• The Argument There Is Determinism And Free Will
    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.
  • Infinite Staircase Paradox
    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?
  • The Argument There Is Determinism And Free Will
    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.
  • Infinite Staircase Paradox
    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?
  • Infinite Staircase Paradox
    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?
  • Infinite Staircase Paradox
    Real numbers are uncountable.jgill
    I see. Why can't I count with natural numbers?
  • The Argument There Is Determinism And Free Will
    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?
  • Infinite Staircase Paradox
    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.
  • Infinite Staircase Paradox
    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).
  • The Argument There Is Determinism And Free Will
    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.
  • Infinite Staircase Paradox
    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 continuumMetaphysician 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.
  • Infinite Staircase Paradox
    Imagining involves a sense image, and this is where the difficulty arises because imagination defers to empirical data.Metaphysician Undercover
    At first sight, that seems to be true. But is the impossibility of imagining a round square based on trying to imagine such a thing and failing? We frequently (in the context of sf fiction, for example, imagine faster-than-light travel between the stars. What picture could possibly constitute imagining it? Or consider @Michael's two-dimensional sensors?
    (I won't bother with the psychologists' empirical claim that people differ in the extent to which they actually make a picture when they imagine something.)

    So the issue is not whether things can be imagined, but whether they can be defined so as to coherently fit into a conceptual structure without contradiction. ..... In this way mathematics removes itself from imagination, and the empirical world associated with it.Metaphysician Undercover
    But people frequently disagree about whether a specific proposition is self-contradictory and/or incoherent or not - as in this thread.

    I don't see the relevance of "+1". The supertasks described here involve an endless division, not adding one in an endless process.Metaphysician Undercover
    The problem for me, then, is that I do not see a relevant difference between "+1" and "<divide by>2" or "divide by>10". (The latter is embedded in our number system, just as "+1" is embedded in our number system).
    So mathematics uses a technique where terms are defined, and the sense image is not necessary. For instance, a non-dimensional point, infinite divisibility, etc.....In this way mathematics removes itself from imagination, and the empirical world associated with it.Metaphysician Undercover
    ... so you don't see a relevant difference, either. I agree with you that the problem arises in applying mathematics to the physical world, specifically to space and time.

    It is this, the idea of dividing a definite section of space and time, indefinitely, which creates the problem.Metaphysician Undercover
    But if that's your problem, you ought to have a difficulty with "+1", because there are an infinite number of non-dimensional points between my left foot and my right foot whenever I take a step. Or are you thinking that "+1" involves adding a physical object to a set of physical objects?
    If you don't have a problem with that, I can't see why you have a problem with a infinite convergent series.
    There are real practical difficulties with the idea that a cheese can be cut up into an infinite number of pieces (which could then be distributed to an infinitely large crowd of people). I don't deny that. But dividing the space that the cheese occupies into an infinite number of pieces is a completely different kettle of fish. It doesn't involve cutting anything up and, hopefully, not imagining cutting anything up either.
  • The Argument There Is Determinism And Free Will
    Can you define "freedom"? Freedom from what?Patterner
    Like Augustine and most of Socrates' interlocutors, I can participate in normal life, but that doesn't mean I can give a definition. The language-games around actions are unbelievably complicated and very difficult to summarize. The same is not true of events.

    Can you give me an example of a free action?Patterner
    Tempting. But it wouldn't be a clear case. Almost everything we do can be described as free from some perspectives and not free from others. I scratch my nose because it is itching. Free or not free? What about going go to work in the morning? or signing a mortgage contract to buy a house/car? or asking a question?

    The important point is that we can meaningfully ask the question about actions, but not about gas leaks or car breakdowns or pandemics or the weather. That's because actions can be free or constrained. The weather is neither free nor constrained - at least in philosophical discussion, which tries to impose a radical distinction.

    Also, by "reasonably reliable", do you mean the casual network is not always reliable? If that is what you mean, can you give an example of it not being reliable?Patterner
    I had an attack of realism, remembering that my car is pretty reliable, but does break down sometimes. Causal determinism is at work either way. The distinction depends on my perspective as a human being. Do we have the same perspective on eclipses? Perhaps, perhaps not.

    The question is this: Did I let go of the pillow in exactly the way I did because all the constituents of my brain - whether we examine them as particles and physics, or molecules and chemistry, or structures and biology, or whatever - acted in the only ways each of them could, all purely physical interactions driven by the physical laws?
    Did I throw the pillow because all the constituents of my brain acted in the only ways each of them could, all purely physical interactions driven by the physical laws?
    The answer to those questions is yes. But the questions are asked in the context of the glass breaking and so lead us to neglect the conceptual difference between the glass breaking (an event) and my throwing the pillow (an action, normally).

    If the answer is Yes, then we are not choosing things any more than the glass is choosing to break exactly as it does, or the debris is choosing to come to rest exactly as it does after an avalanche. We merely have awareness of things that the glass and mountain lack.Patterner
    So you are an epiphenomenalist?
    I don't agree. If the answer is yes, that doesn't justify your conclusion. It defines our problem. If the answer is no, that also doesn't justify any conclusion. It also defines our problem.
  • The Argument There Is Determinism And Free Will
    Most traditional arguments against Fatalistic Determinism are based on Morality.Gnomon
    Yes, and they are less than persuasive for that reason. However, I think that while fatalistic determinism is easy to confuse with causal determinism, it does not pose the same problems. (I'm assuming you mean by "fatalistic determinism" what I think you mean - the ancient form that did not appeal to science and causality, but to logic and metaphysics) Roughly, Laplace's demon is a version of fatalistic determinism and easier to refute on logical grounds than causal determinism.

    It's a feature of Nature that the human mind may be able to exploit in order to impose its will on Nature.Gnomon
    If we think of it like that, we are making a mistake. The human mind is a product of Nature and part of it. Or, to put it another way, to think of Nature as something to exploit perpetuates the practices that have landed us with climate change. Worse than that, although we can and do exploit Nature in some ways, Nature also imposes itself on us - witness climate change and antibiotic resistance. It has to be a balance.

    Lorenz's equations have already been used to explain why the weather is unpredictable. Maybe, in time, they will also reveal why the human mind is unpredictable.Gnomon
    Yes, I'm aware that there are many examples of systems and situations that reveal that the systems at work in the world are much more complex and much less predictable than our classical models have recognized. They do give us a basis for thinking that human life may be, in the end, not incompatible with scientific explanation. But they do not get us there, any more than simple randomness gets us there. I think that the research into self-constituting autonomous systems, feedback loops and ideas like Conway's Game of Life are much more to the point.

    I don't think that unpredictability is a significant phenomenon here. Volcanoes and football matches, not to mention the weather, are all unpredictable. But no-one thinks that free will is involved.

    The determinism holds. But it shows that this determinism isn't at all a limit here.ssu
    Well put. Though perhaps we might say that the causal network is sometimes a limit on what we can do, and sometimes an opportunity to achieve what we want to achieve. Which it is, depends on the context of what we value, what we want, what we need on different occasions. So our attitude to the fact (insofar as it is a fact, as opposed to an aspiration) of causal determinism depends on us, not on what the facts are.

    But that's the incredible thing: there isn't the influence or a controlling force with determinism!ssu
    Yes. I'm impressed by your articulation of this argument. It is very tempting to think that the causal network in our world imposes things on us; we forget that it also enables us to do the things that we want to do, or at least some of them. With respect to our values and desires, it is neutral.

    Now, does this deterministic view of there being your answer 1038, 1039 and 1050 limit what you can write? No. Could they be forecasted? Again no, this isn't simple extrapolation from what has become for.ssu
    Yes. This is essentially the argument against fatalistic or logical determinism, but chimes with the neutrality of the causal network.

    "Chance" and "fate" that has an effect on our lives while others don't,ssu
    I don't think that "Chance" or "fate" have an effect on our lives. "Chance" is just a basket into which we put events that we don't have an explanation for. "Fate" is another basket into which we put the things that actually happen, whatever the explanation may be.
    It's important that "determine" or "determined" or "determinism" has more than one meaning. It can mean "fixed" or "exact"; it can mean "discover" or "reveal"; it can mean "control" or "influence".

    they are trying to convince someone who believes in free will of the strength of their arguments – that a free willist will consider all the evidence and, in the end, choose to believe that determinism makes the most sense.Thales
    Yes, that is self-contradictory. But you don't seem to recognize that the importance of this. Insofar as we are rational, calculating (in the widest sense) animals, with goals and preferences, what we do needs to be explained in particular ways, which are not the same as the ways that we explain the way the world works. There are different, but related, language games here; our problem is to understand how they are related.
    I think we can begin to get a handle on this by thinking about why we consider that computers can do calculations. A physical process can output the result of a calculation. It is clearly possible, but how?
  • The Argument There Is Determinism And Free Will
    Which leaves gaps (junctions?) in the chain of causation for the exercise of personal willpower to choose (decide) the next step.Gnomon
    The orthodox articulation of the debate requires either positing free will as a magical kind of cause that is causally determined and/or a gap in causality that allows this unique kind of event to occur. Neither is at all plausible.

    And that just shows how meaningless the idea is. Because you have to make decisions. That determinism says that with probability 1 you make or abstain from making a decision has no value, because it doesn't give you any more information.ssu
    This is a promising approach, but nonetheless seems to leave our supposedly freely made decisions vulnerable to the apparently controlling force of determinism. It may not give me any information, but it will certainly influence the attitude of others to my decision, and may even influence my own attitude to my own decision.

    The determinist model of you making a choice doesn't help you.ssu
    I think it's more like to hinder me. (There's a classic argument against fatalism, that it tends to make us lazy, since the causally determined outcome will happen "whatever I do" or at least whatever I do will make no difference. I realize it's a muddle, but still...)

    For the hard-core determinist, there's no difference between causes and "actions" performed by "agents". But of course this making the division between causes and actions does understand they have to thought of differently.ssu
    That's certainly true. The practical syllogism, which models rational decision-making about action, is quite different from the paradigm syllogism. Practice syllogism require values, desires &c and lead to action. Neither is true of the paradigm syllogism.
    But that's the point. Thinking about actions (people) is a different language game from thinking about events. But it's not a matter of two different kinds of event, but a different way of thinking about some events. Most philosophers leave the argument there, but that won't do. We have to understand how actions can be (need to be) explained in two apparently incompatible ways - as actions, and as events with causes.

    If that's the key problem - and I'm sure it is - then here are a couple of out-of-the-box thoughts.
    (This will only be a starting-point.)

      1 Freedom is not opposed to determinism; it requires it. We could not act freely if the causal network was not (reasonably) reliable.

      2 The idea that freedom does not apply to causally-determined events is a prejudice of philosophers, in pursuit of their idea of the special cause for actions. Ordinary language is perfectly happy to call such events free, and paying attention to that illuminates what free should mean. Why do we speak of bodies being in free fall? Why do require our wheels and cranks to spin freely? In both cases, we are thinking of what happens if nothing intervenes to prevent it in the context of our lives in the world. Free fall is usually a disaster, so we approach the phenomenon from that perspective - not from the dispassionate perspective of the scientist. Freely spinning wheels and cranks are important for the proper functioning of various machines - again, the human, practical perspective.

      3 The (correct) idea that our brains and bodies are subject to causality is only half the story. The preparation and weighing up of our decisions may have a causal network behind it. If it works properly, we can act freely. When it goes wrong, we don't. In just the same way, when a computer carries out a calculation, success follows when the system works properly and failure follows when it doesn't. It's not about being caused or not. Admittedly, this requires interpreting or explaining the action in the light of the human beings involved in it, and this is not the same view of the world as the dispassionate examination of the workings of the machine (that metaphor is, of course, seriously misleading) that is the universe.
  • Infinite Staircase Paradox
    So we might allow that whatever is not self-contradicting is logically possible, but one logical possibility might be incompatible with another.Metaphysician Undercover
    That seems reasonable. But the question arises whether we can imagine something that is logically impossible. Philosophical practice says no, we can't (thought experiments) and yes, we can (reductio arguments). I suppose if two contradictory statements follow from a single premiss, we can conclude that the premiss is self-contradictory. But then, that's not always obvious, as in this case.

    Infinite divisibility is probably the most useful, but it is incompatible with empirical observation, as these paradoxes show.Metaphysician Undercover
    I'm not convinced of that. I think that the confusion develops from not distinguishing between "+1" as a criterion for membership of the set of natural numbers and as a technique that enables to generate them in the empirical world.
    When we consider the first use, we think of the entire set as "always already" in existence; when we consider the second, we get trapped by the constrictions of time and space in the world we live it. The difficulties arise because it seems on the one hand that we can never specify the entire set by means of applying the algorithm and yet we can prove statements that are true of the entire set. This oscillation between the abstract and timeless and the concrete and time/space bound is very confusing, and, what's worse, it (the oscillation) encourages us to think that an infinite series can be applied to the physical world in just the same way as an ordinary measurement.
    I'm channelling Wittgenstein here. I don't think finitism can make sense of this, but I'm deeply sympathetic to his approach to philosophy.
    That's all wrong, of course. It's only an attempt to point towards an approach.
  • The Argument There Is Determinism And Free Will

    Thanks for the thought. As it happens, I do understand. If one tries to respond to everything, it quickly becomes too much (and I, at least, get muddled). Even if one limits oneself to actual mentions, it still gets too much - especially if some of the replies overlap. But it is nice to get an acknowledgement.
  • Infinite Staircase Paradox
    The purely imaginary concepts of mathematical objects is allowed to penetrate the theories of physics to the point where physicists themselves cannot distinguish between the real and the imaginary.Metaphysician Undercover
    Yes. I am neither physicist nor mathematician, and I'm not sure that a bystander like me has a proper basis for an opinion. But after the discussions on this thread, I understand the point.
    I think there's another bugbear at issue here - the idea that whatever can be imagined is at least logically possible.

    We can assume that they simply exist in their places and are two dimensional or we can assume that they are placed just before the runner reaches the next designated distance.Michael
    Why don't you just stick to the mathematics? If we ask about any specific stage of the series, we can calculate exactly what time, as you show:-
    Say we run at a constant speed. We pass the 100m sensor at 12:00:10, the 150m sensor at 12:00:15, the 175m sensor at 12:00:17.5, and so on.Michael
    That corresponds to what your screens will show. That's all perfectly clear and correct.
    It is also perfectly clear that we cannot place screens at each stage, even with your modifications, because we cannot complete the series. That is reflected in the fact that we cannot calculate the distance and time of the last stage, or the penultimate stage, or the one before that.
    These so-called thought experiments are just distracting fairy tales.
  • Infinite Staircase Paradox
    To avoid the problem , you just assume the impossible. There is a limit to the number of sensors which can exist in that space, depending on the size of the sensors, Because a sensor takes up space. Or, are you assuming that an infinite number of sensors can fit in a finite space?Metaphysician Undercover
    They can if they are infinitely small. Is it possible that you can imagine that? Is there any argument that will settle the issue either way?
  • Why The Simulation Argument is Wrong
    I presume that 'the sims' are the humans in the simulation.
    The hypothesis is that the sims are us, so tautologically they're as self-aware as you are.
    If 'the sims' is a reference to the simulation software, program, or process, well that's a different answer since people are not hypothesized to be any of those things.
    So the humans are entities created by the software? Then how are they not real people and not simulations of anything?
    Particles interact and do their thing. Your experience is a function of matter interactionsnoAxioms
    Quite so. But my experience is real experience, not a simulation of experience. So the people "inside" your software are real people.
  • The Argument There Is Determinism And Free Will
    how is such a "choice" is of no any greater value or interest than is the final arrangement of the rocks and dirt when an avalanche settles?Patterner
    You are missing a trick here. Sure, the final arrangement rocks and dirt is not of any interest. But the outcome of the causal sequence of events in a calculating machine is of interest, because it instantiates a calculation, because we arranged it that way. Again, there is a causal sequence from the keys you press to my reading what you write, and that is extremely interesting. In their various ways all causal sequences are of some interest, but some are more interesting than others. The causal sequences in my brain are much more like those in a computer than they are like the final outcomes of an avalanche.
  • Infinite Staircase Paradox
    The sequences may approach 200m and 12:00:20, but because there is no sensor on the 200m finish line neither 200m nor 12:00:20 will display on the screen.Michael
    Assuming you maintain a constant speed, you will pass 200m at 12:00:20, as you point out. That is also the point I was after.
    One might think that the screen will display the penultimate distance and time. But that is not defined. Nor is the distance and time before that defined. Nor is the distance and time at any other stage defined. You had this discussion a while ago, as I remember it. You can't count backwards because the argument doesn't give you the information you need to do so.
    Ordinary arithmetic will not give you an answer at the limit, or at any other specified stage counting forwards, but not at any stage defined by reference to the last stage of the series. I didn't read the case you proposed carefully enough. I had in mind the Achilles case. My bad.

    Yes, ultra-finitists reject mathematical induction as a proof method, but that is a rather extreme position.SophistiCat
    Thanks for the confirmation. I don't think that position is at all plausible. But are there any non-extreme positions around this topic?

    I was referring to how folk who are unfamiliar with specialist terms that are based on words in the ordinary language try to make sense of those terms: they interpret them in light of the more familiar senses of the words. Naturally, this doesn't always work. Misinterpretations happen even in familiar contexts, and they are all the more likely in an unfamiliar domain. And as with neologisms, some just aren't going to like the coining for one reason or another, even when they understand the context. But that alone shouldn't be a barrier to understanding and accepting specialist terms.SophistiCat
    I think most people in this day and age can cope with specialist jargon. Many of them speak one of the many jargons available. There's an additional problem here, that the context is so startlingly different from common sense.
  • The Argument There Is Determinism And Free Will
    That doesn't help now an outdoors event planner that is looking arranging something for summer 2026.ssu
    The problem is that people don't distinguish between different ideas about determinism. Saying "there are certain days next year when it will rain" and saying "It isn't possible to identify which days will have rain for next year" are very different claims. Both are true. Both can be described as determined or not determined. Though actually, in a case like that, we would retreat to probabilities.

    Determinism doesn't say much.ssu
    That's true. But I think that's because everyone is treating it as an empirical hypothesis, forgetting that not all propositions are empirical hypotheses. Effectively, determinism defines what a complete and final explanation of an event (past, present or future) would be. It's a "regulative ideal", to steal a phrase.
  • Infinite Staircase Paradox
    Anyway, this is just a specialist term. It doesn't have to "make sense" to be cogent and useful.SophistiCat
    There isn't a problem with specialist terms. But "cogent and useful" is both cogent and useful as a definition of "make sense". I would rather not have to try to find another definition. "Cogent and useful" can mean different things in different contexts.

    you only need to establish a procedure of how you would do it, or even just prove that such a procedure exists.SophistiCat
    I don't disagree. But half the problem, for us ordinary folk, is understanding that procedure, especially if, as in this case, it can't actually be carried out. The difficulty is understanding the difference between "and so on" as laziness, when it could be carried out, but one is too lazy or busy to actually do so, and "and so on" in the context of a mathematical induction, when it can't. In the background, I understand, there are people who have doubts about the validity of mathematical induction.

    Locations are in physical space. This isn’t a math problem yet.Fire Ologist
    I think that's too simple. It's about the applied math. The issue is about applying the math to physical space (and time). After all, there is no problem about applying ordinary arithmetic to these situations.

    When we reach the 200m finish line, what distance and what time is displayed on the screen?Michael
    Sometimes, I am so slow I cannot believe it. The answer to the question is available, if only you would apply ordinary arithmetic to the problem. All the paradox proves is that an analysis in terms of a convergent series does not apply to the question.

    The thought experiment is only to examine the internal consistency of continuous space and time, not the practicality of carrying out the experiment.Michael
    It is as well not to confuse the conclusion you want to draw from the analysis with the point of the thought experiment. After all, Zeno did not draw your conclusion from it. Nor do I.
  • Infinite Staircase Paradox
    In the supertasks article, they mention a “hotel with a countably infinite number of rooms”. Right there, at the premise, what does “countably infinite” point to? That’s nonsense. That’s a square circle. We don’t get out of the gate. The infinite is by definition uncountable,Fire Ologist
    When I first saw the phrase "countably infinite", I thought that was absurd, and I still think it is an unfortunately ambiguous description of what it means. I would put it this way - any (finite) part of the infinite set can be counted, even though the whole of the set cannot be counted in one go. But I think that Wikipedia also puts it in a reasonably clear fashion.
    Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time, although the counting may never finish due to an infinite number of elementsWikipedia
    Though I would have said "even though the counting may never finish due to an infinite number of elements."

    If this is a mathematics conversation then why are we ever referring to stairs, lamps, hotels, switches, starting lines at races??Fire Ologist
    I read somewhere that Hilbert never discussed his hotel after the casual mention of it in a paper, even though it provoked enormous discussion. I'm pretty sure he invented it only to help people realize what infinity means. All these cases play in the border country between the mathematical and the physical; they are entirely imaginary (not in the sense that they are possible, but only in the sense we can imagine impossibilities). Consequently, the normal rules of possibility and impossibility are suspended and people think the fact that they can in some sense imagine them means that they are, in some sense, possible.

    when Zeno says Achilles must first travel half, he forgot that Zeno already accounted for the whole so he could claim whatever shorter distance to be some fraction in relation to that whole.Fire Ologist
    I agree with that and for that reason think that to say that the conclusion or limit of the set can be anything at all is misleading. In a convergent series, specifying the limit is essential to defining the series. But that doesn't mean that the function that generates the set can generate it's own limit. In fact, if it could, it wouldn't be an infinite set.
    The other problem is that Zeno, and most people since him, lose track of the difference between an analysis and a dissection. If I measure the length of the race-track as being 10 units long, the race track is completely unaffected; my measurements are an analysis. If I then cut the race-track into 1-unit lengths, the race track is affected, and what I have done is to dissect it. One can analyze the race track in terms of a given convergent series. But that does not exclude other analyses, including my analysis of it as 10 units long.
    My final issue with Zeno is that he forgets that if Achilles is travelling at a constant speed, he will take less and less time to travel each segment of the series, approaching an infinitesimally small time as the segments become smaller and smaller. And, of course, since he can cover a segment in an infinitesimal amount of time, covering an infinite number of them in a finite time becomes less of a problem.
  • Is atheism illogical?
    Sure, they can be realized in actions, but they are not necessarily.Janus
    Surely you don't mean that love or concern may never shows themselves in any actions at all? The moral worth of that is, let us say, debatable.

    I think there are higher and lower states of consciousness.Janus
    There's that higher/lower metaphor again. But I can't see just what you mean without examples.

    I'm not advocating removing the anyone's rights. That would be in the domain of legal policy and that is not what I am addressing.Janus
    Those laws have been developed from what many people think are moral imperatives. Think of Kant's categorical imperative.

    what I've been saying is that one who is concerned only with their own interests is morally lower than one who is concerned with their own interests and the interests of others.Janus
    I'll just substitute "worse" for "lower". OK? Certainly most selfish people are hypocritical at some level, since their personal interests depend on mutual recognition of other people. My property is my own, but only because other people have the same rights as I do.
  • Infinite Staircase Paradox
    Others do, like Zeno's and Bernadete's.Michael
    I don't think that either of them suggests that space or time may be discrete. In any case, you seem to accept that that's a different topic.

    Such sequences may make sense in the context of abstract mathematics but they do not make sense in the context of a lamp being turned on and off.Michael
    That seems to me to be a good diagnosis of the issue with supertasks. All that is then needed to free people from the illusion that walking to the fridge can be mathematically analysed in many ways, none of which affect physical reality.

    I think there are abstract things and concrete things. But physics these days pushes hard on the nature of physical things. Is there a philosopher in the house?fishfry
    The trouble is that many philosophers seem to be hypnotized by physics, and seem to forget that physicists develop their theories and conduct their experiments in ordinary human reality.

    At the very least you've got work to do in "dephysicalising" or "physicalising" the intuitions regarding number and processes you have.fdrake
    Spot on. The difference between analysis (in the head) and dissection (on the bench) seems obvious, but turns out to be quite difficult to trace in certain situations.
  • Infinite Staircase Paradox
    There's no miracle. Motion isn't continuous; it's discrete.Michael
    Your argument doesn't prove that.
  • Is atheism illogical?
    Values are related to action, but they are also related to concern, love, intention and judgement.Janus
    Of course. But concern, love, intention and judgement are all realized in actions.

    For me ethical values are rooted in caring about how we are to live. My earlier talk in terms of higher and lower was meant to show that I think living with care, concern and love for others and for the whole environment, the whole Earth, is a higher form of life than living without such care.Janus
    If you had said that living in that way was a better form of life, I would entirely agree with you.

    I am not sure what you mean by "eradicating people of certain kinds" so I can't comment on that other than to say that I think certain kinds of people certainly need to be restrained; namely those who possess little or no self-restraint or even self-awareness.Janus
    I'm not sure why I express my thought in that way. I was referring to the holocaust in WW2. Of course it is right to restrain people sometimes. The problems arise when you think that some people are not really people.

    I don't agree with dehumanizing people in the extreme, but I do think it is fair to see people who have no such care as being less than fully human. By human I mean something like "able to transcend being ruled by mere self-interest and the passions of the moment, able to be aware of and care about one's effect on other beings, both human and animal and even plant".Janus
    Even "less than fully human" is problematic. There is a concept of "human rights", which aims to establish minimal norms for the treatment of all human beings. Once you have branded a group of people as "less than fully human", you have licensed excluding them from those rights. As so often, a lofty and entirely praiseworthy enterprise is undermined by the exclusion of our enemies. This issue underpinned the battles about the rights of the "common man", women, slaves, and so on.
    I don't for a moment think that you intend to do this. But this kind of language is very, very prejudicial to values that we ought to hold dear.

    By human I mean something like "able to transcend being ruled by mere self-interest and the passions of the moment, able to be aware of and care about one's effect on other beings, both human and animal and even plant".Janus
    In a way, there is nothing wrong with that. Limiting one's scope to narrow self-interest is certainly a bad thing. But it is right to look after one's own interests. I don't see that it is a "lower" value than helping other people to look after theirs. What is wrong is not looking after and helping others as well.
    You are forgetting that it is quite easy to do terrible things in pursuit of a selfless ideology - indeed, I sometimes think that a set of values is often the basis for worse things than self-interest - like tyranny, torture and genocide.
  • Infinite Staircase Paradox
    Saying infinity is a concept doesn't actually tell us anything about it. I don't even know what it means to say infinity is a concept. Is there anything that isn't a concept?fishfry
    Yes, of course you are right. It is no more help than saying that a table is an object. I was trying to re-instate the line between, let us say, a mathematical reality and a physical reality - or between mathematical possibility and physical possibility. (I think we are agreed that what creates the difficulties here is the confusion of the two in the definition of the supertask.)

    Remember the mathematical induction you brought up before?Michael
    I suggest that what creates the problem here is the idea that the mathematical induction is a process that takes time. Perhaps the temptation to do this derives from the analogy with a Hume's inductive process that creates so many issues about empirical laws or generalizations. But once you pose the challenge of actually executing the process to the bitter (and non-existent) end, or think that you can stipulate what happens at the end, you are enmeshed in contradictions. (Achilles' race with the tortoise has exactly the same issues, but in the medium of space rather than time.) This leads us to think that there is some sort of miracle involved in arriving at the fridge to get a beer. But the mathematical induction is one analysis of many that can be applied to either space or time, and does not in any way affect our walking about our kitchen or arriving on time at a party.
  • Is atheism illogical?
    When I say I don't believe in god, I also hold that I don't have a robust idea what the idea of god/s even means. It's pretty hard to believe in something which seems incoherent or unintelligible. But not understanding - and therefore not believing - can not be held as knowledge (I would have thought).Tom Storm
    That's just about where I'm at. That's why I'm taking an interest in this thread, but not adopting a position. I do have various theories, but none of them would be of any interest to a believer. For a start, I'm not merely interested in monotheism. Polytheism (which historically, I think preceded monotheism and derives from it.) is pretty clearly a sort of personification of important elements of ordinary life. "God" in modern religions seems to be a keystone for a way of life and a system of values, rather than an empirical reality. There's also the idea that religion is part of the system of social control that became necessary when cities and agriculture developed. Finally, there are those self-certifying experiences that people have.

    There are many potential versions of god - from the magic space wizard (so beloved by Trump supporters), to the highest value in the hierarchy of values, as per Jordan Peterson.Tom Storm
    I wasn't aware of Jordan Peterson's theory. It seems like a version of Aristotle's theory of the Supreme Good.

    Wouldn't it be the case that to be an atheist or a theist varies radically according to the kinds of god you are or are not believing in, which must surely also impact upon the belief knowledge/question?Tom Storm
    I would agree with that. There's a wide range of different views in circulation. Far too many to classify into just four propositions - unless you think that God is an empirical hypothesis. It's curious, though, that there seem to be both theists and atheists who prefer that approach, no doubt in the belief that favours their case.
  • Infinite Staircase Paradox
    That's not true, as I explained here, and as I alluded to above. It is not just the case that whether the lamp is on or off after two minutes is undefined but that the lamp cannot be either on or off after two minutes.Michael
    I'll think about that.
  • Infinite Staircase Paradox
    I disagree with your claim that with respect to Thomson's lamp we can simply stipulate that the lamp is on after two minutes.Michael
    @fishfry will speak for himself. But I think the point is that, even a convergent sequence, which does have a limit, does not have a end or last step defined - indeed, is defined as not having one. That means that any answer whatever is equally valid and invalid.
  • Is atheism illogical?
    Firstly, I am not thinking in terms of imperatives, but in terms of concern or care; our human capacity to care about justice, beauty, freedom, truth, creativity, love and so on. I see these concerns as being truths about the human condition, about being human. Those who care nothing for such things are considered to be not as fully human, and I think rightly so.Janus
    Well, I can see that there's a difference, but let's not get picky about language. Values are related to action in a way that facts are not. That's the important difference.
    I'm aware that many people like to see ethical values as rooted in the human condition living in the world. I'm very sympathetic.
    However, we do dehumanize people who behave very badly - and it is not difficult to find people doing things that pass my (and, I hope, your) understanding. However, I think this is a mistake. The people who set up a huge administrative and industrial system to eradicate people of certain kinds from their society (to give just one hackneyed example) are human beings. We are capable of heroism and horror. We should not pretend otherwise even though the recognition is not comfortable.
    And there's the problem. If values are rooted in the human condition, how come people behave like that?

    This is why the moral debate between 'objective' and 'subjective' morals is so utterly ridiculous and intractable. They aren't either, independently: They are. together, states of people's minds.AmadeusD
    "States of people's minds" suggests that you are either a relativist or a subjectivist. Or have I misunderstood? I do agree, however, that the binary classification between objective and subjective is most unhelpful when applied to ethics.

    B. Atheism = I do not know whether there's a God;AmadeusD
    (sc. B) Isn't the salient part of atheism's position, I don't believe in a god? It is for me.Tom Storm
    And by the same token isn't a theist someone who believes there is a god? I have a number of theist friends, including priests and rabbis, who would actually count as agnostic theists. They would never say that they know god exists. They would say they believe and have faith.Tom Storm
    There is something of a battle going on at the moment between belief and knowledge as the appropriate category. The (mistaken) idea that the difference between belief and knowledge means that saying one believes in God implies some sort of uncertainty, so people who strongly believe in God want to claim to know, while people who don't believe in God (or don't believe that belief in God can be rationally justified) cannot possibly concede that. It's very confusing.
  • The Argument There Is Determinism And Free Will
    Your reasons determine your decision. I don't see a distinction between "physical" and "non-physical" causation so the act of reasoning is just a type of causal chain.Harry Hindu
    Yes. But the difference is that a reasoning chain justifies its conclusion, whereas a normal, non-reasoning chain does not.
  • Why The Simulation Argument is Wrong
    If two things are doing the exact same thing, it is 'X' if a human does it, and it is not X if a machine does it. That's what I got from it.noAxioms
    I think that is what Searle is saying. Except that he doesn't consider raising an arm to be "the exact same thing" if it is done by you or me and if it is done by a machine. The issue is what the difference is. From what I've seen is that he thinks that there is some causal difference between the two. I think the difference is only partly empirical, but the difference between two different language-games. One, the game that the concept of a person defines; the other the game that the concept of a machine defines.

    OK, by those two strangely unaligned definitions, if Bostrom's hypothesis is true, then your experience of fear is real, but not genuine.noAxioms
    Yes, there is a problem there.

    but it seem that the fear reflex is triggered exactly by recognition of something that can be characterized by dangernoAxioms
    Could we just say "recognition of something as dangerous" or "recognition of a danger"? Anyway, if I've understood what a simulation is supposed to be, it involves feeding me information that is false. False information can easily trigger real or genuine fear. So the fear is not actually appropriate in that situation, but it would be misleading to call it simulated because that suggests that I am not really afraid. I'm not sure what the right word would be.

    You said:-
    It would need an insane amount of power and memory, but a relatively trivial code base.noAxioms
    I said:-
    That's just a version of Laplace's demon. Hand-waving.Ludwig V
    You replied:-
    I don't see that. For one, there is no power requirement for a simulation at all, except the impatience of the runners of the simulation. As for memory, why would a deterministic simulation need any more memory than a non-deterministic one? They would seem to have similar requirements as far as I can see.noAxioms
    I don't understand what you are saying. It may well be true. But I don't care about the difference between a deterministic simulation and a non-deterministic one. I do care about the difference between reality and a simulation of it.

    As do most people. If determinism is true, then you still disagree, but the disagreement isn't free. I also want to point out that my personal opinion isn't one that supports determinism, but that doesn't mean the view is 'hand waving' or that it's wrong.noAxioms
    Well, I don't really think that determinism is just hand-waving. It is much more serious than that.

    This is completely false. 1, I have shown an example just above (Norton) where classical mechanics does not do this. 2, Our universe is not classicalnoAxioms
    None of the interpretations of physics, not even the fully deterministic ones, are consistent with the claim made above by Laplace.noAxioms
    Well, at least we are agreed that Laplace's demon is out of date.

    Do you know what determinism is? I suspect otherwise.noAxioms
    I used to know, but then I did a bit of reading and now I don't. But everybody else does seem to know, or think they know. If determinism is not about physics, - and the SEP does say that it is not - then what is it about? Or is it perhaps as out of date and the demon?
  • The Argument There Is Determinism And Free Will
    What would a decision that was forced feel like compared to one that was freely chosen?Harry Hindu
    Have you never done something that you didn't want to do - sometimes something you had decided not to do?
    You may have felt that you did it without deciding to do it.

    it would feel natural to reach the decision you madeHarry Hindu
    If it felt like that, it was probably based on reason, as opposed to some causal chain.
  • The Argument There Is Determinism And Free Will
    I agree with his claim that seeing ourselves determined in this reductive way by our past leads to more ethical, compassionate behavior toward those who commit acts of violence and other anti-social behaviors than religiously based notions of free will, which tend to embrace harsh, retributive forms of justice.Joshs
    You may or may not be right about those empirical claims. I wouldn't know. But do they constitute an argument for believing that determinism is true?

    What is lacking is the concept of reciprocal, relational determinism, which puts the organism in dynamic touch with its environment on the basis of its moment to moment functioning. In this way of thinking, our present actions are still the result of a determined history, but they don’t simply regurgitate pre-assigned properties.Joshs
    That's certainly an advance on traditional forms of determinism.

    I still believe that we should hold people responsible for their actions. Holding others responsible has an effect on theirs, and others, future behaviors, which is more of the point of punishment, not necessarily to take revenge on past behaviors but provide reasons to behave differently in the future.Harry Hindu
    If determinism is true, people's behaviour is not governed by reasons, but by causes. Similarly, holding people responsible is never possible if determinism is true.
    BTW, the empirical evidence is that what deters people from committing crimes is not the severity of the punishment, but the likelihood of getting caught.
  • Infinite Staircase Paradox
    It's more than that; the lamp can't be on and can't be off, even though it must be one or the other. This is a contradiction, and so therefore the supertask is proven impossible in principle.Michael
    Does the difference matter?
  • Why The Simulation Argument is Wrong
    If Bostrom's hypothesis is true, and your definition of 'genuine' doesn't include simulated cognition influenced by simulated chemistry, then your emotion is indeed not genuine. That's the best I can answer without a clear definition of 'genuine' in this context.noAxioms
    Genuine=Not simulated. If I'm experiencing fear, the fear is real.

    I suppose one could employ wordplay to come up with a scenario illustrating one but not the other, but it seem that the fear reflex is triggered exactly by recognition of something that can be characterized by danger.noAxioms
    But my point is that the recognition and the reflex response are both the fear. Both causally and phenomenologically.

    As do most people. If determinism is true, then you still disagree, but the disagreement isn't free. I also want to point out that my personal opinion isn't one that supports determinism, but that doesn't mean the view is 'hand waving' or that it's wrong.noAxioms
    Well, I don't really think that determinism is just hand-waving. It is much more serious than that.
    It would need an insane amount of power and memory, but a relatively trivial code base.noAxioms
    Isn't that hand-waving? It looks very much like it to me. So does Laplace's description of his demon. In addition, his thought-experiment describes predictability as opposed to determinism.