Metaphysical Madness

In a recent comment, William J. Murray wrote:

Slightly off topic, but relevant

Well, let’s discuss that (all of that comment) here in a new topic where it won’t be off topic.

WJM began that comment with:

There is no way to talk about “things” unless things exist for us to talk about, and unless words mean something in context and not something else. Unless we mean to say something, and not something else. Unless concepts describe something, and not something else.

As a mathematician, I talk about the square root of minus 1.  When mathematicians first talked about that, it was assumed to not exist.  But now most mathematicians would say that it does exist, perhaps in some Platonic sense.  It is actually important to electronics, the technology that we are using when we post on the Internet.

Over 400 years ago, people talked about phlogiston.  It was considered important, and was the basis for some serious scientific research by J.B. Priestley.  These days, we say that phlogiston does not exist and never existed.  We come to this conclusion, partly as a result of the research of Priestley, though he himself continued to defend the idea of phlogiston.

At one time, people seriously talked of the luminiferous æther.  It was considered real enough for Michelson and Morley to devise a now famous experiment to measure the æther drift.  Today, we say that the æther does not exist and never existed.

These examples clearly suggest a problem with what WJM says are the requirements for talk.

Let me include the remainder of WJM’s comment:

Slightly off topic, but relevant: There is a common denominator I’ve noticed in several threads from several posters that is very interesting and, IMO, important. When talking about intelligence, concepts of reality, logic, etc., many posters here take the tack that such things are subjective to human perspective (anthropocentric concepts) that may or may not apply to other “intelligent” beings, or to other perspectives of reality. Logic, it is apparently being argued, is really nothing more than a subjective map humans anthropomorphically apply to their experiences, which may or may not be a “true” description of reality (even though for there to be a “true” description of “reality”, reality would have to be an identifiable thing, requiring the LOI to be valid in terms of its relationship to “reality”.)

So, I’m going to coin a term: hyperskeptical anti-anthropocentrism, or being skeptical of the human perspective to the point of embracing irrationality, or HAA for short.

HAA would be the natural extension of atheistic materialism and the heir to the Copernican Principle, where Earth, and by extension humans, are “nothing special”. Our grip on reality would be nothing more than an evolutionary trait, like scales or hair, neither “true” or “not true”, just an aid to our survival differential. In that sense, a false belief is better than a true belief if a false belief aid more in our survival differential. Logic, epistemology, ontology, sound premises – nothing more than species-centric adaptations produced by mindless interactions of molecules. We can no more know “truth” than an amoeba or a cactus; what we consider to be “true” is just a result of interacting molecules.

Rationality, technically, is based on logic. Logic is fundamentally rooted in axioms accepted as necessary; once one dismisses the necessary validity of those axioms, they have necessarily given up rationality. They can re-define what it is to be reasonable or rational (perhaps by appealing to consensus), but when it comes to logic, they have abandoned reason.

And so we have these claims about how we cannot expect alien intelligence to be like human intelligence when producing a symbology that corresponds to the universe, because they might “see” and consider an entirely different universe than humans do. Their logic might not be the same. They might have 4-sided triangles, and relational distances between objects represented in symbols might be something entirely different than scale of some sort. Two moons orbiting a planet might be symbolically represented as 5 objects around a centered object. Or other intelligences might not identify one thing from another at all. I’m sure that all of life could exist just fine being unable to discern dinner from rocks from the moon, or predator from prey from indigestion.

You either believe that humans are capable of deliberately discerning true statements about the world, or you do not. If you do not, I suggest your presence in a debate forum cannot be construed as intrinsically anything more than a monkey flinging feces around. If you consider logic nothing more than an evolutionary feature that helps in our differential survival, then you necessarily consider flinging feces, killing off the young of our competitors, and consuming one’s mate after copulation equally sound “arguments” to make.

Making an argument that logic is not necessary, or is just an anthropocentric feature that doesn’t necessarily have anything to do with reality, or that some things don’t have to be logically reconciled or supported, is itself an argument defeated by the content of your argument.

So, you can fling some feces (words) around. So what? So can everyone else. How about this view: I’m right, because I say so. If we are going to abandon logical principles where it suits us, that is as good an argument as any.

I will say more about that in comments to this thread.  I wanted to keep contentious issues out of the main post.

I never was quite sure what “metaphysics” refers to, but I’m pretty sure that WJM is making some strong metaphysical claims there.  Hence the title of this thread.

[A note to the site owner:  I put this in Philosophy of Science and Theism/Atheism categories.  They are the closest that I could find, but neither is at all close.  I don’t seem to have the privileges needed to create new categories.  Please feel free to fix the categories for this post.]

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108 thoughts on “Metaphysical Madness

  1. I don’t think we need to have a “rigorous model of reality” in order to test our models. Heck, if we did have such a model, we wouldn’t need science — we’d have the Truth of Things in our hairy little prehensile paws.

    The best argument for ‘convergent realism’ (the asymptotic-approach-to-reality) is this one, I think: what we can empirically confirm is that one model allows for better predictions than another model. But why does it make better predictions? Well, maybe it just does, and that’s the end of it, full-stop. Or maybe not. Convergent realism states that one model makes better predictions because it is closer to the nature of things than the models we’re comparing it with. The claim that one model is closer to the real than another model is not an empirical claim — that’s a philosophical claim about the models in light of the empirical claims that they generate.

    That’s good enough for me, at any rate.

    Just so we can keep track of the different positions at play in this conversation: I’m quite happy to endorse convergent realism, and I’m quite happy to admit that convergent realism is how we make sense of the idea of ‘correspondence’. But I’m not an Aristotelian, or Platonist, or whatever — my views are very close to those of Hegel, though I’m no Hegelian, either. I think of myself as being a pragmatist, and a naturalist; convergent realism is how I make sense of correspondence in light of pragmatism and naturalism.

    As for how we compare models, in the details — well, that’s the beauty of science, and I’ll let the actual scientists here talk about it. I don’t think the law of non-contradiction has much to do with how we compare models, though of course it has a lot to do with how we think about rationality. The comparison of models is one of the tasks undertaken by the community of rational inquirers as that community itself develops, over the course of both evolutionary and cultural history.

    Best,
    Carl

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  2. Carl Sachs: I don’t think we need to have a “rigorous model of reality” in order to test our models.

    I’m putting on my mathematician’s hat. In order to say that a sequence converges to a value, we have to know that the value exists.

    If we have an infinite sequence, and it can be shown to have certain nice properties of convergence, we can say that it converges to a possibly ideal point. The ideal point need not exist for that.

    If we only have a finite sequence, the most we can say is that it has the appearance of converging. And perhaps that’s the best way to look at the “asymptotic” assertions. Then, theoretically speaking (mathematical theory, that is), there’s the possibility that reality is not even finitely describable. It could still be that science is converging. But that would require that reality is countably describable (as a limit of a countable sequence of finite descriptions). Then there’s the other possibility, that reality is a kind of projective limit. This is more general than a sequence, and does not imply that it is countably describable.

    This mathematical way of looking at it is perhaps a bit academic. Scientists are pragmatic. They are looking to find descriptions that are good enough for our use. We don’t actually need perfect descriptions.

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  3. Carl Sachs: I don’t think the law of non-contradiction has much to do with how we compare models, though of course it has a lot to do with how we think about rationality.

    The LNC is a model. So is the LOI. Discard either and we’re incapable of comparing a model to itself since it is what it isn’t.

    Just the same Platonic Idealism, and Convergent realism are models. And I hardly think you need a scientist to come in and tell which works better.

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  4. Neil Rickert: It could still be that science is converging.

    I’m not sure what you’re trying to say with your analogy. Are you stating that it is possible that reality turns its nose up at the Axiom of Foundation (Science in the descent)? Or do you mean that reality is tree structured, that we are the root, and that we’re headed for the leaves? Or the converse of either?

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  5. Neil,

    Neil Rickert: I’m putting on my mathematician’s hat. In order to say that a sequence converges to a value, we have to know that the value exists.

    I’m curious as to what you make the following. It’s an excerpt from something I was working on a few months ago. It’s a contrast between Rorty and Jay Rosenberg (philosopher of science).

    “I now want to turn to a contrast between Rorty and another prominent Sellarsian, Jay Rosenberg. Much like Rorty, Rosenberg notices that picturing is vulnerable to what he calls “the Archimedean Dilemma”: how can we specify a limit to conceptual change that is rich enough in content to constrain our accounts of that change, but which doesn’t simply borrow that content from the here-and-now? Rosenberg argues that we should “grant that there can be no system of concepts which is both framework-neutral and descriptive” (Rosenberg 2007a, 65). Yet whereas Rorty can see no viable solution to the Archimedean Dilemma, Rosenberg attempts a solution. However, Rosenberg’s solution comes at an extremely high cost that bears indirectly (but significantly) on the fate of the concept of epistemic progress.

    The heart of Rosenberg’s solution lies in the contrast between two mathematical conceptions of a series: the Weierstrauss condition for convergence and the Cauchy condition for convergence (Rosenberg 2007a, 65-70). The latter, but not the former, allows us to define approximation of a limit when the limiting term is not a member of the converging series. Analogously, Rosenberg contends that if we think of scientific progress in terms of the Weierstrauss convergence, we will be committed to positing an end to inquiry – Sellars’ CSP – which Rosenberg, along with Rorty, holds is impossible. However, if we construct a different conception of scientific progress modeled off of the Cauchy convergence, then we hold that “[t]he degree to which two theories approach one another can be measured by the absolute numerical magnitude of the correction factors which must be introduced into applications of the strict counterparts of predecessor laws to arrive at the values determined by their successors” (ibid., 69). And doing so, Rosenberg argues, means that we can escape from the Archimedean Dilemma.”

    Best,
    Carl

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  6. In that sense, a false belief is better than a true belief if a false belief aid more in our survival differential.

    Am I the only one that thought “Religion!” when they read that?

    Our grip on reality would be nothing more than an evolutionary trait, like scales or hair, neither “true” or “not true”, just an aid to our survival differential.

    “Nothing more than…”? We’re most likely here to argue the point in part because of that minor “evolutionary trait”. W V O Quine put it rather better, though:

    Creatures inveterately wrong in their inductions have a pathetic but praise-worthy tendency to die before reproducing their kind.

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  7. Maus: The LNC is a model. So is the LOI. Discard either and we’re incapable of comparing a model to itself since it is what it isn’t.

    In my parlance, a model of X tells us why the observed regularities of X obtain, to the extent that they do. So I have simply no idea what it means to say that logical laws are themselves models. Models of what? What are their domains? What do they explain?

    Maus: Just the same Platonic Idealism, and Convergent realism are models. And I hardly think you need a scientist to come in and tell which works better.

    I don’t think of Platonism or convergent realism as models. I think of them as metaphysical systems that provide ways of thinking about what our models of empirical reality are showing us. We need scientists to build the models, run the experiments, collect and interpret the data, and so on — all the excellent things that scientists do. As for philosophers — well, if we’re needed here, it would be to help scientists and non-scientists think about how to understand the success or failure of a model, or set of models.

    Carl

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  8. Carl Sachs: I’m curious as to what you make the following.

    Note that I only quoted enough to get a link to your post.

    I was thinking along the lines of the Cauchy convergence criteria when I wrote that last post. However, it doesn’t quite work. In order to apply those criteria, you need a common metric that applies to all of the approximations, so that you can measure their difference. And I don’t think that fits scientific change, particularly Kuhnian scientific revolutions.

    For the idea of a projective limit, see this wikipedia page, but I suspect the math is a bit heavier than we really need for this topic.

    Here’s another way of looking at science. Imagine an old building in need of repair. The first thing that the repair crew would do, is construct a scaffolding around the building.

    We can look at scientists as constructing a scaffolding around reality. I guess you could call it an intellectual scaffolding, since it isn’t physical. Then we can talk about the scaffolding as a proxy for talking about reality. Part of science is concerned with goodness of fit – making sure that the scaffolding fits well. And part of science is concerned with measuring the scaffolding as a way of finding facts about the reality that the scaffolding approximates.

    A Kuhnian revolution is when you decide to reconstruct the scaffolding with a fresh design that fits better. And Kuhnian normal science is extending the existing scaffolding.

    Where possible, scientists try to build that scaffolding with a mathematical structure. The brain seems to be satisfied with something more ad hoc.

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  9. Carl Sachs: In my parlance, a model of X tells us why the observed regularities of X obtain, to the extent that they do.

    If you consider the qualitative explanatory framework a model, then: Yes, absolutely. If we’re talking about a model in the sense of: These are the regularities we have found, then not so much. Hopefully that clears up where I’m coming from.

    Carl Sachs: As for philosophers — well, if we’re needed here, it would be to help scientists and non-scientists think about how to understand the success or failure of a model, or set of models.

    I spend a lot of time dissing Philosophistry for a number of reasons. Not least of which is that Philosophy is absolutely critical to the scientific endeavour. Indeed, Science is no more interesting then what happens when you bolt empiricism onto Philosophy as one whole. We would get all the same results even if we forcibly (Impossible, but roll with it) divorced them into lab techs and dreamers. And we’d still have an critical need for both.

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  10. Neil Rickert: Oh, nice quote mine there.

    Huh? Is there a need to quote the entire post in the thread in which the post occurs? If you’re terrified of clarity, as a mathematician, then that’s fine. Just say so.

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  11. Maus: Huh? Is there a need to quote the entire post in the thread in which the post occurs?

    No. But when you quote only a minor inconsequential remark, and the rest of your post seems disconnected from what it is supposedly replying to, it does seem a bit strange.

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  12. Neil Rickert: No. But when you quote only a minor inconsequential remark, and the rest of your post seems disconnected from what it is supposedly replying to, it does seem a bit strange.

    Well, no of course you don’t do such things with the neighbor’s children. But I am a bit shocked that you would claim that you do lewd things with barnyard animals. And I fail to see what relevance that has to your addled analogy about infinite sequences.

    —————————————

    1) Given that you reject the LNC we know you have absolutely no objection here. After all the words on this, and everyone else’s, computer display arrived there over the internet from the storage on the webserver. Thus it is plainly true that you have claimed a fetish for livesock which we can all see is right there precisely because it is not.

    2) Counterfactually, if you accept the LNC and are a mathematician then you quite obviously know what a ‘tree’ is and what the ‘Axiom of Foundation’ is. Likewise, on the latter you understand its relevance to infinite series. So there are two cases. In the first you are in incompetent at mathematics. In the second you are incompetent at English and fail to understand what “I’m not sure what you’re trying to say with your analogy.” means. At least one must be true under this scenario.

    3) Counterfactually, if you accept the LNC and indeed are a mathematician and competent at English then you clearly understand the terms used. And so your responses remain sophist twaddle. This seems to be the most likely after you stated that non-sequitors imply X, where ‘imply’ is meant to be understood as not ‘does not imply’.

    Are there any self-contradictory and not-self-contradictory cases I have missed here?

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  13. Neil Rickert:
    If reality has a structure that is independent of us, then there is no way of us knowing that structure.We would all be in the position of robots – mindless mechanical systems with no ability to discern truth independently of what was innately encoded into our mechanisms

    I’m not sure if I’m taking this paragraph out of context, but it struck me in reading it as if it was a complete thought. If so, I have to disagree with it.

    Reality has a structure that is independent of us, although we are not independent of it. Because of that one-way independence, we really do have no way to know that structure with complete certainty. But that does not make us mindless robots. What’s “innately encoded into our mechanisms” is a general-purpose fact-finding algorithm, and that allows us to explore the structure of reality in an iterative and progressive sense. This seems to me to be what Popper was getting at with falsification and the concept of versimilitude. It’s not necessary to know exactly what reality is in order to know that there is a reality, because it announces itself every time it confounds our expectations.

    I don’t think WJM’s ideology needs another ideology in order to confront it, and I think the claim of “no independent reality” is just as much ideological as is the claims of ID.

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  14. William J. Murray:
    So here’s a question:how can any argument that makes the case that truths about reality are unknowable be anything other than sophistry and rhetoric? You can’t live, think, or argue as if truths about reality are unknowable.You can’t even argue that it is true that truths about reality cannot be known. You cannot even argue that they most likely cannot be known without asserting a truth about reality.

    The same is true of LOI arguments; you cannot even express an argument about something without applying the LOI to what you are making a case about, otherwise nobody has any idea what you’re talking about – or even, for that matter, what you’re trying to say, if the LOI isn’t applied to words and concepts.

    What’s the point in arguing with people who aren’t even making truth claims?Are we flinging feces at each other or appealing to emotion or some other manipulative fallacy? Are we just barking to hear ourselves bark? Arguments are either attempts to discern true statements from false, or they are nothing more than either elegant dances or barroom brawls.

    I think you would find it useful to read Karl Popper’s Conjectures and Refutations, as it addresses these questions far more deeply than I could begin to.

    ‘Course, it was a long and tiring slog for me to read — it’s more than a weekend’s lite fare.

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  15. llanitedave,

    llanitedave: “Reality has a structure that is independent of us,..”

    I think a good working definition of “reality” would be, “Mankind’s perception of the environment he operates within”.

    That should hold whether reality is an absolute to-be-discovered structure on one extreme, all the way to a human interpreted universe on the other, and any point in-between.

    This physical reality would look the same no matter which viewpoint we have, but in one case, it serves a secondary purpose as evidence for a designer.

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  16. Toronto:
    llanitedave,

    I think a good working definition of “reality” would be, “Mankind’s perception of the environment he operates within”.

    That should hold whether reality is an absolute to-be-discovered structure on one extreme, all the way to a human interpreted universe on the other, and any point in-between.

    This physical reality would look the same no matter which viewpoint we have, but in one case, it serves a secondary purpose as evidence for a designer.

    I don’t see how it holds across the board, since “Mankind’s perception of the environment he operates within” changes as his operations evolve. Reality can change, perhaps, but not necessarily in response to our understanding of it. And our understanding can change, but not necessarily in response to changes in reality.

    My own working definition of reality is “That which confounds our expectations”, but I don’t claim that makes it any more quantifiable. The reason I invoke Popper in discussions like this is because, like him, I think our only direct experience of reality is in discovering what it is not. A positive and definitive description of what it is will forever elude us.

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  17. William J. Murray: At least you’re using the proper terms of equivocation! You can’t actually assert that reality is unknowable, because that would demonstrate your self-contradiction too clearly.

    William, I would be grateful if you would address my entire post,or at least the entire sentence from which the part you quoted was taken! What I wrote, in full, was:

    I think you are dichotomising a continuum. I would maintain that reality is unknowable – we do not have direct access to reality. However, we have models of reality and we can check those models against data. The better our models fit our data, the closer we know they are to reality.

    There is no self-contradiction here, that I can see. Please point out precisely where you think the self-contradiction lies.

    Except for the truth-correlation claim that we approach reality asymptotically, as it were.

    I’m struggling to understand your point here, but perhaps I see it. You are equating “reality” with “truth”. I think that is equivocation, actually – not deliberate, but perhaps it is a clue to our misunderstandings here. I think it is perfectly true, for instance, to say that pi is an irrational number. I think that truth is perfectly knowable. But the value of pi, in decimal form, is not knowable – the “reality” if you like of the value of pi in decimal form is something that we can only approach assymptotically. Every new digit we learn adds to the accuracy of our decimal model of pi, but we can only get ever closer, we cannot reach the “reality”.

    Asimov’s better example is that our models of the curvature of the earth asymptotically approach the reality of the earth. And we can test the closeness of fit against data. But we can never reach that reality because a model is always a model. Therein lies its usefulness. We use models to generalise – we want them to cover many cases, predictably, and the price of that predictability is some degree of error.

    Can we agree to distinguish what I am calling “truth” from “reality” in this way? It lies behind the old saying that proof is for math and alcohol, not science. It also IMO underlies our perennial argument about “objective truth”! The clash I think is between empiricism and metaphysics, probably.

    I guess I’m a natural empiricist.

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  18. Elizabeth: Can we agree to distinguish what I am calling “truth” from “reality” in this way?

    Then when you said:

    Elizabeth: Asimov’s better example is that our models of the curvature of the earth asymptotically approach the reality of the earth.

    You didn’t mean at all that the reality of the Earth is that it has a curvature. Indeed, it could be a cube. That’s obviously absurd of course. But the point is that ‘truth’ is simply what is. A ‘true statement’ is one that simply claims that what is, is. Per WJM, if we assert that reality is unknowable then we cannot assert the reality that the Earth is not a cube after all.

    I think this is just a case of talking past each other over different definitions of just what ‘truth’ is.

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  19. Addenda: It’s worth noting that if our models asymptotically approach reality then there must necessarily be something to approach. It is necessary that reality itself be constant and stable enough for us to approximate it by any manner. Or we’re stuck stating that we’re getting better at approximating worse; or nothing at all.

    To even be able to state ‘the earth is more round or less round than…’ requires that it remain more round or less round than. To even make a judgement on the matter requires not that our theories approach reality, but that our theories approach the LOI, LNC, and the rest of the discredited Greek nonsense. And that the discredited nonsense is asymptotically approaching reality.

    It’s often stated that a theory should be accepted because it makes useful predictions. But if the LNC, and LOI, do not make useful predictions then it is entirely certain that every scientific theory must, by necessity, makes less useful predictions than that. If then the LNC, and LOI, are so much nonsense then too it follows that everything else is as well.

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  20. Maus:
    Addenda: It’s worth noting that if our models asymptotically approach reality then there must necessarily be something to approach.It is necessary that reality itself be constant and stable enough for us to approximate it by any manner.Or we’re stuck stating that we’re getting better at approximating worse; or nothing at all.

    Absolutely. And the fact that our models converge at all is good evidence, I’d say that there is something they approach! I’m no solipsist, and I think the evidence against solipsism is the very fact that our models converge.

    To even be able to state ‘the earth is more round or less round than…’ requires that it remain more round or less round than. To even make a judgement on the matter requires not that our theories approach reality

    Yes indeed.

    , but that our theories approach the LOI, LNC, and the rest of the discredited Greek nonsense.And that the discredited nonsense is asymptotically approaching reality.

    Don’t understand this part though!

    It’s often stated that a theory should be accepted because it makes useful predictions.But if the LNC, and LOI, do not make useful predictions then it is entirely certain that every scientific theory must, by necessity, makes less useful predictions than that.If then the LNC, and LOI, are so much nonsense then too it follows that everything else is as well.

    I think you are making a category error here. The rules of logic are not theories, they are, well, rules. They are part of a system of rules, like math (well, they are a kind of math) in which propositions can be proven. Science isn’t about proving things, it’s about making models. We use math and logic as tools but they are tools for model-making, not the models themselves. There is a big difference.

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  21. Elizabeth: The rules of logic are not theories, they are, well, rules.

    This is the category error that keeps being made. By way of example it has been stated routinely that “2+2=4” is general abstract nonsense. And yet I can state, without mathematical hieroglyphics, that “two and two together are four all told”. More than that I can take two stones from the left of me and two stones from the right of me and put them together in front of me, noting that I have one pile of four stones. I suggest you try this personally if you are in doubt to this idea.

    What linguistic gyrations we use to describe it are entirely irrelevant unless you hold that the vocalizations of primates manifest reality through air pressure differences. In which case I’d like to request a song that constructs me a Chevrolet. And whether or not mathematics, as a technical field, uses specific linguistic constructions to represent the physical act of you playing with pebbles doesn’t make rocks disappear into fatuous mental entities. We communicate such things with language and we can also believe astounding nonsense. But acknowledging both of those doesn’t make the Earth pop into cubeness.

    Same same with the LNC and the LOI. That logicians represent these things, currently, with mathematical hieroglyphics does not make the linguistic issue disappear. Nor does the disappearance of the general linguistic issue make the reference to reality disappear. Reality is contradictory, or not, and the LNC and LOI are only expressions of our approximation of that.

    But if reality is contradictory then stating that we observed a mutation means that we observed one mutation that both occurred and did not. And if it’s just as well to state that we’ve approximated reality by arbitrarily picking one conclusion as our preference then it’s just as well to state that we’ve approximated reality by arbitrarily picking the other. That is, mutations are fatuous mental nonsense just as with basic addition.

    But if it is arbitrary, because the LNC makes no approximation of reality at all, then it is just as true that Darwinism is a better approximation as it is that ID is a better approximation. And, of course, that it is just as true that both are worse. Just the same we know Asimov was smoking dope as we cannot better approximate the ’roundness’ of the Earth because it is both round and not-round simultaneously by any metric we could pick.

    Therefore, we have proven that the Earth is flat.

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  22. Maus: This is the category error that keeps being made. By way of example it has been stated routinely that “2+2=4” is general abstract nonsense. And yet I can state, without mathematical hieroglyphics, that “two and two together are four all told”. More than that I can take two stones from the left of me and two stones from the right of me and put them together in front of me, noting that I have one pile of four stones. I suggest you try this personally if you are in doubt to this idea.

    2+2=4 is a rule invented to summarize experimental data such as you describe. It works in many situations, but it is not universal. Other rules might be applicable in other situations. For instance, modular arithmetic has 2+2=0 if you do addition modulo 4.

    You can perform an experiment with a wall clock, for which you have to apply arithmetic modulo 12. If its hands show 6 o’clock and you move them 8 hours ahead they will show 6+8=2 (mod 12). Try it!

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  23. Elizabeth: I think you are making a category error here. The rules of logic are not theories, they are, well, rules. They are part of a system of rules, like math (well, they are a kind of math) in which propositions can be proven. Science isn’t about proving things, it’s about making models. We use math and logic as tools but they are tools for model-making, not the models themselves. There is a big difference.

    Liz,

    You will be pleased to know that your perspective was shared by the great mathematician Vladimir Arnold, who considered math to be an extension of natural sciences. Here is a brief excerpt from his lecture On teaching mathematics given in Paris in 1997.

    The scheme of construction of a mathematical theory is exactly the same as that in any other natural science. First we consider some objects and make some observations in special cases. Then we try and find the limits of application of our observations, look for counter-examples which would prevent unjustified extension of our observations onto a too wide range of events (example: the number of partitions of consecutive odd numbers 1, 3, 5, 7, 9 into an odd number of natural summands gives the sequence 1, 2, 4, 8, 16, but then comes 29).

    As a result we formulate the empirical discovery that we made (for example, the Fermat conjecture or Poincaré conjecture) as clearly as possible. After this there comes the difficult period of checking as to how reliable are the conclusions .

    At this point a special technique has been developed in mathematics. This technique, when applied to the real world, is sometimes useful, but can sometimes also lead to self-deception. This technique is called modelling. When constructing a model, the following idealisation is made: certain facts which are only known with a certain degree of probability or with a certain degree of accuracy, are considered to be “absolutely” correct and are accepted as “axioms”. The sense of this “absoluteness” lies precisely in the fact that we allow ourselves to use these “facts” according to the rules of formal logic, in the process declaring as “theorems” all that we can derive from them.

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  24. Systems of logic are either true by definition,i(n which case they are trivial) or they are true by experimentation and evidence (in which they are limited to a range of phenomena or propositions). When you try to extend axiomatic reasoning to worldly phenomena (whether somethings exists or not) you leave the realm of absolutes and enter the realm of empiricism.

    The existences of Jupiter and the moon, are as well established as anything in our experience, but they are not ideals. When you add the phrase “in the same sense” you are abstracting them. Your question is no longer about physical objects, but about propositions in your axiomatic system.

    “In the same sense” is a subtle form of equivocation. It is changing the definition of terms in midstream.

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  25. llanitedave: Reality has a structure that is independent of us, although we are not independent of it.

    I took WJM’s claim to be about categorial structure (division into categories), and not about physical structure.

    To illustrate, we divide the land mass into nations and states within those nations. There are some natural dividing lines, such as rivers and coastlines. But we often don’t follow those natural dividing lines, and instead make up our own.

    Sure, there are aspects of reality could be said to be natural divisions. But we are not obliged to follow those when we structure the world into categories. We might sometimes follow those natural divisions for pragmatic reasons. But that still lives it as our decision, rather than something that is forced on us by reality.

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  26. Relevant experiment:

    Elizabeth said:

    The clash I think is between empiricism and metaphysics, probably.

    Can anyone here tell me what the problem with that statement is?

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  27. I would maintain that reality is unknowable – we do not have direct access to reality. However, we have models of reality and we can check those models against data. The better our models fit our data, the closer we know they are to reality.

    If you have no direct access to reality, how do you know that what you are modeling is reality?

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  28. Elizabeth: The clash I think is between empiricism and metaphysics, probably.

    Personally, I have problems with the idea of a “clash between empiricism and metaphysics” — usually, we think of empiricism as a position about how we acquire knowledge, and we think of metaphysics as an account of reality.

    But here’s another way of putting the point: maybe we should be “metaphysical agnostics” or “metaphysical quietists” –that is, maybe we should adopt an attitude towards metaphysics which holds that metaphysical questions simply cannot be answered, or can’t be answered well enough to do us any good. Maybe our attitude towards metaphysics should be of sheer indifference! (Note: that is not my attitude — I take metaphysics very seriously — I’m just indicating that there’s nothing intellectually irresponsible about not taking it seriously.)

    One could adopt indifference towards metaphysics as a result of empiricism — as Hume did — but one could change the theory of experience and of knowledge without changing the attitude towards metaphysics. So it’s not an out-and-out clash between empiricism and metaphysics.

    Carl

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  29. One could adopt indifference towards metaphysics as a result of empiricism

    Can anyone tell me what the problem with this statement is? Hint: it’s the same problem as with Elizabeth’s statement:

    The clash I think is between empiricism and metaphysics, probably.

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  30. William J. Murray: If you have no direct access to reality, how do you know that what you are modeling is reality?

    Because our models are predictive, and we compare our predictions against data.

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  31. Maus,

    ” Elizabeth: The rules of logic are not theories, they are, well, rules.

    This is the category error that keeps being made. By way of example it has been stated routinely that “2+2=4” is general abstract nonsense. And yet I can state, without mathematical hieroglyphics, that “two and two together are four all told”. More than that I can take two stones from the left of me and two stones from the right of me and put them together in front of me, noting that I have one pile of four stones. I suggest you try this personally if you are in doubt to this idea.

    2 + (2 * 2 ) = 6 but, ( 2 + 2 ) * 2 = 8.

    Where in nature do you find your brackets?

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  32. Carl Sachs: But here’s another way of putting the point: maybe we should be “metaphysical agnostics” or “metaphysical quietists” –that is, maybe we should adopt an attitude towards metaphysics which holds that metaphysical questions simply cannot be answered, or can’t be answered well enough to do us any good.

    That pretty much summarizes my view of metaphysics. I think I would add “There is no need to answer metaphysical questions.”

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  33. William J. Murray: Can anyone tell me what the problem with this statement is? Hint: it’s the same problem as with Elizabeth’s statement:

    I took this to be the attitude adopted by Hume (also by Rorty, though on somewhat different grounds). So why don’t you tell us what you think the problem is with Hume’s attitude towards metaphysics?

    Carl

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  34. Maus: This is the category error that keeps being made.By way of example it has been stated routinely that “2+2=4” is general abstract nonsense.And yet I can state, without mathematical hieroglyphics, that “two and two together are four all told”.More than that I can take two stones from the left of me and two stones from the right of me and put them together in front of me, noting that I have one pile of four stones.I suggest you try this personally if you are in doubt to this idea.

    I don’t have the slightest doubt as to this idea, but the fact that you think I might tells me we have not succeeded in communicating with each other. Can you explain why you think your demonstration contradicts what I have said?

    What linguistic gyrations we use to describe it are entirely irrelevant unless you hold that the vocalizations of primates manifest reality through air pressure differences.

    I don’t understand what you are saying here. Language itself is a reality-modelling symbolic system, a little less precise than math and logic, but none the worse (and in some senses better) for that. But I don’t know what you even mean by “manifest reality”. “Manifest” is means to “show”. When we observe the world, we do so by means of interpreting signals from the world that arrive at our sensory organs – we construct a model of reality, use it to predict the next set of sensations, and, if our model fits the new data, we retain the model; sometimes we tweak it slightly. My point is that we are always working with models and what “manifests itself” to us is an approximate but testable model of the reality before us, constructed by our brains. And, interestingly, we can also communicate our models to each other by means of language – you just induced me to make a model monkeys gibbering in trees.

    In which case I’d like to request a song that constructs me a Chevrolet.

    We seem to be talking past each other.

    And whether or not mathematics, as a technical field, uses specific linguistic constructions to represent the physical act of you playing with pebbles doesn’t make rocks disappear into fatuous mental entities.

    Mental entities aren’t “fatuous” and I did not say, or imply, that math makes rocks disappear.

    We communicate such things with language and we can also believe astounding nonsense.But acknowledging both of those doesn’t make the Earth pop into cubeness.

    You seem to think I think things I don’t think.

    Same same with the LNC and the LOI.That logicians represent these things, currently, with mathematical hieroglyphics does not make the linguistic issue disappear.Nor does the disappearance of the general linguistic issue make the reference to reality disappear.Reality is contradictory, or not, and the LNC and LOI are only expressions of our approximation of that.

    I’m not understanding what you have written here, I’m afraid.

    But if reality is contradictory then stating that we observed a mutation means that we observed one mutation that both occurred and did not.

    Well, I think we’ve agreed that reality isn’t contradictory at the macroscopic level – or even at the observed level. A mutation may be the result of a quantum event, but if there is an alternative reality in which it did not occur, then we don’t have access to it. We are stuck with a reality in which that a cat that is either dead or alive, not a reality in which both exist.

    And if it’s just as well to state that we’ve approximated reality by arbitrarily picking one conclusion as our preference

    We don’t “arbitrarily pick one conclusion”. What makes you think anyone said we did?

    then it’s just as well to state that we’ve approximated reality by arbitrarily picking the other.That is, mutations are fatuous mental nonsense just as with basic addition.

    I’m afraid you aren’t making any sense to me, and if you are parodying someone else’s nonsense (mine?) then I ‘m not recognising the parody!

    But if it is arbitrary, because the LNC makes no approximation of reality at all, then it is just as true that Darwinism is a better approximation as it is that ID is a better approximation.

    I am not saying, and I’m not aware that anyone is saying, that the LNC makes an approximation to reality. I don’t think it’s an approximation at all. I don’t think it’s a model. I think it’s effectively a definition – of an object: something that cannot both exist and not exist at the same time. That’s fine, and it allows us to make inferences about things we can both agree are objects, and which therefore cannot both exist and not exist at the same time. I don’t know what you are saying about Darwinism or ID. Both are explanatory models of reality. To test which is the better model, we have to derive predictions from them. The better model is the one whose predictions best match the data.

    And, of course, that it is just as true that both are worse.Just the same we know Asimov was smoking dope as we cannot better approximate the ’roundness’ of the Earth because it is both round and not-round simultaneously by any metric we could pick.

    I think you have misunderstood Asimov! And also the LNC. And also the nature of approximation.

    The earth’s surface can be, as Asimov says, approximated by a plane. This works excellently for small scale maps. For larger maps we have to be more precise, and use a non-zero approximation of curvature. Interestingly, when the Humber suspension bridge was built, the engineers designing the steel cables had to allow for the fact that the tops of the pylons were about 8 inches further apart at the top than at the bottom, even though both were vertical. In other words, unlike in most engineering projects they could not use a flat-earth model.

    This has nothing to do with any violation of the LNC. It has to do with our models only being an approximation to reality – but we can gauge the degree of approximation by comparison between our models and our data.

    I doubt the Humber engineering model was exactly right, but it must have been a pretty good fit of model to data, because the bridge works just fine.

    Therefore, we have proven that the Earth is flat.

    We don’t prove things in science, as I keep saying: we model them!

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  35. You can’t be a metaphysical agnostic, because metaphysics is the discipline of examing both what we consider being to be, and of what knowledge is and how we gain it, which is what is wrong with both Carl & Elizabeth’s statements: empiricism is a branch of metaphysics. You don’t get to sneak empiricism as the de facto means of gaining knowledge about reality as if one didn’t require any metaphysical principles or justifications for that perspective.

    Which is why the constant reference to empirical evidence, data and fact as if that was how one corroborated a claim about reality is self-referential nonsense. Empiricism can only “corroborate” claims about “reality” if one defines reality as that which can be empirically corroborated. Empirical predictability and repeatability is only a measure of “how close to reality” our “asymptotic” efforts bring us if we define reality as that which is empirically predictable and repeatable.

    You cannot escape metaphysical assumptions by calling them something else.or by ignoring them, and then acting like your assumptions about reality, what knowledge is and how we gain it are simply the default position. You can act and phrase your words as if you are circumventing or avoiding a metaphysical assertion or premise, but you cannot help but imply them every time one goes outside of solipsist language (I think, It seems to me, It suggest to me, I feel, etc.) and makes claims about knowledge and “what reality is”. And even solipsism is a metaphysical position about being and knowledge.

    “Reality is not knowable” = metaphysical claims about reality and knowledge.

    “Logic is a set of rules humans impose on reality” = metaphysical claim about reality and knowledge.

    “Logic are intrinsic principles of reality that are self-evidently true” = metaphysical claim about reality and knowledge.

    “Our ideas about reality can be tested empiricallly” = metaphysical claim about reality and knowledge.

    Empirical data is how we can converge upon true statements about reality = metaphysical claim about reality and knowledge.

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  36. “There is no need to answer metaphysical questions.”

    … if one is content to just assume their metaphysical premises are rational and correct.

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  37. Even simpler, you can’t claim to be a metaphysical agnostic because it necessarily implies that you have a way of knowing something about your state of being.

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  38. Empiricism can only “corroborate” claims about “reality” if one defines reality as that which can be empirically corroborated.

    Well, now. I don’t define “reality as that which can be empirically corroborated”.

    But let’s try to cut some of this thicket down. Here is my basic view of Life, the Universe and Everything:

    • 1. There is a “reality” “out there” that is “out there” since before humans or other living things have existed to observe it, and which will continue to be “out there” long after we are all gone.
    • 2. One of the things that living things do is navigate their world. Animals, in particular, navigate really quite broadly, and one animal, us, has even navigated as far as the moon in person, beyond the outer planets by proxy, and beyond the observable universe by modelling.
    • 3. By “navigate”, I mean figure out where things are and what we’d have to do to get there, even if it isn’t in fact practically possible. It involves making predictive models as to how the world will look after we’ve taken certain actions in regard to it. This is as true whether the action is a change of gaze direction or the sending of a space vehicle to Saturn.
    • 4. It also involves constantly tweaking those models in the light of the differences between what we predict and what we actually find when we get there.
    • 5. The fact that we can do this at all suggests that the reality “out there” consists of predictable events. I know they are predictable because I can predict them. This makes predictable reality accessible, if only by means models of incrementally increasing accuracy.
    • 6. There may also be an unpredictable reality out there. But I have no access to it by means of my predictive skills. If it exists, it will have to find some other way of manifesting itself.
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  39. Neil Rickert: I took WJM’s claim to be about categorial structure (division into categories), and not about physical structure.

    To illustrate, we divide the land mass into nations and states within those nations.There are some natural dividing lines, such as rivers and coastlines.But we often don’t follow those natural dividing lines, and instead make up our own.

    Sure, there are aspects of reality could be said to be natural divisions.But we are not obliged to follow those when we structure the world into categories.We might sometimes follow those natural divisions for pragmatic reasons.But that still lives it as our decision, rather than something that is forced on us by reality.

    Ah, so as I feared, my response was to a different context than your intent. That happens.

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  40. William J. Murray: If you have no direct access to reality, how do you know that what you are modeling is reality?

    You never “know” in an absolute sense. That is why all reality claims are conjectural, and all must be refutable to be useful. But as Elizabeth said previously, the fact that our models converge strongly indicate that there is something to converge to.

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  41. About ‘things’.

    The LNC does not just refer to ‘things’. Only one half of the ‘Law’ refers to a thing, the other half refers to a mental concept, a hypothetical. The Moon that exists is a material body made up of minerals, molecules, atoms and quarks. It has mass and weight and can be seen by anybody with eyes and a clear view of the night sky. The Moon that does not exist is not a thing, it is an imagination, or a memory, a mental construct caused by electric currents in someone’s brains. It has neither mass nor weight and can’t be observed by anyone but the person doing the imagining.

    I see no reason why both could not be true at the same time.

    fG

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  42. faded_Glory,

    The point being made by quantum theory is that our intuitive notion of existence is deficient at the extremes of size and energy. It is not that logic is defective; it is a that certain propositions that seem intuitive do not correspond to reality.

    I like the discussion of color, because to anyone who has studied physiology, color is the poster child for an artifact of our perceptual system. An object does not have color as a property. We see color. We can be made to see color by alternating patters of monochromatic light. We can be made to see in-between colors by blending monochromatic lights. We see divisions in a rainbow that are not really there. If we zoom in on a spectrum, we see a continuum rather than clear divisions. there is no dividing line between red and green.

    http://www.ersimages.com/ecards/hue.jpg
    http://www.ersimages.com/ecards/hue2.jpg
    http://www.ersimages.com/ecards/hue3.jpg

    What quantum theory seems to say is that the existence of objects as objects lies on a continuum of probabilities.

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  43. You never “know” in an absolute sense.

    Which is why I didn’t qualify my use of the term “know” with “absolutely”.

    But as Elizabeth said previously, the fact that our models converge strongly indicate that there is something to converge to.

    Which doesn’t answer the question why one would think they are “converging” on, as Elizabeth said, a “reality out there”, much less frame her statement as knowing it to be so (note lack of “absoultely” qualifier).

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  44. Petrushka:
    Systems of logic are either true by definition,i(n which case they are trivial) or they are true by experimentation and evidence (in which they are limited to a range of phenomena or propositions). When you try to extend axiomatic reasoning to worldly phenomena (whether somethings exists or not) you leave the realm of absolutes and enter the realm of empiricism.

    The existences of Jupiter and the moon, are as well established as anything in our experience, but they are not ideals. When you add the phrase “in the same sense” you are abstracting them. Your question is no longer about physical objects, but about propositions in your axiomatic system.

    “In the same sense” is a subtle form of equivocation. It is changing the definition of terms in midstream.

    This a profound point, and a key to understanding a lot the disputes regarding logical structures and their metaphysical implications (or not). It is precisely the language you identified (‘in the same sense’) that is the source of equivocation. It’s easy to miss because it ostensibly seeks univocality. But that univocality itself only obtains in the propositional framework. It’s not univocal with respect to the dynamics of nature, or our extra-mental reality.

    Wish I’d thought of that, and had pointed it out. Kudos.

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  45. William J. Murray: Which is why I didn’t qualify my use of the term “know” with “absolutely”.

    Which doesn’t answer the question why one would think they are “converging” on, as Elizabeth said, a “reality out there”, much less frame her statement as knowing it to be so (note lack of “absoultely” qualifier).

    That’s a pretty weak quibble. If you took what people wrote more at face value and less as a projection of “sophistry and rhetoric”, you might be able to make stronger points.

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  46. William J. Murray: Empirical data is how we can converge upon true statements about reality = metaphysical claim about reality and knowledge.

    Just to be clear about the various positions at play here: I haven’t claimed, or even implied, that I object to this. I would phrase it somewhat differently, that’s all.

    Indeed, that’s just what I was getting at when I said, above, that there’s a presupposition of metaphysical realism in order to license the following inference:

    (1) theory A makes better predictions than theory B, therefore
    (2) theory A is a better map to (or model of) reality than theory B

    Without the presupposition of metaphysical realism, all we have is claim (1). Which is fine, for almost all intents and purposes.

    The only point at which I take issue with William, and side with Neil, is over the question as to whether it makes sense to be a metaphysical quietist — to simply not have any metaphysical views one way or the other — and if doing so is intellectually irresponsible. I share Neil’s attitude that there is no need to have an attitude towards metaphysics — it’s just that I want one.

    Carl

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  47. My metaphysical view is it’s turtles all the way down, by which I mean there is no fundamental force or particle, nothing that can be fully comprehended by human intelligence.

    It’s more of a guideline than a Law.

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  48. olegt: Other rules might be applicable in other situations. For instance, modular arithmetic has 2+2=0 if you do addition modulo 4.

    Of course modular arithmetic is an express and different language that uses the same symbols as another language. That is, you are engaging in a fallacy of equivocation. As 2+2=4 is just as correct as (2+2)/4 = 0 is correct as is 2 + 2 is congruent to 0 mod 4.

    But your broad point is nonetheless valid. If we take a general principle of physical reality and then move it into general abstract nonsense then we can, of course, make up any old rule we like. And it is indeed done regularly in math and logic. But inventing rules for games does not make stones disappear from reality.

    Petrushka: When you add the phrase “in the same sense” you are abstracting them. Your question is no longer about physical objects, but about propositions in your axiomatic system.

    “In the same sense” is a subtle form of equivocation. It is changing the definition of terms in midstream.

    IOW, it approximates reality and I’m glad to see that we’re in agreement. However, noting that it is valid only ‘in the same sense’ is not equivocation unless all produced definitions are equivocation. Your argument just doesn’t follow.

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