinary language philosophers was at variance with the rhetoric about ordinary language.

It's worth saying that the rhetoric of ordinary language was meant to distinguish their work from the predominately idealist philosophy that was the orthodox of many philosophers at the time, and the analytic and positivist revolutionaries who had emerged in opposition to them. There were good grounds for rejecting both and I would certainly resist returning to either.

And why can't a philosopher do this, instead of sitting around and describing how the term is actually used. — Richard B

There's no reason why not. Nussbaum, Rawls, Russell, and Singer come to mind as stellar examples. It seems to me that WIttgenstein's practice was also at variance from his remarks about just describing. In his case, the business about saying and showing gives some sort of explanation.

My main point with this example is that Rawls is not looking to the ordinary use of "Just" to come up with his conception of "Justice" nor should he. — Richard B

Nor did I mean to imply that he was. Criticizing Rawls doesn't mean that I think we should retreat to describing how the term is actually used. I rather think that the ordinary use of justice would almost certainly lead us to describe it as a term that is the ground of a battlefield, (intellectual and physical) rather than a coherent concept.

Give me that "arm-chair" we can do better. — Richard B

I realise you don't mean that literally, but here's the problem - who is "we"? That's not just a problem for ordinary language philosophy. It's a common usage in philosophy to say "we" say this and that or "we think" this and that.

OK, for example, I live in an environment where "street justice" rules. ........... I understand its use, the action, and the context. — Richard B

It's a very distressing story. It does indeed throws into high relief the simple points that the ordinary is not the same for everyone, and not necessarily justifiable. I have not the slightest inclination to argue against either. If only it were possible to establish an agreement without using force....

The fact that the conjunction of these premises with the performance of a supertask entails a contradiction is proof that the supertask is impossible, not proof that we can dispense with the premises at 12:00. — Michael

Sorry. I have something else to do. I didn't expect to convince you, but our discussion has helped to confirm my opinion.

But, if the button is pushed at t1/2, t3/4, t7/8, and so on ad infinitum then the lamp is neither on nor off at t1. This is the contradiction. — Michael

Not quite. The lamp is not defined as on or off. It's just that the rules don't apply at 12:00. But tertium non datur does apply. So it must be (either on or off).

I'm really sorry, but my fat thumb syndrome struck and my last message got posted before I had finished with it. This version is finished.

His stipulation that the lamp is on (or off) at t1 is inconsistent with the premises of the problem. — Michael

Benecerraf's sentence is not exactly that:-

Certainly, the lamp must be on or off at t1 (provided that it hasn't gone up in a metaphysical puff of smoke in the interval), but nothing we are told implies which it is to be. — Benecerraf

Aren't you forgetting tertium non datur?

The rules of the problem stipulate whether the lamp is on or off at 11:00, 11:30, 11:45, and so on ad infinitum, but not whether it is on or off at 12:00.

I grant you that they will tell you whether it is on or off at any specific time before 12:00, but they does not tell you whether it is on or off at 12:00.

Am I contradicting you?

So what are you arguing about?

That supertasks are metaphysically impossible. — Michael

Is is not the case that "logically impossible" implies "metaphysically impossible"?

Yes. And therefore the antecedent is necessarily false. Supertasks are metaphysically impossible. — Michael

I don't know about metaphysically possible or impossible. Logically impossible, certainly. So what are you arguing about?

— Michael

If the button is only ever pushed at 23:00, 23:30, 23:45, and so on ad infinitum, then the lamp is neither on nor off at midnight — Michael

So we can agree that the consequent is false. Ex falso quodlibet, so a plate of spaghetti.

Even some subsequent midnight button push is of no help because of C2 and C3. — Michael

You missed out "The lamp is either on or off at all times."

Benacerraf argues that neither outcome is inconsistent with the rules of the problem, — fishfry

That seems to be true, so Benacerraf is right.
Doesn't it follow that both outcomes are consistent with the rules of the problem?
If both outcomes are consistent with the rules of the problem, doesn't that imply that they are not self-consistent (contradict each other)? If so, Michael is right.
But if they contradict each other, doesn't ex falso quodlibet applies (logical explosion)?
The logical explosion implies your conclusion, that justifies your plate of spaghetti, doesn't it? So you are right.
End of discussion? Maybe.

The rules must be consistent with each other where they apply. The problem is that the rules don't apply to the limit, because the limit is not generated by the function, that is, it is not defined by the function.

The limit is defined, however, as part of the function, along with the starting-point and the divisor to be applied at each stage. In that sense, they are all arbitrary. But the idea that they could all be replaced by a plate of spaghetti is, I think, I mistake. Don't we need to say that these numbers are not defined by the function, but are assigned a role in the function when the function is defined, which is not quite the same as "arbitrary"? The range of arbitrary here, has to be limited to natural numbers; plates of spaghetti are neither numbers nor, from some points of view, natural.

I wasn't crazy about writing it. :grin: I don't always know how to express myself in these matters. And sometimes it's not even my fault, As ssu just pointed out regarding the definitions of cause and reason. — Patterner

We all have our idiosyncracies and few of us come up with the perfect phrase every time. I tend to be a bit cautious, if you like, and perhaps scrutinize the text more closely than I need to. The reason is that one of the ways I come to understand meaning is by asking what the opposite would be and what would make it apply. (See below). The dictionary definitions of cause and reason were a bit of a blow. The philosophical use of "cause" and hence of "reason" is, if you like, specialized.

I'm not "actually choosing" if physical determinism literally prevents any other possibility. — Patterner

That start me wondering what it would mean if physical determinism only metaphorically prevented any other possibility. But I'm not arguing that we are not prevented from some choices in one way or another. The question is whether this is always the case or just sometimes and what the factors are that can prevent choices. See?

If I'm aware of all the possibilities, but I have no possibility of "choosing" from the myriad options, and can do only the one that the physical factors determine, then awareness is only watching the show. — Patterner

The question is whether you have no possibility of choosing from the options. But determinism effectively says that you have no options, because an option is by definition something you could choose to take.

Come on. It's a metaphor. You seem to have a problem with both Metaphors and Metaphysics. Do you remember how I define "meta-physics", not as religious doctrine, but as philosophical reasoning? — Gnomon

The difficulty is to understand metaphors. If one takes them literally, they are usually false or meaningless. They can have a meaning, and even a truth, of their own.

But soft, what light through yonder window breaks?
It is the east and Juliet is the sun!
(William Shakespeare, Romeo and Juliet, 2. 2. 2–3)
Of course, Juliet is not the sun. But, at the least, the comparison expresses how Romeo feels about her, and so tells us a truth about the place of Juliet in his life.

—History, Stephen said, is a nightmare from which I am trying to awake.
(James Joyce, Ulysses, chap. 2)
This takes a simple metaphor which states a perspective on history. (Since we often apply "nightmare" to anything disastrous or upsetting that happens to us, it is perhaps not even a metaphor.) One could reply, calmly, that there are good bits as well as bad bits. But do the good bits outweight the bad bits? Stephen thinks not, but that the bad bits far outweigh the good bits and maybe even that the good bits aren't really good at all. Adding "from which I am trying to awake" makes it into a metaphor, and tells us that he thinks it may be possible to see things differently.
How would you feel if I said that Determinism is a nightmare from which I am trying to awake?

I do have a problem with metaphysics. I had forgotten your definition of it. I can work with that, although there are still problems.

I'm getting the impression that you don't do philosophy. I'm not sure what you think this forum is all about, if not attempts to construct or destruct a "philosophical position". — Gnomon

It depends what you think doing philosophy is. Does Heidegger or Derrida do philosophy. Many people (including most analytic philosophers) think not? Did Wittgenstein or Ryle do philosophy? Many people (including many analytic philosophers) think not. That's how it works.
I usually find it very difficult to construct or destruct philosophical positions. So I improvise. Jazz philosophy? A metaphor! Too pompous, certainly if I reference Wittgenstein.

FreeWill is not a physical (empirical) question, it's a metaphysical (theoretical) inquiry. My compatibility position is ultimately a Monism : Causation comes in many forms. — Gnomon

This changes everything. But let me ask whether you think that determinism is not a physical (empirical) question? I'll tell you now that I don't think it is. It is a way of thinking about the world and science. Whether it would count as metaphysical inquiry, I wouldn't know. But I certainly think it is a theoretical enquiry. Freedom (Free Will) is a way of thinking about certain parts (components - people) of the world. Understanding these two as ways of thinking, especially whether and how far they are compatible, not deciding between them, is (should be) the project.

My compatibility position is ultimately a Monism : Causation comes in many forms. — Gnomon

Well, we can talk about that.

That internal Causation (willpower) is different from external Determinism (energy) in the sense that a meta-physical Mind is different from a physical Rock. — Gnomon

There are some specialized causal processes that seem to be crucial to our functioning. They are not often found outside living things, so we may be fairly close to each other.

In Mathematics there is this well ordering theorem, so we can assume we can put them into order. Plato did it with his Dog 1, then on one side the dogs that eat more, and on the other side the dogs that eats less. — ssu

Yes. That will work fine if the criterion for their order can't change. But you have posited that they can change how much they eat. You need another, independent, criterion for "same dog".

If you move the dog that no longer eats the same amount to its new position, you've no criterion to establish whether you moved the same dog or a different one. (Watching it eat won't help. However much it eats, you need to know whether it is now eating the same amount as it did before or a different one.)

Perhaps our dog just automatically changes its position, as soon as they start eating differently. But if one dog can change how much it eats, other dogs can. But you have no way of telling whether they have changed or not and so no way of telling whether they are eating differently.

Rather, by rule #2, the one that eats "the most" and the one that eats "the least" are conceptual quantities that differ from any other quantities already given. — L'éléphant

Yes. But there is the supposition that how much they eat can change. To establish individuation, you need an additional criterion that is not empirical.

the meaning of a mathematical concept is not an object or 'configuration' but rather, the totality of rules governing the use of that concept in a calculus." Mathematical propositions are not about anything (in a descriptive sense) yet neither are they meaningless: they are norms of representation whose essence is to fix the use of concepts in empirical proposition. — Richard B

If one thinks about the various developments from, say, to Copernicus to Newton, "fixing the use of concepts in empirical propositions" seems like a more complicated process than this, and it might be thought to violate the purity of mathematical autonomy. The crucial step is the one from "mathematical hypothesis (which the theologians could accept) to description of reality, (which Newton's theory eventually achieved). True, the reality described was modified to accommodate this, but that itself raises questions about the autonomy of systems. I would prefer to say that the application of mathematical propositions to empirical propositions is an extension or development of their theoretical use. How could I rule out other extensions or developments?

Hence Godel was barred by virtue of the logical grammar of mathematical proposition from claiming that he had constructed identical versions of the same mathematical proposition in two different systems. — Richard B

Surely the question whether Godel had or had not achieved that aim is a question for mathematicians. But mathematicians disagree, (don't they?) and perhaps Wittgenstein counts as a mathematician. So the question does not have a determinate answer. That seems to me to be closer to what one might call the truth. I do not rule out the possibility that mathematicians might eventually devise rules for the use of the relevant concepts that would resolve the question. Fortunately, I am barred from attempting the project.

"In Philosophical Remarks Wittgenstein insisted contra Hilbert that ' In mathematics, we cannot talk about systems in general, but only within systems. They are just what we can't talk about(PR 152). The argument as presented sounds dogmatic, but it follows from the preceding clarification of the meaning of mathematical propositions as determined by intraliguistic rules rather than a connection between language and reality. — Richard B

Except when we come to applied mathematics, when that issue becomes central.
________________________

From Wittgenstein Blue Book "Philosophers very often talk about investigating, analysis, the meaning of words. But let's not forget that word hasn't got a meaning given to it, as it were, by a power independent of us, so that there could be a kind of scientific investigation into what the word really means. A word has the meaning someone has given to it." — Richard B

It is better to think that a word has the meaning someone has given to it than to think that the meaning of a word is an eternally existing (subsisting entity floating about in some alternative world. But at face value, for those of us using the words, that is simply false. We learn what words mean - we do not make it up; we discover what they mean (what the rules for its use are), or we do not learn to speak. So there can be a scientific investigation into what the word means - and how its meaning changes. To be sure, sometimes we know who gave a word its meaning, but even if it was coined by someone, its use is the result of a process of dissemination which is rarely documented and we do not altogether understand. But dictionaries often include remarks about it and it could be the object of a "scientific" investigation.

It is fair to say that Austin treats language as a tidy abstract structure, rather than a dynamic and messy collection of language-games, and this undermines his claim to be talking about ordinary language. But still, the resulting arguments are at least worth of serious consideration, so I'm not inclined to get too sniffy about his methodology.

From Quine, Word and Object, "There are, however, philosophers who overdo this line of thought, treating ordinary language as sacrosanct. They exalt ordinary language to the exclusion of one of its own traits: its disposition to keep evolving." — Richard B

"Overdo" is the right word, though whether it applies to specific texts is always going to be debateable. Ryle in "Dilemmas", as I recall, talks about technical and untechnical concepts and concepts that everyone uses whatever technical language they are using, rather than ordinary language.

from John Rawls "Principles of Justice", "My aim is to present a conception of justice which generalizes and carries to a higher level of abstraction the familiar theory of the social contract as found, say, in Locke, Rousseau, and Kant. In order to do this we are not to think of the original contract as one to enter a particular society or to set up a particular government. Rather, the guiding idea is that the principles of justice for the basic structure of society are the object of the original agreement. They are the principles that free and rationale persons concerned to further their own interests would accept in an initial position of equality defining the fundamental terms of their association — Richard B

The difficulty is that I don't trust myself to dispense with all my selfish interests during this imaginative exercise. It is rather easy to say that if I was a slave, I would accept my slavery because those are the rules. It is equally easy to say that if I was a slave, I would do my level best to escape, despite the rules. For my money, it is much better to start where we are. Other people may start in different places. When we disagree, we shall have to have an argument. That's how it works. How can Rawls' exercise help? Back to ordinary language?

You cannot take Plato's dog, add the food of the dog which eats less than every other dog, and then get more than Plato's dog eats. — ssu

I'm sorry. I just don't follow this. Is there a typo somewhere?

If you would get a different amount of food, then that could be divided even smaller portions and the dog that eats the least wouldn't be the one eating the least. — ssu

Nor do I follow this. But I can agree that if you mess about with the food, some other dog might get less than the dog that eats less than any other dog.

"Plato's dog" is the dog that Plato chose. Let's call the dog that eats less than any other dog "Dog One" and the dog that eats more than any other dog "Dog Two". and the dog that gets less than Dog One "Dog Three".

In that Case, Dog One would no longer be the dog that eats less than any other dog, because Dog Three is getting less than Dog One. We will have to take the rosette off Dog One's collar and pin it on Dog Three's collar. What's the problem?

while the dog that eats less than any other dog, does this the definite it separate from all other dogs? — ssu

Each dog is an individual, so we will always be able to find a unique description or assign a unique name to each dog. Unfortunately, we won't be able to assign a number to each dog in the order they were created, but we can assign a unique number to each dog according to how much they eat, starting with Dog One. That won't work if you start messing about with how much they eat.

I'm afraid I don't see that the Small Worlds model affects the issue at all. Sorry.

… although in the strict physical sense our actions might be determined, we can still be free in all the ways that matter, because of the abilities we evolved". — Gnomon

I have a lot of time for Dennett. But that doesn't mean I agree with everything that he says. This is just throwing in the towel. We all have limitations - things we cannot do. But doesn't really affect the issue.

It's not the heavenly ideal, but a free-roaming mind is better than being a sentient mind trapped in an imprisoned body. — Gnomon

But I'm not a sentient mind trapped in an imprisoned body. I'm a person, as free as anyone is.

In a Matter-only world, "it is what it is" ; but in a Mind & Matter world, what is imagined might also become realized. — Gnomon

I wouldn't know. I don't live in a mind-and-matter world, nor in a matter-only world, not, for that matter, in and ideas-only world. On Mondays, Wednesdays and Fridays, I'm a monist. On Tuesdays, Thursdays, and Saturdays, I'm a uncountable pluralist. On Sundays, I don't do philosophy.

"I feel that as human beings with free will, the mind tends to limit itself from living to the fullest when we become prisoners of our own mind." Is your mind locked-in? :chin: — Gnomon

Well, I suppose I can make some sort of sense of that. But not enough to add up to a philosophical position.

Creativity and Invention: Imagination often precedes innovation and creation. Many of the inventions and creations that shape our world start as ideas in someone's imagination. When these ideas are acted upon and brought into the physical world through effort, experimentation, and implementation, they can become a reality. This process involves turning abstract thoughts into tangible products, technologies, or works of art. — Gnomon

Either we are free all day and every day, or we are not free. It is entirely mundane, not special in any way. But perhaps you just want to change the subject.

Perhaps, but the "cause" of willful action --- as contrasted with physical actions --- is presumed to be within the agent. Otherwise, the action would be pre-determined instead of free-will. :cool: — Gnomon

What is wilful action as contrasted with physical action? In what way is a cause "within" me any different from a cause "without" me? How can an internal cause not determine the action unless it is not a cause or it is in some way special? What reason is there to suppose that an internal cause is in any way special - apart from the fact that it is inside me? (We have opened people up and not found any special causes.)

Remember, the story is told by Plato, not by a third actor. — ssu

Oh, you're imagining that you have discovered a previously unknown manuscript. Who wrote it - Plato, Zeno, Themis, Athene, Zeus? Or a rat, skulking in a corner.

Did he? Or did he try to make an counterargument to Plato? During the time, you tried to make questions that the one answering you would make the argument. So could it be that Zeno was arguing that by Plato's reasoning you get into the silly ideas like the Achilles cannot overtake the tortoise. Or the Arrow cannot move. Remember, the story is told by Plato, not by a third actor. — ssu

I thought it was Zeno who got the silly ideas. But then, perhaps this is a non-standard analysis.

In Abraham Robinsons nonstandard analysis that dog that eats the least exists and is fine. — ssu

So long as it is a non-standard dog, I guess it'll pass muster.

then you get the problem. — ssu

I'm glad of that. It doesn't mean I have any answers.
I'm afraid I have enough trouble getting my head around standard analyses. If I take on non-standard analyses, my head will go pop.

Your second statement goes with the lines of Plato then. Poor of Zeno's dogs. — ssu

Well, I don't know how this works. I have imagination deficiency. Doctors have tried for years to cure me. Don't worry, it's not fatal.

I know that there is no smallest member of a convergent sequence and no largest member of an increasing sequence (I've forgotten the proper term for that.) You may like to consider the possibility that Zeno's dogs don't exist. (After all, he told lies about Achilles and the tortoise.)

It's true that both sequences have a limit, but a limit is not a element of the sequence. So if they do exist they are not members of the pack. The other dogs would tear them to pieces.

So it's kind of a happy ending? — ssu

I suppose it is, if you think the misery of two dogs a satisfactory price for the happiness of the others. I'm sure it would get a majority vote from the dogs.

I would suggest the transfinite system as a home for the other dog - since it's the last one and w (omega) is the limit of the series.

It seemed that the number of the dogs couldn't be counted — ssu

I'm pretty sure that was an illusion. After all, each dog can be counted and the counting can continue for as long as there are any dogs that have not been counted.

There are real mathematical and philosophical issues about infinity. I think they may be insoluble. But philosophers are suckers for an insoluble problem.
The gods, the dogs, the beach and the food all exist but only in your imagination. The conversation between Plato and Zeno happened but only in your imagination. Athena and Themis are proxies for you. The rest of the gods are proxies for those of us who are enjoying the mischief that you have created.
I fear the dogs will starve to death. But they are innocent victims of your imagination and the incompetence of Plato and Zeno. Can you imagine a way to rescue the dogs? Can you resist that picture? Please? (I don't care whether Plato and Zeno starve to death - they're choosing to co-operate with you, so they deserve whatever happens to them. Anyway, they're dead already.) :grin:

It's about whether or not I can actually choose one path or another. — Patterner

That little word actually is interesting. What does it mean? Either I have a choice, or I do not.

I'm just saying that you can't have no ability to choose any but one of multiple equally possible paths and have free will in the matter. — Patterner

In one way, you are right. But there are some kinds of coercion that are compatible with the capacity to choose. Determinism eliminates the capacity to choose, and so eliminates the possibility of coercion.

When the cop arrests me and asks me to hold out my hands for the cuffs, do I have a choice? When I drag myself in to work on a Monday morning, do I go because I have chosen to go? When my opponent forces me to take his rook (castle) in order to get my queen, what choices do I have? When I pay my taxes, what choice do I have? Assume in all these cases that I have a normal capacity to choose.

Coercion usually means forcing someone to do something he or she doesn't want to do. — ssu

Quite so. Does the sun want to rise in the morning?

Finally on 12:20 she explains why she believes that determinism eliminates free will. — ssu

Interesting. Is that because she thinks that determinism forces me to do things, or because choice is meaningless in a determinist framework?

In many occasion giving a prediction doesn't affect what is predicted. That the Earth revolves around the Sun even a hundred years from now is a sound prediction. Giving that doesn't effect the future, the Earth or the Sun. — ssu

Yes. That means that the prediction does not force me to do anything.

Yet they disregard then the "more is different" argument, the emergent properties, and make simply a category error. — ssu

Yes, it is a category error. I'm not sure about emergent properties. There doesn't seem to be much agreement about them and maybe those arguments are giving too much away. Yet we are physical beings, and physics doesn't have exceptions. Understanding that is the problem.

Compatibility does not require total chaotic indeterminism, but only a few short-cuts on the road to destiny. — Gnomon

I get the first half of the sentence. But the meaning of the second half is not at all clear to me. Your diagram in your "Small world model" doesn't help.

Our physical actions may not be free, but our meta-physical intentions are free as a bird, to defy gravity by flapping. "If god intended man to fly, he would have given him wings". Instead, he gave us imagination. — Gnomon

Are you suggesting that an imagined freedom is any substitute for the real thing? Seems like a very poor exchange to me.

Note --- The man is not free --- he can be imprisoned --- but his mind is free : to roam the world of ideas. — Gnomon

No, it is not the case that the man is not free just because he can be imprisoned. If he is not imprisoned, he is free. In case, the freedom to "roam the world of ideas" is no substitute for the freedom to go home to you partner and kids.

3) the causes of voluntary behaviour are certain states, events, or conditions within the agent: acts of will or volitions, choices, decisions, desires etc... — The Chapter you cited entitled Compatibilism

So an action is free if its causes are inside the agent. If the causes of those causes are outside the agent, can we conclude that his acts of will, etc are not free?
By the way, can you identify his acts of will etc independently of the actions they cause to provide the basic empirical information you need to carry out an induction?

Compatibilism is determinism with a slight modification for the sake of appearances and for our language use. It is a position taken because of the perceived need to have some idea of accountability or responsibility for human behavior. — The Chapter you cited entitled Compatibilism

So compatibilism is window dressing - a concession to the ignorant. Why would I be interested in this?

Large societies need predictability, for example when driving in traffic, I think everybody is happy if you predictably stay on your own lane. — ssu

Quite so. Only, if at all possible, I would like to be regarded as only coerced by the law when I do so. Keeping the law means that one could break it.
That nicely reveals some of the complications about freedom.

When, exactly can someone who is capable of being free be said to be coerced? We say a blackmailer coerces their victim, but, from another perspective, the victim collaborates with the blackmailer. When I walk into my favourite bar (pub) and the person behind the bar pours my usual drink for me, I would normally be said to be choosing freely even though I am entirely predictable.

As the sun rises over the horizon, is it appropriate to say that the air is coerced to become hotter? If determinism excludes the possibility of freedom, as it seems to, then it also excludes the possibility of coercion. This is about what are called categories or language games. Certain concepts are said to be inapplicable (neither true not false, but rather meaningless) when applied outside their home language game. How much does the number 2 weigh? Does it weigh more or less that the number 3? Are both numbers weightless? The earth is neither free nor coerced as it orbits round the sun.

It's been long argued starting from J.R. Lucas (1961) and then continued with Penrose that human mind is different because we can understand Gödel's incompleteness theorems and computers cannot, but that argument is a confusing. — ssu

Well, that might be right. Though I would be a bit concerned if people who did not understand Godel were then to be classified as not free.

I don't think LD has any problem in predicting billiard balls as they follow exceptionally well even Newtonian physics. — ssu

But the billiard balls do not roll as they do because LD predicted how they would.

Yet LD has a problem of making an equation when the future depends on his equation, especially the negation of it. — ssu

Well, yes. I think feedback loops are an important part of enabling us to control our actions and hence act freely.

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

We started this discussion because you said:-

In my view both are very useful concepts. I will argue that you can have determinism and free will. — ssu

I think I may have interpreted this in a way different from you. It's complicated. You can't play both language-games at the same time, any more than you can play chess and draughts ("checkers" in the USA, I think) at the same time. The tricky bit is that, while there is no problem about playing both those games on the same board, there does seem to be a problem about playing both language games in the same world. Moreover, while I would like to say that it is just a question of how you consider or articulate the phenomena, I don't think it is as simple as that. So I think there is scope and need to see if some bridges might not be built. But we might need to revise the rules of both games.

It would be reasonable to think that one cannot have one's cake and eat it, but here are some possibilities:-
Here's one possibility. Follow this link to Rubin's vase. It is both a picture of two profiles and of a vase, depending on how you look at it. Because there is definitely just one "it" that you are looking at, there is also a third possibility, that "it" is neither, though it is arguably a picture, even if one cannot say, in the normal way, what it is a picture of. Wittgenstein features this issue, but it was a big topic in the early 20th century in psychology.
Here's another, simpler, possibility. The same events can be a meteorological event, a humanitarian disaster, an economic set-back at the same time.
This is about analogies. None of them is true, all of them are suggestive.

The first point to get one's head around is that it is sometimes very helpful to think of a person as a machine. That doesn't mean they are a (simply) machine. (Nor does it mean that the solar system is a machine). The second point to get one's head around is that although homo sapiens (a misnomer if ever there was one!) is the only animal that is a person (that we know of, so far), other animals have person-like traits, and that we can attribute person-like traits to machines - in fact, it is possible to attribute full-blown personhood to certain inanimate objects or phenomena - then we call them gods. What follows? "Machine" is not simply a classification of objects, but a way of thinking about objects. Similarly "person" is not a simply a classification of objects, but a way of thinking about them.

in what way is a path taken for such causes by a person who comes to an intersection different from a path taken by a boulder rolling down a mountain? — Patterner

The person who comes down the mountain is not in a free fall, as the boulder is - though they might be. Their descent is under control. It's not about which path they take.

You can even innovate, do really something that hasn't been there before in your mind. — ssu

I'm not at all sure this is relevant for our problem. In the first place, the billiard balls can travel along paths they have never travelled before. In the second place, if we are only free when we innovate, then we are in chains for most of our lives.

But for entities that are conscious and sentient, free will is a really great model to use! — ssu

I don't disagree, but I do wish we could stop talking about free will, with all its baggage, and concentrate on freedom.

Case in point, the arrangement of games, as described in Toulmin's article, seems to have nothing to do with 'metaphysics' as traditionally used. — Lionino

Yes. Exactly.

"Metaphysical possibility" is sought as distinct from logical and physical possibility. — Lionino

I'm afraid I couldn't follow your account of this. I'll have to take another look at it later on. But I'm not sure that the project of trying to articulate the Venn diagram is necessarily the best way to go. It may be constraining, rather than guiding, your thinking.

Some philosophers make away with both the a posteriori / a priori and analytic/synthetic distinctions, — Lionino

Yes, but are the philosophers who want to make synthetic necessity among them?

I take the traditional view and accept all those distinctions. — Lionino

I'm afraid that I was brought up in the tradition that says that the analytic/synthetic distinction is the only one that means anything. My dilemma is that can see some sense in the point that that one only applies to language, where a priori applies to knowledge and contingent applies to "the world".

No, the infinite sum is the limit of the sequence of the finite sums. — TonesInDeepFreeze

Yes. Sorry. Careless.

But we don't need to run the code. We can understand the logic of it and so know that there is no consistent answer. It cannot be true, cannot be false, and cannot be anything other than true or false. — Michael

Fair enough. But that's a much better description, IMO. What more is there to say?

No no no! Sorry, I wrote badly. I didn't mean you, I meant in general "Now if you go" referring to people who go for scientism. And I'll change it to be more readable! — ssu

There was no need to do that. It was my misinterpretation of you. But I appreciate the gesture.

I did assume you were endorsing the view you quoted. I should have been a bit more cautious. But I wasn't annoyed or anything. You don't seem particularly upset, so I'm not sure whether an apology is appropriate?

I don't think it is obvious what label we should have for this phenomenon. But I do think there are problems with the proposal. For the record:-

1 I don't see this use of "metaphysical" has any strong relationship to the traditional meaning of the term, so the choice could be regarded as misleading. "New metaphysics" might work.
2 If this is "synthetic necessity", I wonder how we might define "contingent" - the opposite of "necessary" in the traditional structure of these terms.
3 This is classified as "a posteriori" because it is contingent on the relevant rules existing and applying. But all analytic truths are contingent on the relevant definitions (rules of language) existing and applying, so does the term "a priori" have any use?

The following pseudocode provides a demonstration of C3 and is the correct way to interpret the logic of Thomson's lamp: — Michael

Why don't you just run the code and see?
You call it a pseudo-code, but one assumes that you could turn it into real code.

Expecting more of a dictionary would be a mistake. A dictionary is limited to describing words with other words - there's inevitable circularity to it. There's something of a Munchausen Trilemma involved in writing a book full of words describing other words. — flannel jesus

You are quite right. But it's not often that I come across such egregious examples.
.

Now you go too far with applying the scientific method and hold a bit extreme views of scientism, but this usually comes from that the person doesn't understand that other fields do use logic too. — ssu

Dear, oh, dear. I thought it was the causal determinist who was guilty of scientism. I'm more than happy to insist that the methods (and concepts) of science do not apply when thinking about thinking. It's not really a strictly a question of logic, but of a more general conception of rationality. Or, put it another way, of a different kind of syllogism (though it was also invented by Aristotle) known as the practical syllogism.

That said, why should philosophy not have a normative role as well. — Richard B

I don't understand the question. I think that's because norms are not an optional extra in Wittgenstein's philosophy. Perhaps they are not so clearly visible because he is showing through describing.

That collection of quotations was very thought-provoking. Wittgenstein seems to be saying, on one hand, that philosophy is all about description:-

PI 124 “Philosophy may in no way interfere with the actual use of language; it can in the end only describe it. For it cannot give it any foundation either. It leaves everything as it is.”
PI 126 “Philosophy simply puts everything before us, and neither explains nor deduces anything. Since everything lies open to view there is nothing to explain. For what is hidden, for example, is of no interest to us.” — Richard B

But on the other hand:-

What is your aim in philosophy? To show the fly the way out of the fly-bottle. — PI 309

So, a clear description shows the fly the way out. Making a clear description is itself a norm-governed activity, with its own norms and rules and criteria, which philosophy may (rightly) call into question. But these descriptions have a use in the service of the philosophical project - and their contribution to the project is also a criterion by which to judge their success. There is a goal, which (one presumes) is supposed to be a Good Thing. None of these norms are optional extras.
Note that the fly has to do some work as well. It has to grasp what Wittgenstein is showing it for itself. As he says in the introduction to PI:-

I should not like my writing to spare other people the trouble of thinking. But if possible, to stimulate someone to thoughts of his own.

But Wittgenstein has several goes at articulating his project:-

A philosophical problem has the form: ‘I don’t know my way about. — PI §123

There is not a philosophical method, though there are indeed methods, like different therapies. — PI §133

The philosopher treats a question; like an illness. — PI §255

The real discovery is the one which enables me to stop doing philosophy when I want to. The one that gives philosophy peace, so that it is no longer tormented by questions which bring itself into question. — PI § 133

What I give is the morphology of the use of an expression. I show that it has kinds of uses of which you had not dreamed. In philosophy one feels forced to look at a concept in a certain way. What I do is suggest, or even invent, other ways of looking at it. I suggest possibilities of which you had not previously thought. You thought that there was one possibility, or only two at most. But I made you think of others. Furthermore, I made you see that it was absurd to expect the concept to conform to those narrow possibilities. Thus your mental cramp is relieved, and you are free to look around the field of use of the expression and to describe the different kinds of uses of it. — Lectures of 1946 - 1947, as quoted in Ludwig Wittgenstein : A Memoir (1966) by Norman Malcolm, p. 43

He once greeted me with the question: 'Why do people say that it was natural to think that the sun went round the earth rather than that the earth turned on its axis?' I replied: 'I suppose, because it looked as if the sun went round the earth.' 'Well,' he asked, 'what would it have looked like if it had looked as if the earth turned on its axis?' This question brought it out that I had hitherto given no relevant meaning to 'it looks as if' in 'it looks as if the sun goes round the earth'. My reply was to hold out my hands with the palms upward, and raise them from my knees in a circular sweep, at the same time leaning backwards and assuming a dizzy expression. 'Exactly!' he said. In another case, I might have found that I could not supply any meaning other than that suggested by a naive conception, which could be destroyed by a question. The naive conception is really thoughtlessness, but it may take the power of a Copernicus effectively to call it in question. — G. E. M. Anscombe, An Introduction to Wittgenstein's Tractatus, Chap. 12

Whether we are expected to weld these together to form a consistent and complete whole or just regard them as variants on a theme, either to allow different methods for different problems or just to prevent mental cramp, I do not know. Of course, in the end, it is up to us to decide what we will do.

Insofar as one reflectively reasons in order to critique and interpret norms (i.e. rules, criteria, methods, conventions, customs, givens), philosophy is performative. To say, for example, 'one ought to philosophize' does not seem a philosophical statement. — 180 Proof

Does what I have said articulate what you mean here?

PI 130 “Our clear and simple language-games are preparatory studies for future regularization of language--as it were first approximations, ignoring fiction and air-resistance. The language-games are rather set up as objects of comparison which are meant to throw light on the facts of our language by way not only of similarities, but also of dissimilarities.” — Richard B

At first I thought this was inconsistent, harking back to the idea that logic could be the basis of an ideal language, free of all the dross that natural languages carry. But perhaps he doesn't mean re-forming, changing, language, but grasping the order that is already there.

But this is a bit of chicken and an egg: the causal determinist will simply say that a person, thanks to his thinking, reasoning and experience came to this conclusion because of the current situation that was can be traced to the past occurences, which can be then traced back to, well, the Big Bang. — ssu

In fact, when doing a quick search on the definitions of reason and cause, I got:
reason: a cause, explanation, or justification for an action or event.
cause: a reason for an action or condition : motive, something that brings about an effect or a result, a person or thing that is the occasion of an action or state — ssu

Yes, that's a classic example of what dictionaries can do, otherwise known as a circular definition. I believe it is somewhat frowned upon in philosophical circles. Fortunately, we are free to disagree with a dictionary, even if we have to be a bit cautious about it. It doesn't make it easier to articulate what's going on here.

There is a truth here. It is perfectly possible to apply the concepts (language-game) of persons to inanimate objects, and we are very familiar with partial cases - animals (anthopomorphization) - and even applications to inanimate objects (polytheistic gods, personification). It is also perfectly possible - even helpful - to apply the concepts (language-fame) of inanimate objects - machines - to persons and partial persons. So the radical move of applying both language-games simultaneously to everything is just pushing those tendencies to the extreme - and much philosophy depends on tactics like that. (Hume called it "augmentation".)

But I really don't think that my "thinking, reasoning and experience " is particularly amenable to the scientific method (methods, approach). Certainly, much philosophy has derived from those difficulties. Sweeping them all away with a few key-strokes is not an appealing solution.

That's the best I can do for now.

There is no truth of the matter, because it is a matter of deciding how to apply the rules to a situation which they were not designed to cater for. — Ludwig V

Which sequence? There are different sequences involved in the puzzles here. — TonesInDeepFreeze

I was thinking of a term that would apply to sequences in general.

0 is the value at the arguments 1, 3, 5 etc — TonesInDeepFreeze

I think I can work with that. But I see that you used "entry" elsewhere. That's simpler.

I was speaking in the context of the completion times halving. — TonesInDeepFreeze

I didn't realize that is the context. Then most of what I said is irrelevant.

An infinite series that has a sum (some might say the series is the sum) requires first having an infinite sequence (each entry in the sequence is a finite sum) that converges, and the sum is the limit. The sequence whose entries are 0, 1, 0, 1 ... does not converge. However, whatever you mean by 'complete', there are infinite series that have a sum. — TonesInDeepFreeze

I agree with all of that. There is a twist, of course. The sum is not the total addition of all the entries, but the limit of the total addition of all the entries. The total addition of all the entries up to a specific point will converge on/with the sum.

For that matter, I don't think the particulars about buttons, jabbing, or especially about human acts such as fingers reaching to touch a device are relevant, as the problem could be entirely abstract, as what is essential only is that the lamp goes on and off at the increasing rate mentioned, or, for that matter, it's not essential even that it's a lamp or any other particular device (could be clown klaxon going off an on for all it matters) as long as there are alternating states, whatever they may be. — TonesInDeepFreeze

I agree with all of that. That's why I ended up formulating the problem in terms of 1 and 0 alternating. Unfortunately, that doesn't resolve everything. But I need time to work out how to articulate this reasonably clearly. Sorry. I will get back to you.

They hold there is an identity that is metaphysically necessary, and it is metaphysically necessary because it is a a posteriori necessity. — Lionino

Well, I don't want to quarrel about a name. Call it metaphysics or call it a posteriori necessity, my account of the problem derives from Wittgenstein, Ryle and Toulmin. That's what matters.

There is no truth of the matter, because it is a matter of deciding how to apply the rules to a situation which they were not designed to cater for. — Ludwig V

The same comment applies to much of the discussion in this thread as well. Ryle seems to have thought it applies to all philosophical problems, but I wouldn't go that far.

We are being asked about the causal consequence of having carried out a supertask. — Michael

My problem is that I don't understand what carrying out a supertask is. So I can't even think about the consequences of carrying one out. @TonesInDeepFreeze, This is the best that I can do to articulate what bothers me.