• Is Logic Empirical?
    I think I see how this could be problematic. Suppose you did a double slit experiment with two entangled particles separated by a significant distance. Then turning on the detector for one of them would communicate an effect to the motion of the other which would travel faster than the speed of light. Is that what you have mind?Dusty of Sky

    Yes, although the problem can be demonstrated with just the standard double-slit setup. Just place a single detector on one of the slits, say A1. That is sufficient to make the interference pattern disappear, even for just those photons that go through A2 that one might think should not be physically disturbed from their path.

    I don't think Euclidian geometry is necessarily universally true in the same way that classical logic is. A principle like "there is exactly one straight line passing through any two points" is always true with regard to our perception of space. We can't imagine a non-Euclidian realm in which the principle does not hold. But just because non-Euclidian space is unimaginable does not mean it's inconceivable. Non-Euclidian space violates the principles of sensory perception but not the principles of rational thought. My claim is that a logic in which the principle of distributivity is false does violate the laws of thought such that any claim made in such a logic, regardless of its usefulness, amounts to nonsense if we actually try to conceive of its meaning. It is impossible to think the proposition "((A1 or A2) and R) and not ((A1 and R) or (A2 and R))". You can write it out in symbols and claim that it is true, but you don't actually have a concept of what you are affirming any more than you have a concept of a married bachelor.Dusty of Sky

    We can observe the surface of a sphere which is a non-Euclidean surface. Consider a geodesic such as the Earth's equator. A geodesic in non-Euclidean geometry generalizes the notion of a straight line from Euclidean geometry to instead be the shortest path between two points on a surface. In the special case where a surface is flat, the geodesic is a straight line.

    Similarly, consider a flipped coin where the result is heads or tails but we don't know which. The coin is definitely either heads or tails, which is a classical disjunction. Now consider a quantum coin that is in a linear superposition of heads and tails. Quantum logic generalizes classical logic to include superpositions. In the special case where the state of the coin has collapsed to a definite state, quantum logic just reduces to classical logic.

    So is Putnam's argument that we ought to sacrifice the universality of classical logic in order to preserve realism and locality?Dusty of Sky

    I'm not sure if Putnam was aware of Bell's theorem at that time. But his position can be seen as rejecting realism in Bell's sense, i.e., as rejecting counterfactual-definiteness. To give a tangible/visualizable sense of what quantum logic is, I'll outline a geometric proof-of-concept in a separate post.
  • Platonism
    If I understand you correctly, we're talking about conceptual dependence here. That I can deal with. It even has a natural connection to Frege's saturated/unsaturated distinction: "___ is thinking it's going to rain" is unsaturated, incomplete, and therefore an abstraction, and therefore has only dependent existence.Srap Tasmaner

    Yes.

    I was seriously afraid that "independent existence" was going to lead to having to say what the ultimate constituents of the universe are!Srap Tasmaner

    Yes, no need to go there! I see those as dependencies in a physical sense, which is how natural objects relate to each other and their dynamics - the subject matter of physics and other sciences.

    Whereas the conceptual sense provides a schema for locating mind, colors, actions, events, statements, etc., in the world. That is, as abstractions that conceptually (or logically) depend on natural objects.

    You have a comfort level with QM that I don't, so I thought that might not scare you as much as it does me; or, rather, it might be something I would rather not have to do just to talk about what ordinary sentences mean, but you might not mind!Srap Tasmaner

    As it happens, I think an understanding of how language functions in ordinary experience is enormously helpful for getting a handle on more specialized and formalized fields. I like the way Scott Aaronson approaches the topic of teaching QM:

    The second way to teach quantum mechanics leaves a blow-by-blow account of its discovery to the historians, and instead starts directly from the conceptual core -- namely, a certain generalization of probability theory to allow minus signs.Scott Aaronson - Lecture 9: Quantum

    So consider how you might teach someone classical probability. You show them a coin and discuss how probability applies to it. In a similar way, you can show them a quantum coin and discuss how quantum probability applies to it (i.e., with the minus sign aspect added). So it's a good example of generalizing and abstracting for the purpose of teaching something.

    For Aristotle, ordinary objects (his primary substances) were the fundamental entities.
    — Andrew M

    So here maybe we're talking about what is conceptually fundamental, and for what Sellars calls the "manifest image" (or for Strawson's "descriptive metaphysics") that is indeed going to be sensible objects and persons.
    Srap Tasmaner

    Yes. My view is that science (as well as math and logic) is a natural extension of ordinary experience. So there need be no conflict between an ordinary and scientific view, at least in principle.
  • Is Logic Empirical?
    I think I understand, but please tell me if I am missing something. So when the photon hits R, as long we hold to a realist interpretation, we must assume that it passes through either A1 or A2. So R is true, and (A1 or A2) is true. The former is verified by observation and the latter by realist assumptions. Therefore, their conjunction is true.Dusty of Sky

    Yes.

    But neither (A1 and R) nor (A2 and R) can be verified as true, since we don't observe the photon to pass through either A1 or A2. So the statement "(A1 and R) or (A2 and R)" is evaluated as false, because neither disjuncts can be verified. (Or can they in fact be verified as false? When we measure A1 and A2 individually, do we never or only sometimes detect a photon passing through them?)Dusty of Sky

    They can be verified as false. In this case, we observe the photon pass through either A1 or A2 (since we place detectors there), but we never observe it hit R (i.e., we observe it hit some other region). Which is to say, no interference occurs in this case.

    I don't think that this proves that the principle of distributivity fails. It may be useful to not apply distributivity when dealing with quantum phenomena, but that doesn't mean that the principle is false. It is inconceivable for the principle to be actually false. If R is true and A1 or A2 is true, then either R and A1 is true or R and A2 is true. That's a simple tautology. Just because we can discover more in quantum mechanics by not applying a principle does not necessarily mean that the principle is false. And if we have reason to believe that the principle is necessarily and universally true, as I think we do in the case of distributivity, then its usefulness in quantum mechanics should make no difference. Even if we treat it as false in quantum mechanics, I don't think we must interpret this as invalidating the principle's universality.Dusty of Sky

    OK, so it's interesting to consider Putnam's argument here. He notes that you could says exactly the same thing about Euclidean geometry. It might be considered necessarily and universally true, but it nonetheless fails to describe the world we live in. Whereas if you drop the parallel postulate you get non-Euclidean geometry which does describe the world we live in. That relegates Euclidean geometry to a special case of non-Euclidean geometry that just so happens to approximate what we observe in everyday experience.

    Similarly, if you drop distributivity you get quantum logic. Classical logic is a special case within that more general logic that approximates what we observe in everyday experience. That is, the Boolean lattice that characterizes classical logic emerges as a special case within a more general non-distributive lattice. So, for example, if you fired bullets at a suitably robust double-slit apparatus, they would clump behind each slit whether or not you measured which slit they went through. Interference is rarely observed at a macroscopic level, so classical logic closely approximates what we normally observe there. As Putnam puts it:

    We must now ask: what is the nature of the world if the proposed interpretation of quantum mechanics is the correct one? The answer is both radical and simple. Logic is as empirical as geometry. It makes as much sense to speak of 'physical logic' as of 'physical geometry'. We live in a world with a non-classical logic. Certain statements - just the ones we encounter in daily life - do obey classical logic, but this is so because the corresponding subspaces of H(S) form a very special lattice under the inclusion relation: a so-called 'Boolean lattice'. Quantum mechanics itself explains the approximate validity of classical logic 'in the large', just as non-Euclidean geometry explains the approximate validity of Euclidean geometry 'in the small'.Putnam: The logic of quantum mechanics, p184

    In a sense, we can ask what the world would look like if distributivity was generally false, but was approximated in everyday macroscopic experience. Well, it would look just like our world.

    Perhaps it is true that either (A1 and R) or (A2 and R), but since we can verify neither disjunct, we treat it as false, not because it is false in reality because our measurements fail to demonstrate it. (Or, if our measurements in fact demonstrate the contrary, that the photon passed through neither, then we would have to interpret the act of measurement as affecting the photon).Dusty of Sky

    If one of the disjuncts were true in reality, it would be a hidden variable. But that would require a non-local interpretation, per Bell's Theorem.

    But otherwise, yes, it comes down to the measurement problem.
  • Platonism
    Right, this is the part of your position I've ignored: abstract entities have only dependent, not independent existence. By "reify" you mean precisely attributing independent existence to something that doesn't have it.

    Here's one way we can talk. There is a general event type, someone thinking it's going to rain; there is a particular event type, Alice thinking it's going to rain; and then there are particular instances of that, Alice's thinking yesterday that it was going to rain. (Obviously lots of other ways to carve that up...)

    That last is a particular, but in your terms it is not a concrete particular, not because of anything to do with types and instances but because every instance of Alice thinking it's going to rain is dependent for its existence on Alice existing, is inseparable from Alice. We separate what Alice is thinking from Alice only fictively, by means of abstraction.

    And then two people thinking the same thing is still as simple as I want it to be, just a matter of using the same words to describe what you fictively detach as "what they're thinking." If you then generalize, you can talk about the idea "that it is going to rain" as what anyone you would describe as thinking it's going to rain is thinking.
    Srap Tasmaner

    Yes, exactly. Well put.

    One little question: in this analysis, every instance of Alice thinking it's going to rain is dependent for its existence on Alice existing, not on Alice independently existing, right? I'd love to stay away from saying what that's supposed to mean, but we don't seem to rely on it anyway. Do you agree?Srap Tasmaner

    Well, thinking needs a subject (such as Alice). But Alice doesn't, in turn, have a subject - any chain of dependencies terminates with her. So in that sense, she is not dependent on anything further for her existence.

    This just means that ordinary objects - things we observe or could potentially observe - just are our starting point for investigation, and the dependencies and relations between things flow from there. It's the view from somewhere as opposed to the Platonic view from nowhere (beyond the cave).

    So far we're juggling general vs. particular, abstract vs. concrete, and dependent vs. independent. There are obvious temptations to match them up (respectively) that I'm trying to be careful about.Srap Tasmaner

    Indeed. Anyway, to begin with, ordinary objects are particular, concrete and independent.

    The dependency relation between ordinary objects and abstractions characterizes Aristotle's fundamental disagreement with Plato. For Aristotle, ordinary objects (his primary substances) were the fundamental entities. Whereas for Plato, the eternal Forms were the fundamental entities, and ordinary objects depended on (participated in) those Forms.
  • Platonism
    So glad you've chimed in, Andrew M!Srap Tasmaner

    Thanks, and I'm enjoying the discussion! :-)

    Your approach (which you would say is broadly Aristotelian?) seems very sound: there is only one sense of "abstraction"; it is what we do when we consider a particular concrete context selectively.Srap Tasmaner

    Yes (and, as you note, it's broadly Aristotelian).

    I wonder, though, why is existence -- as in the first quote
    Even if not, it doesn't follow that abstractions are nothing.
    — Andrew M
    -- part of this story at all? If Alice is thinking it's going to rain, why even say that there is a thing, the thought that it is going to rain, that does exist, only it doesn't exist independently of Alice thinking it is going to rain, or of someone thinking it is going to rain?
    Srap Tasmaner

    I don't think existence needs to be part of the story, at least in any metaphysical sense. "Thing" is simply a common way to refer to abstractions as well as concrete things.

    For example, suppose a mother asks her son, "Is there something you should be telling me?" Her question should be understood in an ordinary sense, not as having metaphysical implications. Certainly, she would not expect to be told by her son that abstractions don't exist.

    I ask for two reasons:

    (1) If I'm of a mind to deny that Alice thinking something entails there is something Alice is thinking (( that is, except as a matter of grammar; I mean to deny only that "there is" should be taken in the full-blooded sense of something existing )), and you insist that we can consider what Alice is thinking independently of the concrete occasion of Alice thinking it, I do not need to deny this -- why would I? I only need to deny that us considering what Alice is thinking entails there being something we are considering.
    Srap Tasmaner

    I think it's just a matter of grammar. I don't think there are metaphysical implications in that phrasing.

    (2) If the point is to emphasize our capacity to consider things selectively, and to describe this somewhat picturesquely as an ability conjure abstract entities for our consideration rather than being compelled always and only to consider the totality of the concrete situation, I will point out that we are already doing that all the time simply by using language in the first place.Srap Tasmaner

    Agreed.

    Insofar as we want to ignore whatever else is going on with Alice except her thinking about the chance of rain and taking her umbrella, we say, "Alice is taking her umbrella because she thinks it's going to rain." "Considering selectively" is not a special thing we do sometimes with language; it's practically all we ever do.Srap Tasmaner

    Agreed.

    But there does seem to be an exception to the idea that language is always selective: names of concrete particulars. When we refer to Alice, we mean everything about her, or at least intend not specifically to exclude anything about her.

    The question then is whether, in creating "names" on-the-fly, we are referring to abstract particulars such as "Alice taking her umbrella" (an action or an event), and that question seems particularly acute when the name is anaphoric and thus somewhat open-ended: "what Alice said" or "what Alice did" or "what Alice was thinking".
    Srap Tasmaner

    As long as we take care not to reify such abstractions, is there really a problem here?
  • Platonism
    The tl;dr is that if what's being thought is an abstract entity, is that because there's something special about thinking? or because thinking is acting? or because thinking is an event occurring? Is it abstract because it's thinking, or because all our descriptions are abstractions?Srap Tasmaner

    No, not because it's thinking.

    By an abstraction, I simply mean something that does not exist independently of a concrete and particular context but can be considered independently of that context. Whether that be events, actions, thoughts, descriptions, or whatever.

    So, by abstract entity above, I'm just referring to Alice thinking that it is going to rain. We might call it a thought or a belief or a sentence or a proposition. But the main point is that we can treat it as a separate entity for the purpose of analysis. We might care that it is about to rain, not specifically that Alice thought it. And certainly we can investigate the idea that it might rain without needing to involve Alice further.

    Similarly, actions don't happen independently of agents that act. But we might only care about that action in abstraction (e.g., somebody took the last umbrella and now I'm going to get wet), not that it was specifically Alice's action.

    So to address your points, which will hopefully make sense in the context of the above.

    1. "Alice is grabbing her umbrella" is also an abstraction, right? We are leaving out whatever else is going on with Alice in describing her current behavior as "grabbing her umbrella".Srap Tasmaner

    Yes. But, also, this is the concrete context. Grabbing doesn't occur in the abstract. There's Alice and the umbrella here as well. This is relevant because ...

    2. "Alice thinks it's going to rain" is an abstraction in the same way (1) is -- we're not talking about whatever else may be going on in her mind -- but is it an abstraction in some other way? Is there another sense of abstraction in play here?Srap Tasmaner

    ... ideas don't happen in the abstract. Alice is here as well. So it's that sense of dependence of the abstract on the concrete and particular that I'm emphasizing here (rather than selectiveness, though that's true as well). And the same sense of abstraction as above.

    3. Alice is a concrete entity and Alice's umbrella is a concrete entity; is "Alice grabbing her umbrella" an abstract entity? Is that what actions are? Or events? How do we capture the difference between "Alice grabbing her umbrella", a sort of abstract event that might occur, and "Alice is grabbing her umbrella" which, while an abstraction in the simple sense of (1) is pretty concrete -- it's a realization of "Alice grabbing her umbrella" after all.Srap Tasmaner

    I would consider this the concrete context. We can observe Alice grabbing her umbrella, which is concrete for medium-sized, dry goods such as ourselves. But after observing many people grabbing their umbrellas, we might abstract out that commonality.

    4. Is there yet a third sense of "abstract"Srap Tasmaner

    I'm intending just the one sense. In considering something abstractly, we are being selective as you note, and there are different ways that might manifest, including at increasingly complex levels. But the key point is that it depends on something concrete.

    That, I think, is sufficient to contrast it with Platonism. (And Nominalism, as it happens, since events and actions can occur independently of naming and minds.)
  • All mind, All matter, Dualistic
    Which camp do you roughly fall into and what are your arguments for it?khaled

    I chose "Other". My view is hylomorphism, which is the Aristotelian view that reality, starting with the ordinary objects of experience, can be analyzed in terms of matter and form. My argument, as it were, is that it provides a useful framework for understanding the world. Aristotle himself introduced it in response to the problems posed in his day by Parmenides, Plato and others.

    Aristotle introduces matter and form, in the Physics, to account for changes in the natural world, where he is particularly interested in explaining how substances come into existence even though, as he maintains, there is no generation ex nihilo, that is that nothing comes from nothing.Form vs. Matter - SEP
  • Platonism
    Sure, but what goes in place of "something" in "Alice is kicking something"? It's a noun phrase of some kind:

    (a) A proper name: "Alice is kicking Steve";
    (b) An indefinite noun phrase: "Alice is kicking a ball";
    (c) A definite noun phrase: "Alice is kicking the ball."

    Can we do the same thing with "Alice is thinking something"? No, no, and no.
    Srap Tasmaner

    Even if not, it doesn't follow that abstractions are nothing. Consider:

    • If Alice is thinking that it is going to rain, must we conclude there is something that Alice is thinking?

    Yes, that it is going to rain.

    Anaphoric constructions aside, we know what goes in place of "something" in "Alice is thinking something"; it's constructions like

    "that the roof will never hold"
    "of going to graduate to school in the fall"
    "about her grandmother's house".

    Any of those look like things to you?
    Srap Tasmaner

    They're not concrete things, they're abstractions. When we see Alice grab her umbrella, we assume she thinks that it is going to rain. But that is an abstraction over her behavior, not some additional thing that has an independent existence. And we can consider that abstraction separately from its concrete context, i.e., as an abstract entity.
  • Platonism
    So this is the question:

    If Alice is thinking something, must we conclude there is something that Alice is thinking?
    Srap Tasmaner

    Yes, I think so. The only difference is that the grammatical subject and object is switched. Compare with:

    • If Alice is kicking something, must we conclude there is something that Alice is kicking?

    Yes, for example, a ball.

    The deeper issue raised by your question is that that "something" is abstract. We can consider that abstraction (in this case, an idea or thought) separately from the concrete context it is found in, but it's not actually separate. So Platonism doesn't follow (i.e., a prior and separate realm of Ideas or Forms).
  • Philosophy....Without certainty, what does probability even contribute?
    I've always been interested in 'certainty' and our existence.

    Now, if we can't be certain about anything, even our own existence, then how does probability help support that we exist?
    Tom343

    It doesn't. To use probability, to evaluate evidence, to make posts, or to think and say anything at all, presupposes an agent that does those things. Since you do those things, you are such an agent and, unless I'm replying to an AI, a human being. We typically say that people, animals and anything else that we encounter, such as trees, rocks, computers, etc., exist. Whereas dinosaurs, square circles, and ghosts, don't.

    Assuming you accept that model of the world, and use the term exist conventionally then ...

    Surely I am as likely to exist as I am not to exist?Tom343

    ... you can't assert something if you don't exist. At least on conventional usage.

    If we cannot prove certainty, how does probability come into play? How am I more likely to exist than not?Tom343

    What do you mean by certainty and prove? Do you mean a firm conviction that something is the case? Able to be firmly relied on to happen or be the case? Deducible from premises? Infallibility?
  • Is Logic Empirical?
    I don't think this necessarily contradicts the principle of distributivity. It seems that measuring which slit the photon goes through affects the conditions of the experiment. So if you don't measure, then both ((A1 or A2) and R) and ((A1 and R) or (A2 and R)) are true. If you do measure, then both are at least potentially false because not-R can be true. Am I still missing something?Dusty of Sky

    If you don't measure, you don't know whether those propositions are true. So it would be an interpretation.

    Alternative interpretations are (A1 and A2 and R) and ((neither A1 nor A2) and R) as suggested by @Pfhorrest and @magritte earlier.

    Instead of trying different combinations of classical conjunctions and disjunctions, Putnam instead reinterprets them based on a non-distributive lattice. Here's an example of how it works:

       1
     / | \
    A1 A2 R
     \ | /
       0
    

    The rule for disjunction is that while there is no common node, go up the lattice. The rule for conjunction is that while there is no common node, go down the lattice.

    So for the photon going through (slit A1 or slit A2) and hitting region R, we have:

      (A1 or A2) and R
    = 1 and R
    = R
    

    Whereas for the photon (going through slit 1 and hitting region R) or (going through slit 2 and hitting region R), we have:

      (A1 and R) or (A2 and R)
    = 0 or 0
    = 0
    

    For a nice explanation of this, see Alex Wilce's talk, A Gentle Introduction to Quantum Logic. At 34:20, Wilce connects this to von Neumann and Birkhoff's quantum logic - if subspaces are ordered by set inclusion, we have a non-distributive lattice.

    Also, here's a derivation of one side of the principle of distributivity. The principle follows from more basic logical principles, so if you reject distributivity, you must also reject at least one of the other principles used in this derivation.Dusty of Sky

    See 37:00 where Wilce mentions non-unique complements which affects negation. Also see Disjunction in quantum logic.
  • Is Logic Empirical?
    I can't conceive how an observation which violates principle of distributivity could be possible. What would that even look like? Putnam is an accomplished and respected philosopher, so I'm sure there's something I'm missing. I'll try to read the paper again at some point and hope I have better luck with it. But if you think you understand what he's saying, please try to explain.Dusty of Sky

    Putnam is saying that the photon going through (slit A1 or slit A2) and hitting region R describes an interference experiment. That is, you don't know which slit the photon went through but, on conventional realist assumptions, it went through one slit or the other. However the photon need not hit region R if you do measure which slit it went through. Now we know this already since this is just what QM predicts. But Putnam's claim is that those two experimental observations are the left-hand-side and right-hand-side of the principle of distributivity, and so violate it.

    Addendum: after glancing at the equations on pp180-181, I see that he's using probability. I don't have a good grasp of probabilistic logic, but my understanding is that it adds a number of layers of complexity and uncertainty to classical logic. I may be wrong, but I think that the principles of probabilistic logic are quite contentious among logicians. Perhaps quantum mechanics only violates ordinary principles of probabilistic logic, not classical logic.Dusty of Sky

    Putnam is rejecting classical logic - see statement (10) on p190, where he states the principle of distributivity and says that it fails in quantum logic. Also:

    Mathematically, quantum mechanics can be regarded as a non-classical probability calculus resting upon a non-classical propositional logic.
    ...
    For Putnam, the elements of L(H) represent categorical properties that an object possesses, or does not, independently of whether or not we look. Inasmuch as this picture of physical properties is confirmed by the empirical success of quantum mechanics, we must, on this view, accept that the way in which physical properties actually hang together is not Boolean. Since logic is, for Putnam, very much the study of how physical properties actually hang together, he concludes that classical logic is simply mistaken: the distributive law is not universally valid.
    Quantum Logic and Probability Theory - SEP

    Perhaps quantum mechanics only violates ordinary principles of probabilistic logic, not classical logic.Dusty of Sky

    Most quantum physicists accept and use classical logic. But QM can be understood as a generalization of probability theory that, in addition to positive numbers, also allows negative and complex numbers (i.e., probability amplitudes).
  • Is Logic Empirical?
    That’s because the photon doesn’t go through A1 OR A2, it goes through A1 AND A2.Pfhorrest

    That would be an interpretation. As SMBC puts it, 'Sweetie, superposition doesn't mean "and", but it also doesn't mean "or"'.

    It's a complex linear combination of going through both slits.
  • Is Logic Empirical?
    I tried to read the paper by Hillary Putnam, but there were too many difficult equations, so I'm hoping that someone here can make his case in more ordinary language.Dusty of Sky

    Here's a link to Putnam's paper, republished as "The logic of quantum mechanics".

    Putnam's argument is that the principle of distributivity fails for quantum mechanics. That is, he claims that there are instances where (A and (B or C)) is true, yet ((A and B) or (A and C)) is false.

    Putnam gives an example of the double-slit experiment on pp180-181. On his view, the photon goes through (slit A1 or slit A2) and hits region R, yet it is not the case that the photon (goes through slit A1 and hits region R) or (goes through slit A2 and hits region R).

    If his view is correct, then that is an example where classical logic fails for empirical reasons.
  • David Hilbert’s thought experiment known as ‘Hilbert’s Hotel
    Whoever Craig and Mooreland are, they might wish to take a college-level course in mathematics. There’s no paradox that I can see here, only a metaphor for some bijections from N to a subset of N.Olivier5

    It seems that Craig is following Hilbert (and others) on this, which is to make a distinction between the mathematical idea of infinity, which he accepts, and its existence in nature, which he rejects.

    Craig:

    Hilbert's Hotel is absurd. Mind you, it's logically correct for the mathematician but it's impossible for something like Hilbert's Hotel to really exist. You can describe it on paper but it cannot exist in reality. Illustrations like these showed that the existence of an actually infinite number of things is impossible.

    Now sometimes people react to Hilbert's Hotel by saying that these paradoxes result because we can't understand the infinite - that it's just beyond us. But this reaction is in fact mistaken and naive. Infinite set theory is a highly developed and well understood branch of modern mathematics.

    These absurdities result not because we do not understand the infinite but because we do understand the nature of the actual infinite. Hilbert was a smart guy and he knew well how to illustrate the bizarre consequences of an actually infinite number of things.
    Hilbert's Hotel and Infinity - William Lane Craig (from 4:30)

    Hilbert:

    We have already seen that the infinite is nowhere to be found in reality, no matter what experiences, observations, and knowledge are appealed to. Can thought about things be so much different from things? Can thinking processes be so unlike the actual processes of things? In short, can thought be so far removed from reality? Rather is it not clear that, when we think that we have encountered the infinite in some real sense, we have merely been seduced into thinking so by the fact that we often encounter extremely large and extremely small dimensions in reality?
    ...
    In summary, let us return to our main theme and draw some conclusions from all our thinking about the infinite. Our principal result is that the infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought — a remarkable harmony between being and thought. In contrast to the earlier efforts of Frege and Dedekind, we are convinced that certain intuitive concepts and insights are necessary conditions of scientific knowledge, and logic alone is not sufficient. Operating with the infinite can be made certain only by the finitary.

    The role that remains for the infinite to play is solely that of an idea — if one means by an idea, in Kant's terminology, a concept of reason which transcends all experience and which completes the concrete as a totality — that of an idea which we may unhesitatingly trust within the framework erected by our theory.
    On the infinite - David Hilbert
  • David Hilbert’s thought experiment known as ‘Hilbert’s Hotel
    We can conduct experiments to determine a specific finite age of the Earth. But how would we test whether something was infinite in age, size or number as opposed to just really, really large?
    — Andrew M

    Obviously, not by counting or measuring directly. We don't hold a stopwatch to measure the age of the earth either - we use other measurements to establish theories in which the age of the earth is a bound variable. Same with the size of the universe: it makes a difference to the theories that we use to explain astrophysical observations - their accuracy, simplicity and compatibility with other well-established theories. You can't just arbitrarily choose a size without breaking a bunch of stuff.
    SophistiCat

    :up:
  • David Hilbert’s thought experiment known as ‘Hilbert’s Hotel
    I don't know why they think that. But if it's to be a thought experiment about the physical world, then we have no experimental evidence that there is, or can be, anything infinite. And what would such an experiment look like? How would it be measured?
    — Andrew M

    Same way as how we establish anything in science: that Earth is ~4.5 Gyr old ("How could you possibly know? Were you there?!"), that pulsars are neutron stars, etc. We develop models and evaluate their closeness of fit, simplicity, and other epistemic and scientific virtues.
    SophistiCat

    Which is to say that principles other than experiment and measurement are appealed to.

    We can conduct experiments to determine a specific finite age of the Earth. But how would we test whether something was infinite in age, size or number as opposed to just really, really large?

    We already know that things with finite ages, sizes and number exist in nature. But, as Tegmark points out, "The assumption that something truly infinite exists in nature ... [is] an untested assumption".
  • David Hilbert’s thought experiment known as ‘Hilbert’s Hotel
    Why Craig and Mooreland think that the existence of Hilbert’s Hotel would be absurd?
    Why they think the absurdity of Hilbert’s Hotel implies that no actual infinite collection can exist?
    jay232

    I don't know why they think that. But if it's to be a thought experiment about the physical world, then we have no experimental evidence that there is, or can be, anything infinite. And what would such an experiment look like? How would it be measured?

    Let's face it: Despite their seductive allure, we have no direct observational evidence for either the infinitely big or the infinitely small.
    ...
    Not only do we lack evidence for the infinite but we don't need the infinite to do physics.
    Edge - 2014: What Scientific idea Is Ready For Retirement? - Infinity - Max Tegmark
  • Coronavirus
    Mayor Trump's advisors:
    There's a fire raging towards us and it might destroy our town.

    Mayor Trump:
    That's terrible! But I love my town and I don't want to scare the people. So we should downplay the fire. Tell them to stay calm, it will go away.

    Later...

    Townspeople:
    A fire burned through our town and, devastatingly, we lost people and property. Shouldn't we have taken a precautionary approach to the fire?

    Mayor Trump:
    Nobody could have predicted something like this.

    --

    From the New England Complex Systems Institute, January 26, 2020 - on Coronavirus:

    Conclusion: Standard individual-scale policy approaches such as isolation, contact tracing and monitoring are rapidly (computationally) overwhelmed in the face of mass infection, and thus also cannot be relied upon to stop a pandemic. Multiscale population approaches including drastically pruning contact networks using collective boundaries and social behavior change, and community self-monitoring, are essential.

    Together, these observations lead to the necessity of a precautionary approach to current and potential pandemic outbreaks that must include constraining mobility patterns in the early stages of an outbreak, especially when little is known about the true parameters of the pathogen.

    It will cost something to reduce mobility in the short term, but to fail do so will eventually cost everything—if not from this event, then one in the future. Outbreaks are inevitable, but an appropriately precautionary response can mitigate systemic risk to the globe at large. But policy- and decision-makers must act swiftly and avoid the fallacy that to have an appropriate respect for uncertainty in the face of possible irreversible catastrophe amounts to "paranoia," or the converse a belief that nothing can be done.
    Joseph Norman, Yaneer Bar-Yam, and Nassim Nicholas Taleb, Systemic risk of pandemic via novel pathogens – Coronavirus: A note, New England Complex Systems Institute (January 26, 2020).
  • Counterfeit
    But we needn't be and I hope are not on opposite sides, but rather put such understandings that we generate and evolve through "to the question" as simply a part of a shared goal of getting a handle on an idea that at first look seems to me fatally problematic.tim wood

    :up:

    Information (or state) is an abstraction of physical systems (PS).
    — Andrew M

    Would you agree, on reflection, that in this context (hereinafter to be understood if not stated), that either this is exactly wrong, or needs qualification to be right? If information corresponds to state, then information just is itself and cannot be other than itself - without being other. If information is descriptive of any PS, then it is not that PS, but its own distinct PS, and if that PS is the idea of the thing, then that itself becomes difficult.
    tim wood

    Be careful not to reify information. Consider a coin that has landed tails-up on a table. The state of the coin (tails) is not itself a system, it's the form of the system in a specific context (where form is the linguistic root of information).

    Or another, that from the metamorphic rock from under an ancient and long gone streambed it is possible to recover what stone what sauron kicked into it on a day 100,000,000 years ago, and the configuration of the splash. Of course some of that evidence went up as water vapor, so part of the recovery must involve the entire atmosphere of the earth - or not? Is the information complete in parts or does it require the whole?tim wood

    It depends. For the stone-kicking question, perhaps the whole atmosphere (or even light cone) is required. Whereas the question of whether it rained earlier today could be answered from more easily accessible evidence.

    Information is conserved in both cases and accessible in principle, if not in practice.

    Consider again the no-hiding experiment referenced earlier where the system was randomized via a bleaching process. The original state of the system was recoverable from the ancilla qubits. But if that information had instead leaked into the external environment, then it would not be recoverable by present technology, but that information would still be somewhere.

    I mean in these to evoke a sense of the aporia I think intrinsic to the problem. If information is just state, then it is at the moment and not otherwise. If information is knowable, then the state-as-information must also create some kind of meta-information/state (or something without yet a name) that travels through time, or endures through time, that preserves the original state, somehow. And that asks as to the question of meta-meta-...-meta information/states.

    For the theorem to be meaningful it must cut through all of this, yes?
    tim wood

    I'm not sure I understand your objection. But let's apply your comments to the six-state die system that I presented in the previous post (which cycles from 1 to 6). Given the rules of that system and a current state (e.g., 3), then the previous state is necessarily implied (i.e., 2). I don't see how a meta-state arises here.
  • Counterfeit
    And again, whatever QI is, to be information in any sense must (yes?) mean that it "contains" something that it itself is not, that can be extracted from it, apparently non-destructively, which implies repeatedly. And that something in every case is part of a recoverable path to the unbounded future and the unbounded past, somehow, someway.tim wood

    Conservation of information also applies in classical physics. Here's a couple of snippets from Leonard Susskind's lectures on statistical mechanics and classical mechanics (videos available on Youtube):

    Proper laws of physics are reversible and therefore preserve the distinctions between states - i.e. information. In this sense, the conservation of information is more fundamental than other physical quantities such as temperature or energy.Statistical Mechanics - Entropy and conservation of information - Susskind

    Liouville's theorem can be thought of as information conservation. The laws of mechanics are equivalent to the rules governing state transition.Classical Mechanics - Liouville’s theorem - Susskind

    To give an example, consider a simple system with six states, like the sides of a die. The dynamical laws in this system for each time step are:

    1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 1

    Information is conserved. For any given state, the next state and the previous state can be predicted. Whereas in the following system, information is not conserved since the state prior to state 3 can't be predicted.

    1 -> 3 <- 2

    And it seems quickly clear that this kind of language and thinking is not adequate for this task. If the theorem is true - one supposes it is - then the language has to be very tightly defined and constrained. I suspect past the breaking point. Information must finally reduce to mere being, and being as information leads to some ferocious paradoxes.tim wood

    Information (or state) is an abstraction of physical systems. Quantum information is just a different abstraction than we're used to with classical information. A classical bit is just a 0 or a 1. Whereas a qubit is a linear combination of 0 and 1 that, when measured, collapses to a 0 or a 1. That seems like information has been erased. But the lost information has simply moved elsewhere (e.g., to an ancilla qubit or heat in the environment).
  • Counterfeit
    Do we know, of this "quantum information," if a) it can ever be what we call knowledge, i.e., known, and, b) can it always be known, in the sense of retrieved? Or not retrieved? Or not retrievable?tim wood

    Whether something can be known (or retrievable) or not depends on what is being done. If a coin is flipped inside the event horizon of a black hole (and subsequently destroyed), then it is going to be essentially impossible for external observers to retrieve the result. On the other hand, if you send a photon into a suitably configured Mach-Zehnder interferometer, it can be predicted with certainty which detector the photon will arrive at (despite being impossible to predict using classical theory).

    In both cases, quantum information is conserved. Here's a PBS Space Time video on this - Why Quantum Information is Never Destroyed. The idea of quantum computing, then, is to exploit the special characteristics of quantum information (i.e., qubits) to solve problems that are beyond the capabilities of classical computers.

    I imagine throwing a stone into the ocean thereby disturbing the water. And maybe that determines uniquely the future of the ocean. The ocean, then, stores a record of that disturbance. But how is that to be recognized as such, and how retrieved as to the particulars that make that what it is?tim wood

    The way I would put it is that information about the stone hitting the water is exhibited in the ocean itself. We can see it in the ripple. Of course there is a lot that we don't see and measure, and the ripple soon disappears. But that information is nonetheless retained in the environment which is, in principle, measurable.

    Might it be the case that the no-hide theorem merely means that change is in some sense permanent? Anyone?tim wood

    In terms of the no-hiding theorem, if a system is randomized, information about the randomization operation will be stored in the environment external to the system. That information can then be used to perfectly reconstruct the original system. Here's an experiment demonstrating this:

    In order to make the first qubit “lose” its information, the scientists had to make the system undergo a bleaching process. In their experiment, they bleached the system through quantum state randomization, in which the qubit transforms from a pure state to a mixed state. Although the randomization operation causes the qubit to appear to lose the information contained in the pure state, the scientists showed that the information could be found in one of the two ancilla qubits. They also demonstrated how to use the ancilla qubits to reconstruct the original state, showing that no information was hiding in the correlations between the original qubit and the ancilla qubits, which is the essence of the no-hiding theorem.Quantum no-hiding theorem experimentally confirmed for first time
  • Counterfeit
    I would answer the same way if the information were merely irretrievable, since the information does still exist.
    — Andrew M

    But if it were irretrievable, from our perspective the situation is identical with that where it doesn't exist.
    hypericin

    For all practical purposes, sure. But I think the conceptual distinction remains. Before the bills go in the box, you know which one is real and which one is the counterfeit. After the bills go in the box, you lose track of them, but they still have a definite history as their positions change over time.

    So, in effect, all that has changed before and after is your knowledge of that definite history.
  • Counterfeit
    Which one doesn't matter. But what does matter is that one is erased so that the records are kept right.apokrisis

    Yes. Which is to say, there's no difference between the bills that makes a difference. ;-)
  • Counterfeit
    I'm having a hard time wrapping my head around the no hiding theorem. Right now I'm thinking of a 10 digit number. I'm not repeating it, and there's no way I will remember it in 5 minutes. Could a sufficiently clever alien, arriving on a venus like earth 10 million years from now, retrieve it?hypericin

    In principle, yes. For example, suppose the Earth's system were isolated with respect to the alien. Since no information has been lost, the alien could perform a physical transformation on the Earth's system that, in effect, runs the laws of physics in reverse until it's back to you thinking of the number. That process would be akin to unscrambling a scrambled egg.

    Would you answer the same way if the no hiding theorem turned out to be false? Or true, but information can still be irretrievably, in principle as well as practice, lost and inaccessible?hypericin

    I would answer the same way if the information were merely irretrievable, since the information does still exist. But if the information does not exist, then there would be no basis for a distinction between the real and counterfeit bills.

    As it happens, exactly this issue arises in quantum mechanics - see the Hong–Ou–Mandel effect. Suppose the photon coming in from above represents the real bill and the photon coming in from below represents the counterfeit bill (see the four possibilities diagram). State 2 has both photons transmitting, while state 3 has both photons reflecting. In the experiment, states 2 and 3 destructively interfere (i.e., are not experimentally observed) which means that there is no "which-way" information distinguishing those two states. So for states 1 and 4 that are observed, there is no longer any basis for regarding one photon as representing the real bill and the other photon as representing the counterfeit bill - that information does not exist. There are simply two photons that have a shared history.
  • Counterfeit
    Open the box. What is the status of the 2 hundred dollar bills?hypericin

    The physical assumptions underlying this thought experiment could be questioned. For example, the no-cloning theorem says that it is impossible to make an exact copy of a physical system. And the no-hiding theorem says that information is never destroyed.

    That aside, it's of course possible for a human being to lose track of which bill is the real one. That just means that the status of the bills is unknown, it doesn't change the fact that one is real and the other is counterfeit (per the original designation).
  • Coronavirus
    Compare NZ's elimination strategy with Trump's "positive thinking" strategy.

    Embattled US President Donald Trump has once again taken aim at New Zealand over our recent resurgence of coronavirus, describing yesterday's five new cases as a "massive break out" as US cases continue to grow by tens of thousand everyday.

    Speaking to a crowd in Pennsylvania, Trump said: "You look at our mortality rates, you look at all the things but they like to compare us to others so they were talking about New Zealand.

    "New Zealand, New Zealand, it's over for New Zealand, everything's gone, it's all over - they're beautiful," said Trump, referencing the global acclaim New Zealand received for its response.

    "They had a massive break out yesterday."

    ...

    "New Zealand, by the way, had a big outbreak, and other countries that were held up to try and make us look not as good as we should look, and we've done an incredible job," he claimed.

    "They're having a lot of outbreaks, but they'll be able to put them out, and we'll be able put them out."

    ...

    The US death toll from Covid-19 is rapidly approaching 175,000 while New Zealand's stands at 22.

    On the day that we recorded five new cases, the US recorded 46,500 according to the Centre for Disease Control.

    Trump's comments are the third time this week that he has referenced New Zealand as he attempts to paint his handling of the pandemic in a better light.
    NZ Herald - Covid 19 coronavirus: Donald Trump takes aim at NZ again
  • Lazerowitz's three-tiered structure of metaphysics
    Where or what is this entity, "the state of affairs representation", if it isn't the wet stuff it represents, and it isn't a part of the report? I suppose you will say that it's an abstraction.bongo fury

    Yes. The state of affairs (i.e., that it is raining) is a formal abstraction of the wet stuff, just as the statement (i.e., that it is raining) is a formal abstraction of Alice's utterance.

    It can be convenient and useful to operate on abstractions instead of the concrete stuff they represent. Compare adding two and three stones formally versus adding two and three actual stones. And patterns can be noticed. In this case that what the weather is and what Alice says the weather is are the same (i.e., that it is raining and thus the formalisms pick out the same wet stuff).

    Ok, but please stop implicating modern nominalism in any such business?bongo fury

    I'm not. So what would be a nominalist model of the rain situation and how would it differ in substance?

    And on your view?
    — Andrew M

    The pointing of symbols at things by social animals.
    — bongo fury

    Animals who, if they have any sense, regard

    is it raining or not independently of any report or statement?
    — Andrew M

    as an invitation to confused logic, with cycles in it. And usually do, and get on with the weather report, instead.
    bongo fury

    It's the ordinary language convention. If the weather report said that it was raining when there was no wet stuff, then the weather report was mistaken even if no-one noticed that.

    So I've presented a model and shown how logical operations can be applied. Where are the cycles?
  • Lazerowitz's three-tiered structure of metaphysics
    On your view, is it raining or not independently of any representation?bongo fury

    No, it's not raining or not independently of the state of affairs representation. But it is raining or not independently of any report or statement.

    And on your view?
  • Lazerowitz's three-tiered structure of metaphysics
    No, because I make a distinction between what the weather is and what a person says the weather is.

    It seems that you don't make that distinction.
    — Andrew M

    I make it when it makes sense: as when a weather report for any reason offers comparison of its own findings with those of Alice and Bob.
    bongo fury

    On your view, is it raining or not independently of any report or statement?

    ... or which, in other words, SA2 and SA3 were talking about, as I said.

    So, SA1 (or asserting it) is talking about the weather, while SA2 and SA3 are talking about the talking?

    But SA1 isn't the weather (e.g. it isn't wet), but rather represents or talks about it.
    — bongo fury

    Or not?
    bongo fury

    The states of affairs represent the weather and the talking. But states of affairs are not themselves talk. The only talk within the model are the statements S1 and S2.

    If so, then "obtaining" is plainly interchangeable with "true", and the SA layer gratuitous.bongo fury

    They aren't interchangeable. A statement presupposes a person making the statement, which is a concrete situation (e.g., as represented by SA2). So to use a statement to represent that concrete situation would, in turn, presuppose a person making that statement. Perhaps that person could be me. But I am not in the model. So there needs to be something statement-like in the model that doesn't have that presupposition. A state of affairs is statement-like and doesn't have that presupposition.

    If not, and the SA is the concrete situation, and is literally wet, then an SA isn't composed of subject and predicate, and you need to rethink the "isomorphism" supposedly grounding your truth "function". If you still think that some such mapping is required.bongo fury

    The SA is a representation of the concrete situation so, no, not literally wet.
  • Lazerowitz's three-tiered structure of metaphysics
    But both her statement and the state of affairs refer to rain, not predication.
    — Andrew M

    If so, perhaps one of them would suffice?
    bongo fury

    No, because I make a distinction between what the weather is and what a person says the weather is.

    It seems that you don't make that distinction. And thus lack a model for what it means for a statement to be true.

    I can represent the original concrete situation in a model with the following obtaining states of affairs:

    (SA1) It is raining
    (SA2) Alice says that it is raining
    (SA3) Bob says that it is not cloudy
    — Andrew M

    So, SA1 (or asserting it) is talking about the weather, while SA2 and SA3 are talking about the talking?

    But SA1 isn't the weather (e.g. it isn't wet), but rather represents or talks about it. (Likewise, SA2 and SA3 aren't the weather-talk by Alice and Bob but merely talk about that weather-talk.)
    bongo fury

    Statements S1 and S2 are the weather-talk by Alice and Bob (which are derived from states of affairs SA2 and SA3 respectively).

    So SAR doesn't, as implied here...

    Finally, a conditional can be added that relates statements to states of affairs
    — Andrew M

    ... relate talk about the weather to the weather, but only to more talk.
    bongo fury

    Per SAR, the (truth) value of the statement is a function of the (obtain) value of the state of affairs. Alice and Bob are already talking about the weather. The only question is whether what they say is true, which is what SAR determines.
  • Lazerowitz's three-tiered structure of metaphysics
    Whether it's comparable will depend on whether you proceed to analyse the weather as a collection of physical particulars related in physical ways,bongo fury

    See the example below.

    or as some bizarre kind of weather sentence... with a fifty percent chance of predication, perhaps... something like that? :wink:bongo fury

    Your comment would apply equally to Alice's statement. But both her statement and the state of affairs refer to rain, not predication.

    Such as? (You may need to decide if you are talking about the weather, or about the talking, or both.)bongo fury

    Yes, but note that that information is implied by the structures.

    I can represent the original concrete situation in a model with the following obtaining states of affairs:

    (SA1) It is raining
    (SA2) Alice says that it is raining
    (SA3) Bob says that it is not cloudy

    I can add conditionals (note that this is a simplified model):
    (SA4) If it is raining then it is cloudy

    Further states of affairs can be derived:
    (SA5) It is cloudy (from SA4, SA1)
    (SA6) It is raining and it is cloudy (conjunction of SA1 and SA5)

    And so on. Similarly statements can be derived:
    (S1) It is raining (Alice's statement from SA2)
    (S2) It is not cloudy (Bob's statement from SA3)

    Finally, a conditional can be added that relates statements to states of affairs:
    (SAR) The statement s is true if and only if the state of affairs s obtains (where s has a logical form)

    So Alice's statement (S1) is true (from SAR, SA1) and Bob's statement (S2) is false (from SAR, SA5).
  • Metaphysics Defined
    A nice way to put it. I will keep it in mind. I meant only the distinction between the two, The, on the one hand, "great blooming, buzzing, confusion" that is input, and the coherent, consistent image we make of it.tim wood

    :up: With possible quibbles about "image". ;-)
  • Lazerowitz's three-tiered structure of metaphysics
    If, for example, you were to explain a "state of affairs" (like a raining) as a type (or set or common property) of concrete situations (which ground or constitute it in a reasonable sense), I might be challenged to show how nominalism can improve on that analysis, or is any less committed to abstractions itself.bongo fury

    I'm not clear on what you're really objecting to or what the above would look like. So I'll try a somewhat different approach and see if we make any progress.

    So the concrete situation is that it is raining outside and Alice says, "It is raining outside".

    Now suppose I want to model that situation. In my model, I can represent the weather formally as a state of affairs. This, it seems to me, is at least comparable to a physicist representing a physical system formally as a state. I can also represent Alice's utterance formally as a statement.

    The benefit of so doing is that it is now possible to apply logical operations or transformations on those formal structures.

    I'll stop there for now. Is that still metaphysics, on your view?
  • Metaphysics Defined
    That interaction is a physical process involving light reflecting from Aunt Betty to your eyes and subsequent brain processing.
    — Andrew M

    And thus it is completely clear that whatever "see" means informally or practically, the expression, "I see Aunt Betty," in some senses is completely misleading in the sense that Aunt Betty is never, ever, seen.
    tim wood

    In conventional use, the term "see" abstracts over the physical process, the details of which are a scientific matter. People (including children) use the term proficiently without needing to understand the details at all.

    So I'm not sure how you are using the term "see". That you instead see photons and infer that Aunt Betty is there? Or instead see a mental representation of Aunt Betty? Or see nothing at all?

    Interesting on task and achievement parts of speech. We're not about that book, idea, or author; feel free to ignore this question. How does Ryle tell the difference between task and achievement words in use? That is, it would seem he has access to other criteria - that are already available. What is his purpose then in making the distinction?tim wood

    Ryle just noted what people were doing when described by those words and analyzed the logic of their use. For example, when Alice is searching for her car keys, she is engaged in a task, searching here, searching there. What she is wanting to do, however, is not merely search for her keys, but to find them - that is her goal and motivation for searching. When she has found them, she stops engaging in that task since she has achieved her goal. So searching is a task word (with the goal of finding something) and find is an achievement word.

    Similarly Alice might be looking for a friend in a crowd and then finally she sees them. She doesn't continue to look for her. So in this case, looking is the process (a task or try word), and seeing is the logical condition that marks the end of that process (assuming it was successful - alternatively she might give up looking). So as an example of the logic of the usage here, Alice can look for her friend unsuccessfully, but she can't see her unsuccessfully.
  • Lazerowitz's three-tiered structure of metaphysics
    Oh well that's a relief... thank goodness that these intangibles are really quite grounded, and far from being any kind of metaphysical fantasy! :gasp: :rofl:bongo fury

    Exactly! :up:

    But they are both abstracted from concrete situations.
    — Andrew M

    Oh fine, so: not me guvnor, not really hardcore phantasmagoric abstractions but only made from solid "concrete situations"; then ok, I'll have a look. Can "that it is raining outside" please be the actual raining? Can Alice's statement please be her actual utterance?
    bongo fury

    Yes, of course. All of these abstractions are grounded in the actual raining and Alice's actual utterance.

    I guess you needed to go bold with your belief in abstractions to have confidence in this:

    They are sharing a pattern, which just is the abstracted common form.
    — Andrew M

    ... in the absence of any semblance of isomorphism between the utterance and the raining. No no no, you will be able to say to that complaint, poor philistine, doesn't understand about abstractions...
    bongo fury

    Briefly, the raining can be abstracted as an obtaining state of affairs, while Alice's utterance can be abstracted as a true statement. Now note that the same subject and predicate is present in both the state of affairs and the statement (i.e., it is raining outside). The pattern, then, is that the logical form of a state of affairs is the same as the logical form of a statement (i.e., they both contain a subject and a predicate).

    What is different about them is that a state of affairs has an obtain value while a statement has a truth value. So if that difference (i.e., the specific type of value) is abstracted away, then all that remains is the subject-predicate form with an abstract two-state value. So they are the same type of thing. In the absence of a better name, I'll call it a subpred. Now all that's needed are mappings between the two subpred structures. Which is that { obtains, does not obtain } maps to { true, false }, and vice-versa for the inverse.

    Diagrammatically:
    (1) Rain -> the obtaining state of affairs that it is raining outside -> the subpred that it is raining outside
    (2) Alice's utterance -> the true statement that it is raining outside -> the subpred that it is raining outside
  • Metaphysics Defined
    Give it a bit of thought. What, exactly, do you receive that your mind makes sense of? Aunt Betty or Uncle Jake? Certainly not! What you receive - is incident on you - is waves of some or another kind. If you think that what you see is the tree or a person or anything else, please give an exact account - or as best you can - as to how that happens, how it works.tim wood

    Sure. For your earlier example, there is an interaction between two physical systems - you and Aunt Betty. That interaction is a physical process involving light reflecting from Aunt Betty to your eyes and subsequent brain processing.

    Now suppose by the end of that process you have formed the (mistaken) belief that Uncle Jake is there. In conventional use, the word "see" is an achievement verb [*], but in this case the achievement criterion has not been met, i.e., that Uncle Jake is actually there. So you have not seen Uncle Jake, you only think you have. When you subsequently notice that it's actually Aunt Betty, the achievement criterion has been met. So you have seen Aunt Betty because she is actually there.

    Against all of this is what I called the language of convenience, which certainly gets the world's work done, and no complaints. You an even call it language based on perception. But on rare occasions it's best to acknowledge and attempt to understand that perception and underlying reality are not the same thing.tim wood

    Yes, we might sometimes meaningfully contrast what is seen in some sense (given signal travel times and reference points) with what is measured. But even here, what is being perceived is the world, not a Cartesian theater or something similarly mind-dependent.

    --

    [*] In ordinary use, terms like "see" and "find" are achievement verbs, as contrasted with task (or try) verbs such as "look" and "search". As Gilbert Ryle notes:

    One big difference between the logical force of a task verb and that of a corresponding achievement verb is that in applying an achievement verb we are asserting that some state of affairs obtains over and above that which consists in the performance, if any, of the subservient task activity.
    ..
    Merely saying ‘I see a hawk’ does not entail that there is a hawk there, though saying truly ‘I see a hawk’ does entail this.
    Gilbert Ryle - The Concept of Mind, p131-p135
  • Metaphysics Defined
    As a practical matter, absolutely. But I infer you understand perfectly well the objection and thereby can make the distinction between how it is and how it seems on those occasions that require it.tim wood

    Yes, we make the distinction between how something is and how it seems when required. But your claim was that we never see something as it is ("Alice actually is seeing zero"). I'm not sure whether that also carries over to knowledge, for you (i.e., that we never know something as it is).

    That is the entire production of the mind. One kind of evidence is that perception can be wrong. I think that's uncle Jake; oops, it's actually aunt Betty.tim wood

    You didn't see uncle Jake, you just thought you did. But the broader point is that even if you "saw" uncle Jake on your usage, it doesn't follow that seeing aunt Betty is a production of your mind. That you seem to think of it in that way suggests that you're positing sense data.
  • Metaphysics Defined
    I'm not sure I understand you. Suppose Alice sees a bird fly by and land on a branch. She perceived the bird flying and then perceived it landing. The difference in those two cases is with the thing perceived (the bird) not the perceiver (Alice).

    So that is an example where how the world is perceived and understood depends at least in part on the thing being perceived.
    — Andrew M

    Eh? All I get from this is that there is a bird and the bird is not Alice. If you mean only that there must be something (usually) that is perceived that is itself not the perceiver, ok. But the perception itself as a perception - which is what I'm thinking we're talking about, depends on the perceiver. Whatever it is that Alice perceives is the product of her mind.

    One way to make it clearer about the bird - although less clear about the phenomenon itself - is to remind yourself that "sees the bird" is simply language of convenience, and that of the bird itself or the branch or anything else, Alice actually is seeing zero.

    What Alice is working with is her own mind's production. Inputs? Sure. And as a purely practical matter we all agree she "sees" the bird, and that there is a bird and a branch. - Here, another way. That which is in Alice's perception, is that the bird and the branch? Of course not.
    tim wood

    In ordinary use, perceptual terms are usually understood to refer to independent things like birds and branches, not the products of minds. So I disagree that "sees the bird" is simply language of convenience and that "Alice actually is seeing zero".

    This may just be a terminological disagreement or a more substantive disagreement about sense data but, either way, I don't see any reason not to take ordinary use seriously there.
  • Lazerowitz's three-tiered structure of metaphysics
    So, it is their actually sharing a pattern? As with the case of a written melody and the sound represented?

    But apparently not, and you shrink from analysing situation and statement both into component parts, and abstracting out a common form:

    For example, it is raining outside (the state of affairs) and Alice says that it is raining outside (the statement).
    — Andrew M
    bongo fury

    They are sharing a pattern, which just is the abstracted common form.

    To transform a state of affairs to a statement, quote it. To transform a statement back to a state of affairs, unquote it.

    A state of affairs is an abstraction - something that obtains or not. A statement is also an abstraction - something that can be true or false.

    But they are both abstracted from concrete situations. For example, that it is raining outside (a state of affairs), or that Alice says that it is raining outside (a state of affairs where Alice makes a statement).

    That they are abstracted from concrete situations is what prevents them from being Platonic Forms (which would "exist" prior to any concrete situations).

    I'm asking how you use the term "true".
    — Andrew M

    I point it at the sentences I assert.

    For example, I assume you believe there were dinosaurs roaming the Earth millions of years ago based on evidence such as the fossil record. Is your belief true because you have formed it based on that evidence? ...
    — Andrew M

    Meh. Attitudes... obviously I can assert the wrong sentences, or (equivalently) call those wrongly chosen sentences true. So?
    bongo fury

    By "wrong" or "wrongly chosen" sentences, do you mean false sentences?

    If so, then I take it you hold either a deflationary or correspondence-style theory of truth, not a coherence theory of truth (which is what I was assuming). Would that be right?