In this sense QM is a kind of 'card' that sophisticated parlor gamers overrule, perhaps justifiably, with a disdain 'card.' — csalisbury

QM is the "trump" card. But if we don't like the idea of trump, and think it's a cheat, we can just make rules allowing us to ignore whoever's playing trump.

Then I would say there is still a problem, if the mind at all was involved with the movement of the physical body. — Rich

How the non-physical moves the physical is a complex issue, this involves free will, intention, etc.. I believe it can only be understood through a thorough understanding of the nature of time. No one has such an understanding of time. Do you notice that the past is radically different from the future? Think about the future. It is always right in front of you but you cannot see or sense anything in the future. That is because there is no physical existence in the future. The fact that, through a free willing act, the human being can change, or destroy any physical thing within its power, at any random moment of the present, demonstrates that there is no physical existence prior to the present. The continuity of existence at the present, which we take for granted in laws such as Newton's first law of motion, is not necessary. This means that the entire physical world must come into existence at each moment of the present. The soul, having its existence anchored in the non-physical side of the present, has some capacity to control how the physical comes into existence at each moment. Therefore it moves the physical body.

There is also the issue of how does the mind "grasp". How does the physical convert into something that can be grasped by the non-physical. I believe Bergson, as he was extremely well studied and reknown for his understanding of mathematics, biology, psychology, and philosophy, set out in his own metaphysics to — Rich

I am not familiar with Bergson, perhaps you could explain some of his principles. As far as how the mind grasps the physical though, I understand this in traditional Aristotelian terms of matter and form. It is not that the mind converts the physical into something that can be grasped, it is that the physical already exists in such a form. Under Neo-Platonic principles, the Form of any, and every object, must pre-exist that object in time. How I understand this, is that the form of the object, exists in the future of the object, and this determines how the physical object will come into existence at each moment of the present. To change the object is to change its form, such that when it comes into existence at the next moment, it will be different. So the form is fundamentally separable from the physical object, as the existence of the physical object relies on the form, but not vise versa. When the mind grasps the object, it grasps the form of the object. Being a form itself, I believe the soul has the capacity to reproduce aspects of the form of the object, in sensation, or in conceptual structure, without actually altering the object. It is a representation. The material aspect appears to be beyond the grasp of the mind, and this limits our ability to apprehend, and change the world.

Traditional dualism would not say that the soul is insubstantial, because the assumption would be of a substance dualism. What the mind grasps is the form of the object, not the object itself which consists of matter and form. If the form must have matter to exist, then there must be a material element within the mind that grasps the form of the object. Many dualists though, would argue that a form could exist independently of matter, but matter cannot exist without a form.

The problem is that they are distinct then what is the bridge? — Rich

The bridge is "matter" itself. Physical objects exist as forms, we describe their properties. The human body is such a physical form. We assume that physical objects consist of matter, and the matter substantiates the form that an object has. But physicists have not yet determined "matter".

As I have said a million times, Non-Euclidean geometry does not refute the axiom that the shortest distance is the perpendicular - among many other axioms that aren't refuted. So you have to explain to me where does this axiom get its certainty from, because it seems that regardless how our space is, it can't be refuted. — Agustino

I never said that one refutes the other, remember, I said we establish compatibility between the two. The heliocentric model of the solar system does not refute the claim that the sun rises in the morning. It just allows us to see this in a different way.

As I said before, your axiom gets its certainty from empirical verification, measurement. Without measurement you could state any random axiom such as "the shortest distance from a line to a point is at an 80 degree angle to the line". How is your axiom of the perpendicular more certain than this axiom of the 80 degree angle, without measurement? The only reason why your axiom cannot be refuted is because it can be demonstrated empirically, measurement. Therefore it does derive its certainty from "how our space is".

If you want to look for principles which do not derive there certainty from empirical verification, true a priori principles, you should look to mathematics. I already suggested two possibilities, the equality between units, and the order. I'm starting to think that order may not be truly independent of experience, because it may be derived from the experience of temporal order. So let's look at the equality of units.

How is it that we know, with a very high degree of certainty, that there is an equal difference between one and two, two and three, three and four, etc.? Where do we derive this idea of equality? It seems that in all empirical observations we see no examples of such absolute equality. However, we seem to know with absolute certainty that there is an absolute equality with respect to the difference between the integers.

experience occurs on a stage which is ideal and not real. — Agustino

You are the one using a fiction. You rely on seeing those lines being curved in a Euclidean analogy to non-Euclidean geometry to say that they are curved in non-Euclidean geometry which is patently false.

The straightness of a line is governed by its intrinsic curvature. Non-Euclidean curvature is an extrinsic curvature - space itself is curving. This has nothing to do with the straightness of the line - with its intrinsic curvature. — Agustino

OK, we both seem to be saying the same thing, the straight line is really curved. It has an "intrinsic curvature", so its straightness is just an illusion. If you want to say that its straightness is real, and the intrinsic curvature is an illusion, that's fine by me. But remember, you are the one who said "experience occurs on a stage which is ideal and not real". As far as I can tell, the straightness is ideal and not real.

In any case, the reason I wanted to separate geometry from mathematics is that I think all geometrical principles are dependent on empirical evidence, and therefore uncertain. I think this discussion only serves as proof of that point. I would prefer to move on to the principles of mathematics, in an attempt to determine whether there are any purely a priori principles.

No it's really no illusion at all. If you are a two dimensional creature living your live on a two dimensional piece of paper which is curved to form a cylinder, when you're walking around the cylinder on a curved line, you yourself necessarily perceive it to be a straight line, and cannot perceive it as curved. — Agustino

Show me a two dimensional creature living on a two dimensional surface. That's fictitious. Why do you need to refer to a fictitious scenario to demonstrate your claim unless your claim is itself fictitious?

The only way you can infer the curvature of your space, is if you find a way to alter it. — Agustino

You are proceeding in the exact opposite way of reality, away from reality instead of toward reality. You base your unreal claim that two dimensional geometry is true by referring to a fictitious scenario. Then, you claim that you can only understand the true nature of space by altering it. But that's only because you are starting from your fictitious 2d assumptions, then claiming that the only way to make the reality of space compatible with you fictitious assumptions is to alter it. You fail to realize that the proper procedure is to alter your fictitious assumptions, because you cannot alter the reality of space.

This is irrelevant though. A geodesic appears as a straight line to observation - in fact, it actually is a straight line in a curved space. Non-Euclidean geometry includes Euclidean geometry - Euclidean geometry occurs when space simply has 0 curvature. But that the perpendicular is the shortest distance between a point and a line holds true in either Euclidean or Non-Euclidean space. In Non-Euclidean space, the perpendicular straight line (or geodesic) is still the shortest distance. — Agustino

To say that it "appears as a straight line", indicates that you recognize this as an illusion, which is not the true reality of the situation. The straight line is one dimensional. The perpendicular employs a second dimension. So it is just an extremely simplistic way of looking at the space around us. The fact that we can establish compatibility between the simplistic way of seeing things, and the more complicated (but more accurate) way of seeing things, does not indicate that the simplistic way is true. It is just the case that in order to convert one's mind from seeing things in the simplistic way, to seeing things in the more accurate, but complicated way, compatibility must be established. This is evident when we went from a geocentric to a heliocentric way of looking at the solar system. Despite the fact that the movements of all the planets, sun and moon, could be predicted from the geocentric model, and these movements had to be made consistent with the heliocentric model, it would be wrong to argue that the geocentric model is still a true way of seeing things.

If you look here — Agustino

So all that is being done here, is that the more complicated, and more accurate conception, "curved space", is being made to be consistent with "a straight line" that you may see. But you only actually see a straight line on a 2d surface, or a 1d string line. And this does not account for the space which exists between 2d surfaces, or all around the string line. It's an extremely simplistic, artificial and manufactured way of "seeing" things. Even the 3d representation does not account for the fact that time is passing, so it is still way too simplistic, artificial and manufactured. It is not a true representation of "space-in-itself" because it is too simplistic. Space-in-itself does not exist independently of time passing, so any representation which cannot account for time passing is inaccurate.

But I would not feel so all alone.
Everybody must get stoned.

Because there is a space-in-itself whose effects we notice, despite our inability to perceive this space-in-itself. — Agustino

Let's suppose there is a "space-in-itself". Isn't this contradictory to Schopenhauer? Space cannot be a pure intuition, nor an idea. And this validates what I have said, none of our spatial principles, Euclidian or otherwise, can be certain. They are all susceptible to doubt.

Nevertheless, I think dualism has a big problem indeed. If we say mind is not anywhere in space and yet it is obviously temporal then why we don't hear each other's thoughts? That is what bothers me. If the thought occur at the same time then what makes us not here all the thoughts? — Veronika Pugach

I think you need to distinguish between being non-spatial, and being located in space. My soul may have a location, coinciding with my body, but it can still be non-spatial itself. Consider the dimensionless point. The point may have a location in space, but it is dimensionless, occupying no space, and therefore non-spatial. Two non-spatial points will have space separating them.

The part of me which is non-spatial, my soul, and the part of you which is non-spatial, your soul, are separated by space and therefore we have no direct access to each other's thoughts. Even within my own body, "my soul", may consist of numerous such non-spatial points which have established control over the immediate spatial environment, through the creation of "my body". You and I, and others, may communicate, and attempt to establish control over a larger spatial environment.

I disagree with this. There can be no situation where measurement would indicate that the perpendicular from a line to a point isn't the shortest distance from the line to the point. If you think there can be, please conceive of and give me such an example. — Agustino

I am not a physicist, but I understand that this is the case with 4d space-time. Space-time is curved according to the principles of general relativity. Do you know what a geodesic is? You can research this on Wikipedia and other sources. Euclidian geometry assumes a static space, as if there is a static "present time" at which measurements can be made. But once we account for the fact that nothing is static, everything is moving in time, so that the present time is indefinite, our concept of space must be adjusted to allow for this. That is why a straight line cannot be consider to be the shortest distance between two points. Physicists now take into account that time is passing when they make such measurements. The entirety of Euclidean geometry can be dismissed because it assumes a static space without the influence of passing time. The concept of space which Euclidian geometry presupposes, has been demonstrated to be inaccurate. Therefore Euclidian geometry itself is inaccurate.

Before I proceed, I want to distinguish mathematical from geometrical. I think that this is important, and the importance may become evident when we bring time in relation to space. So far we've discussed spatial geometry independently of time, in an abstract way. When you say "the shortest distance from a line to a point is the perpendicular", this is not a mathematical truth, but a geometrical truth. That this is true, is proven with measurement, and when we measure we apply mathematics. Geometrical principles are proven with mathematics.

The problem is that this process of proving, measuring, is an empirical process. One could state any random geometrical principles, and the truth, falsity, or certainty of them is only revealed through the empirical proof. Because of this, geometrical truths are not really a priori. They might be in principle a priori, but that the shortest distance from a line to a point is the perpendicular, rather than some other angle, is true, is a posteriori.

So let's take the basic principle, the shortest distance between two points is a straight line. That there is a separation between two points assumes that there is something between them. This we call space. So even to demonstrate that there is separation between two points requires an empirical process, so all geometrical concepts are fundamentally a posteriori.

What Kant/Schopenhauer do, is that they go further and claim that, instead of being a posteriori to experience, they are a priori - hence why they are certain. — Agustino

I think that this is a mistaken principle then. These geometrical principles are a posteriori, and therefore they are not certain. This is due to the nature of the empirical proof, and it is well demonstrated by Einstein's relativity theory. The problem is that when we assume a separation between point A and point B, we assume space between them. To measure this separation, something such as a beam of light must traverse the space between point A and point B. This requires time. Due to this passing of time, the shortest distance between two points is no longer considered to be a straight line. That's the curvature of space-time. So even the most fundamental geometrical principle, that the shortest distance between two points is a straight line is not certain. It has been proven uncertain by the empirical process which is required to demonstrate its truth.

Yes, but put yourself in Schopenhauer's shoes. Euclidean geometry is capable to perfectly represent your reality in spatial terms. How is that possible? It's because the form that our mind imposes on experience (space) ensures that this is so. There is nothing to wonder about - they are certain because they are of subjective origin - they are forms through which experience itself is possible. In fact, remove those forms, and our experience itself becomes impossible. The world as representation is impossible if there is no space, time and causality. Why? Because any representation is a representation by virtue of being situated in space, time and causality. And these three are ideal - they are the structures of the mind - the forms provided by the mind. — Agustino

So I believe this is all backward. Euclidian geometry is not capable of perfectly representing spatial reality. It is deficient because it does not take into account the way that time is related to space. When we bring time and space into relationship, which is necessary in order to understand spatial reality, Euclidian geometry fails us. So instead of what you say, ("It's because the form that our mind imposes on experience (space) ensures that this is so"), the reality of space imposes itself onto the forms which our minds produce, forcing us to change what we may have previously considered to be a certainty.
And as I explained in the case of space, all three of these, space, time, and causation, are concepts which we are forced to produce in order to account for our experience. We produce a concept of space to account for our experience of separation

Some parts of mathematics evolve - BUT, not all. — Agustino

Now, that we have separated geometry from mathematics, and I think that this was necessary because it is evident that all aspects of geometry are uncertain, and are evolving, we can ask whether there are aspects of mathematics which are certain, and cannot evolve. I believe that there is, and that this is to be found in a number of aspects. First, there is a necessary equality of units, and second there is a necessary order. Each of these may be an a priori certainty.

Yeah well said... which is tragic. It makes reality unintelligible. There is no controlling factor at all. — Agustino

Why would you say this? Surely there is a controlling factor, that is the passing of time. What do you have in mind as a "controlling factor"?

Let me first provide more detail on Schopenhauer. Now why is it important that space, time and causality are ideal? Well, their ideality explains both why they are (1) a priori, (2) synthetic, and (3) apodeictic, and hence certain. The Scholastics had trouble in proving the certainty of their principles. Why is the principle of causality certain for example? Schopenhauer answers that it is certain because it is an ideal form applied by our own mind - that also explains why the mind intuitively knows it. — Agustino

Actually, I think you have contradiction here Agustino. Something which is purely ideal cannot be (2) synthetic. It's being analytic which makes it ideal, and this is what guarantees that it is apodeitic as well. Are you sure that Schopenhauer is not arguing that these ideals are analytic?

So empirical reality is the domain of science. It is empirically real, and therefore worth studying. It is the external aspect of reality - one side of the coin (the other being thing-in-itself). The forms of the intellect (space, time and causality) are the study of metaphysics and theoretical mathematics (which is why metaphysics and mathematics are guaranteed certainty). — Agustino

I would not class metaphysics with mathematics here, because being concerned with ontology, metaphysics must have respect for empirical reality as well. But, as l explained earlier, mathematics itself changes and evolves in relation to what is practical, so even mathematics cannot guarantee certainty. The fact that mathematical principles have changed through the passing of time, as we have progressed with our understanding of empirical reality, demonstrates that even mathematics does not guarantee certainty.

The Will is the study of ethics (and metaphysics) and approaching the thing-in-itself. The thing-in-itself is the study of mysticism. The beauty of Schopenhauer's system is that it renders to all these sciences or areas of study their proper place, and also explains how it is that they are possible in the first place. — Agustino

It may be the purpose of Schopenhauer's metaphysics to put all the areas of study in their proper place, but this itself is an empirical practise. It is a process which describes each existing science, and is therefore empirical.

If we do this, then how do we explain the certainty of mathematics? How do we explain its a priori nature and also it's non-logical, synthetic character? — Agustino

You mean non-logical analytical character don't you? The point is, that from the perspective which I described, even the absolute certainty of mathematics is revealed as an illusion. It may be the case that there is something which is a priori, in an absolute sense, the intellect, the will, the soul, God, or some such thing, but even the principles of mathematics are tainted by empirical practicality. This is why Plato is forced to posit "the good" in The Republic. The good is what makes all intelligible objects intelligible, and there is no exception here, not even mathematical objects. They are only intelligible in so far as they have a relation to the good.

No you're not, because for Schopenhauer the thing-in-itself is one side of the coin, and the other is the phenomenon. Hence "World as Will and Representation". It doesn't seem like you have two sides here. That's a problem, because how will you account for mysticism, romantic love, character, etc? — Agustino

You don't see the two sides of the coin here? There's matter in the physical world, and matter as content, subject matter. They both appear to be the same thing, looked at from two distinct perspectives, two sides of the same coin. In one case we look outward into the physical world, and we find it necessary to assume "matter" to substantiate our empirical observations. In the other case, we look inward, and must assume content, subject matter, to substantiate the existence of intelligible objects, ideas. And this is where we find your mysticism, romantic love, character, etc..

We have the same "two sides" in a lesser developed way with Plato's "the good". There is "the good" in the sense of what is intended, what is desired, wanted, and this is within your mind, an ideal. Then there is "the good" as it is brought into existence in the physical world. In your mind, the good is a desired state, something to be brought into existence, what is wanted. When we act we actually bring something into existence. The intent is to bring into existence the good as it is desired, as it exists in the mind. But the action does not necessarily bring into existence that very same good which was intended, and this is the source of uncertainty. So the "two sides" are not actually two sides at all, they are two distinct things which bear the same name, "good". This is the same in the case of the assumed matter in the sensible world (thing-in -itself), and the internal subject matter, the mystical content. They are not really two sides of the same thing, they are completely distinct. The fact that we do not have here two sides of the same thing, rather two distinct things, is why we adopt a dualist metaphysics.

To clarify, the model (often called a "world") in which these two propositions are consistent is one in which ravens do not exist; hence X is not a raven, regardless of whether X is black or not black. This goes back to the point about universal propositions not asserting the existence of anything. — aletheist

The point about whether or not ravens exist was very relevant, but the argument was not formulated in a very logical way, which is necessary to reduce the appearance of paradox.

Yes kind of. For Schopenhauer, what necessitates the assumption of the noumenon is the fact that experience occurs on a stage which is ideal and not real. — Agustino

If we take the Platonic route, we resolve this problem by making the ideal the real. Now the stage, which is the ideal, is what is real, and the sense world is illusionary.

So the question arises as to what lies behind the curtain so to speak. If space, time and causality are ideal, then all of experience, which is structured by these, becomes mere phenomenon. So the structure of experience is ideal, but the content must be real. — Agustino

Next we have the issue of content. Under the Platonic scheme, the content is no longer real. This comes out as Aristotle's "matter". The form is what is real, and matter is something which we need to assume the existence of, in order to make change intelligible. So as much as "the structure of experience" is real, it is only intelligible through the assumption of matter, which is not real, it is only assumed. Content is assumed in order to make experience intelligible.

Therefore what is the source of this content? — Agustino

Under this model then, the source of the content is the mind itself, matter is an assumption, it is purely theoretical, produced by the mind itself. Matter, content, is what the mind creates.

The Will is the closest we get to thing-in-itself, because the Will is outside of space and causality, but not outside of time. We find ourselves willing so and so; nothing causes it. And neither is our will as we experience it subjectively in space. But our will is in time - one movement of the will occurs after another. These are obviously paraphrased for what Schopenhauer says, which is a lot more nuanced, than my brief and very downgraded remarks here. — Agustino

Now we are nearly consistent with Schopenhauer, the thing-in-itself, matter, content, is what is created by the mind. Schopenhauer may represent it as the creative power of the mind, the Will itself. Or, as you say, the Will is "the closest we get to the thing-in-itself" We've removed Will from all spatial context, so what we can do next is to see if it has temporal context. By referring to Aristotle's concept of matter, which has now become consistent with mental content, as subject matter, we find that this concept refers to that which violates the law of excluded middle. It is what may or may not be, potential. We can give this "potential" temporal context at the present, the middle, between the past and future.

This is contradiction. If two statements are logically equivalent according to contraposition then ipso facto they have the same truth value in every model. — Michael

No that's not the case, we've already gone through this with the raven example. Reread my posts if you do not understand.

P is "X is a raven". Q is "X is black". So, P → Q is "if X is a raven then X is black". Which is logically equivalent to ¬Q → ¬P, "if X is not black then X is not a raven". — Michael

Now consider the other proposition "if X is black then X is not a raven". This is consistent with "if X is not black X is not a raven", but it is not consistent with "if X is a raven then X is black", so the two statements do not have the same truth value in every model. In this model, the one which holds that "if X is black then X is not a raven", the one may be true while the other is false.

I really don't understand what you're trying to argue here. I have provided references that show that P → Q is logically equivalent to ¬Q → ¬ P and that two statements that are logically equivalent have the same truth value in every model. — Michael

What we have been discussing is the raven paradox. I've demonstrated how the two statements are not what you call semantically equivalent. They are logically equivalent according to contraposition, but they do not have the same truth value in every model, so they are not semantically equivalent.

Now you have presented me with symbols, "P" and "Q". Unless these symbols are meant to symbolize something, how are we to discuss semantic equivalence? To say that the two statements have the same truth value in every model is meaningless, because P and Q are just symbols which don't represent anything, so there is no truth or falsity of those statements to discuss. How can we discuss whether "if P then Q" is true or false if the symbols have no meaning?

I would if I knew Schopenhauer's transcendental idealism, but I don't, so I can't. The existence of numbers and mathematics is difficult because it appears as purely ideal. Geometry is easier because it is clearly not purely ideal. Geometry surely gets shaped by its practical application just as much as it does by its free creation in theory. In the case of mathematics it is not so clear, but I believe that there are examples of the theoretical principles of mathematics changing according to practicality. Mathematical principles evolve. We've seen the zero come into existence. We've seen calculus and algebra come into existence. We now have imaginary numbers, and to my mind imaginary numbers allows for contradiction within the mathematical principles.

This implies that there may be no such thing as pure a priori. Perhaps only time will prove to be purely a priori. I think that Kant allows that geometry and spatial concepts are a priori. Schopenhauer may have wanted to limit the pure a priori to mathematics. Ironically it is the existence of the pure a priori which necessitates the assumption of the noumenon (noumena), because this is what transcends experience. By confining, limiting, that which transcends experience, we get closer and closer to the noumenon itself.

This is a semantic concept; two statements are equivalent if they have the same truth value in every model".

There really isn't anything to argue here. — Michael

That's right, there is nothing to argue here. So long as you separate logical equivalence, equivalence according to contraposition, and semantic equivalence, equivalence of meaning, and do not equivocate between them, as you have been doing, then there is no paradox, and nothing to argue.

However, I generally do not like arguments that revolve around relatively new physics concepts given that, as Arkady mentioned, we know that our current understandings of modern physics, quantum mechanics included, do not mesh together and are currently incomplete. Yes, there may be some interpretations that allow for immaterial causes to influence material causes, but unless we have reason to believe those interpretations over others, I do not see the point here. — Chany

The point is that science gives us evidence that there is no good reason to consider (4). There is no good reason for the claim that the immaterial cannot interact with the material, because modern science clearly demonstrates that it is possible that the immaterial interacts with the material.

I find arguments directly confronting dualism that amount to "your metaphysics are weird and has mysterious elements" to be poor. — Chany

I agree. Once we clear that up, the fact that there is no good reason to reject dualism as a metaphysics, then we can move toward assessing the benefits which dualism offers. These include a rational approach to the existence of freewill, intention, and human creativity, as well as an empirical approach to the nature of time, the past being distinctly different from the future.

Furthermore, I'm not saying that it says something about the ontological nature of space. I'm simply pointing a fact that Schopenhauer doesn't seem able to account for the non-Euclideanness of space as it is not an a priori perception generated synthetically through a form our cognitive faculties impose on us - this only raises the question, where does it come from? And at least one part of space is not transcendentally ideal, and therefore, it can only be empirically real. — Agustino

Start from the proposition that space is purely conceptual. It doesn't have to be Euclidean, it doesn't have to be any particular way at all, it is however we as the conceptualizers, make it to be. For example, the circle doesn't have to be 360 degrees, it doesn't have to be divided into four right angles, or anything like that. Human beings chose to do this. They chose to do this because they had a system of numbers, and they wanted to apply the number system to the sensible world, in measurement. So they produced geometry in order to apply numbers in measurement.

Now we have a concept of "space" which has been constructed through the use of geometry. You talk about the "non-Euclideanness of space", but all this means is that you opt for a conception of space which is non-Euclidean. Why would you opt for such a conception? Well, if Euclidean geometry proved to be inadequate for certain activities of applying mathematics to the sensible world, in measurement, then we would have to produce a Non-Euclidean geometry which was adequate. This geometry would produce a non-Euclidean concept of space, and so, the non-Euclideanness of space.

So the question of where does the non-Euclideanness of space come from, is answered with "it comes from the inadequacies of the Euclidean concept of space to fulfil our purposes of measurement". We do not need to make any judgements about whether or not space is "empirically real", all we need to judge is whether or not our geometry (and therefore concept of space), is adequate for measuring the aspects of the world which we judge to be empirically real.

The total mind-body problem, at least as I was taught, contains four premises:

(1) the mind is res cogitans (immaterial).
(2) the body is res extensa (material).
(3) mind and body interact.
(4) res cogitans and res extensa cannot interact.

Dualists deny premise four. — Chany

I think that this is a better representation than Arkady's. Now if we want to bring the evidence of physics into this, there are interpretations of QM, hidden variables and non-local interaction, which allow for an "immaterial" which interacts with the material. Once we establish through the principles of physics, that the immaterial may interact with the material then we have no basis for a denial of #4.

No it doesn't. How have you derived that? Certainly not with the law of contraposition. — Michael

Look Michael, take (2) as a proposition. "Everything that is not black is not a raven.". Now take the proposition "Everything that is black is not a raven". Is there any contradiction evident here which would exclude those two propositions from being consistent within a particular model? I don't see any. This is model #1.

Now take a model which has as a proposition "All ravens are black". This is model #2. Model #2 is not consistent with model #1 because "all ravens are black" contradicts "everything that is black is not a raven.

The definition of logically equivalent is "Two statements have the same truth value in every model." It is evident that "all ravens are black" is not true in model #1, but true in model #2, yet "everything that is not black is not a raven" is true in models #1 and #2. Therefore "everything that is not black is not a raven" is not logically equivalent to "all ravens are black", according to the definition.

Yes they are. It's guaranteed by contraposition. — Michael

If contraposition guarantees a type of equivalence, then clearly it is other than "logically equivalent" as per your definition.

Here is the issue. Logically equivalent, as per the definition ensures that logically equivalent statements have the very same meaning, as you've been arguing. But two statements which are equivalent by contraposition do not necessarily have the very same meaning, as I've been arguing. Therefore logical equivalence, as per the definition, and "equivalence" as guaranteed by contraposition are not both the same form of "equivalence".

(2) Everything that is not black is not a raven. — Michael

The problem is that this (2) also allows that "Everything that is black is not a raven" is true as well. So it is impossible that (1) and (2) are logically equivalent, under that definition of logically equivalent.

No, that would be material equivalence. We're discussing logical equivalence. — Michael

OK, I wasn't clear on your definition of "logical equivalence". If this is your definition of logical equivalence:

Two statements have the same truth value in every model — Michael

Then (1) and (2) of the op are not logically equivalent. That is the problem, you are assuming that they are logically equivalent, without adhering to your definition of "logically equivalent".

Actually, what we are looking at is two statements which have the same truth value within the same model. So you need to adjust your claim to read:
"Two statements have the same truth value in the same model iff they mean the same thing."

What I would like to see, is if you can justify the following claim. If this can be justified, then you might have an argument:

Two statements have the same truth value in every model iff they mean the same thing. — Michael

All you are saying is that logical equivalence is not "the same" as numerical equivalence. You have just provided evidence for my argument, that "equivalent" does not mean 'the same".

Two statements have the same truth value in every model iff they mean the same thing. — Michael

Again, I think you're mistaken. You've applied an unjustified condition to "mean the same thing".

Here's a little example. Let's say that 2+2=4. There is a logical equivalence between (2+2) and (4). Now we can have a look at what each of those means. I assume that (2+2) means that one group of two is added to another group of two. I also assume that (4) means one group of four. I see a difference between the meaning of (2+2) and the meaning of (4). You have applied an unjustified principle, to say that because the two are equivalent they have the same meaning.

Here is the result of your application of that unjustified principle. If we observe, and therefore have evidence, that one group of two objects was added to another group of two objects, we can claim to have evidence of a group of four objects. But if we have evidence that there is a group of four objects, this does not constitute evidence that a group of two objects was added to another group of two object.

Two statements that are logically equivalent mean the same thing, and so have the same truth value in every model. — Michael

You might say that two statements which are logically equivalent have the same truth value. But that is my point, they are equivalent according to this system of "value", and this does not imply that they "mean the same thing".

Two statements that are logically equivalent mean the same thing... — Michael

Again, I think you're mistaken here. Logical equivalence is not defined as two statements which are logically equivalent "mean the same thing".

To be "equivalent" logically, does not mean the same thing as to be the "same". This is a mistaken assumption.

They do not say the same thing, they say an equivalent thing. Therefore what they say is equivalent, not the same. Likewise the table and the chair are both "one" object. They are equivalent, as "one", but not the same

Given the logical equivalence, any evidence in support of (2) is also evidence in support of (1). — Michael

The issue here, which creates the appearance of a paradox, is with the notion of "equivalent". Logic proceeds by doing a very neat little trick, (which is extremely evident in mathematics), of making two things which are not the same, "equivalent". So the key to understanding the paradox is to understand what is meant by "logical equivalence". We know that (1) and (2) do not say the same thing, they are said to say equivalent things.

When we make two different things equivalent, we assign to them the same value. We do this by neglecting some qualities as accidentals. We can say the chair is one object, and the table is one object, so that they each have the value of one. They are equivalent, but not the same. They are each one. Likewise, (1) and (2) are equivalent by having some sort of logical value assigned to them, but they are not the same. Since they each state something which is qualitatively different from the other (though what is said is in some way equivalent), we cannot say that everything which is evidence of the truth of one is also evidence of the truth of the other.

They're logically equivalent because of the law of contraposition, and evidence for one is evidence for the other because they're logically equivalent. — Michael

I do not think that the law of contraposition entails that everything which is evidence of (1) is also evidence of (2), or vise versa, because it does not take into account what differentiates (1) from (2). Though they are equivalent, (1) and (2) are different. Because they each state something different, evidence of the truth of (1) is not necessarily evidence of the truth of (2). When we make them equivalent, they are equivalent based in some principle of logical validity, not in a principle of empirical truth. So evidence that (1) is true is not equivalent to evidence that (2) is true. We would need a different principle of equivalence to make this conclusion, one which does not exist, because (1) and (2) each say something different.

No because an icon is not made to represent God.

What is an image? And what is a non-image? — Agustino

An image, or idol, is a material object taken to be a representation of the immaterial God. You are not supposed to worship the material object, you are supposed to worship the immaterial God. Therefore there is no purpose in making such an image. It was for the same reason that many insisted God should not have a name. The name being a representation, or image of God. If God has a name, then we may start to worship the name, and forget about God. This is important because it is how we affirm that we all worship the same God. If we worship an idol, or image, then different groups start to worship different idols and therefore different gods. Then no one pays attention to God.

Trump believes X because he believes X, and seeks to make X win. — Agustino

That's nonsense. I vote with Wayfarer and Banno.

It may be impossible for us to be able to put ourselves in the position of our future locations, but the break in the wall remains doubtful to me; as when you walk around a circular wall you have no idea what is to come, yet you are still able to walk with the same wall adjacent to you. — GreyScorpio

But the point was that we cannot find this continuity in the wall, we cannot "walk around" the wall because there is a break in it, and that is the present. See, there is a wall to the past of us, and a wall to the future of us, and these two walls have completely different features. As much as we try to connect these two walls, by claiming that what "is", is at the present, we cannot validate this "what is at the present", so the two walls remain as distinct. We cannot connect them.

In other words, if there were a break in the 'wall' there would be no intention of us progressing to the future (the broken wall) as it would be detached from existing in time. Though it may be correct that what hasn't happened does not yet exist, but the intention for there to be a future does. — GreyScorpio

What is detached, is "existing in time". This is what we make up, fabricate, as what is existing at the present. From our perceptions, we create a concept of what it means to exist at the present, and this is our fabricated world. In reality though, things are behind the two walls, past and future. However, we are given a glimpse at reality through this separation between the two walls, when things pass from being in the future to being in the past. From this glimpse of reality we create our "world".

Though it may be correct that what hasn't happened does not yet exist, but the intention for there to be a future does. Therefore, it is only logical that there must be a 'wall' for us to continue down to process, as we progress in journeys with a similar was adjacent to us. — GreyScorpio

What I think, is that there is separation between us, there is separation between your mind and my mind. I am not thinking your thoughts, and you are not thinking mine. Because of this separation we think that there is some sort of wall at the present. the wall separates us. This validates our claim that there is a material world, the separation which exists between us. We apprehend this separation as a spatial separation, that is what we perceive, there is space between us, we can measure the distance. But when we try to comprehend this separation with our minds, it takes on the character of a temporal separation. You are always in the past from my perspective at the present, and I am always in the past from your perspective at the present.

Opportunism is choosing your views based on whether they're winning. Trump CLEARLY doesn't do this, by sheer virtue of the fact that his views are very unpopular. — Agustino

Where there are winners, there are losers. "Winning", means others are losing. Having as a goal "to win", makes you unpopular. The two things which you said Trump has strong views on, trade and torture, are both means for winning. Come on, "America First", is not a goal of winning?