We're talking past each other here. Sure if you want let's say that there is space between objects and that objects occupy space. You agree that this space is conceptual, that it comes from measurements, either measurements between objects or measurements of objects themselves. — leo

We're talking past each other because you are not listening to what I am saying. The point I was making, is that the space which is between objects (which is how you define "space"), is apprehended, or conceived of as being substantial. When you measure, there is necessarily something which is being measured. When you measure the distance between objects that something is space.

So what does it mean to say that space "bends", or "curves", or "expands"? It simply means our measurements are changing, that is the distance between objects changes, or the shape of the objects change. It decidedly does not mean that space is not merely a concept but a tangible substance that physically bends or curves or expands and is responsible for the changing distance between objects. An object is a tangible thing, a measuring device is a tangible thing, space is not, you said it yourself it's a concept, you can't take a spoon of space, you can't boil space or cut it in half, you can't throw space, you can't lick space, ... — leo

So this is wrong, when we say that space bends, curves, or expands, we are saying that space is substantial, and these are the properties that it has. Yes, "space" is a concept, but within that concept, as necessarily implied, or dictated by the concept, is that space is something real, substantial. This can be readily understood through what I said above. When we measure, there must be something which is measured or else the measurement is meaningless. It is invalid as an actual measurement if there is nothing substantial which is being measued. So when we measure the distance between objects, we presuppose the substantial existence of "space", as the thing being measured.

Objects move and change, because time is passing. In our attempts to understand and conceptualize these changes we've come to the conclusion that space curves, bends, and expands. This is what happens to space, as time passes, and this new, more comprehensive way of understanding space has left the ancient concept, of a static space, as inadequate for the progression, and evolution of knowledge. But it is implied within this new concept of space, that space is real, substantial, as the thing with these properties.

So, when people say that planets revolve around the Sun because they follow straight lines in a curved space, that's wrong, the curved space is not the cause, it is a model, a representation, we don't detect a space substance that is physically curved, and we are not forced to invoke a curving space to model the motions we observe. To say that curved space is a cause of the motions we observe is to give an illusion of explanation and to reify space as a tangible thing. — leo

Everything that we say about things is a model, or representation, that's just a fact of how we speak. But that doesn't mean that we are not speaking about, referring to, what we believe are real, substantial things. One might say "the sky is blue", and that's a model or representation, but 'the sky" is referred to as a real thing. You might say, that "the sky" is not a real thing, by your ontological principles, but in that model, the sky is a real thing, the thing referred to as being blue. It would require that you produce another model, one which doesn't hold 'the sky" as the real thing being referred to, in order to support your ontological principles. But it's inconsistent, and contradictory to use the model, and also claim that the sky is not a real thing.

Likewise, you use a model which represents "space" as a real, substantial thing, the thing that exists between objects, which is measured when we measure distances, but you claim to hold as an ontological principle that space is not real or substantial. Well, to support your ontology, you need a model of "space" which does not represent space as something real, substantial. What is it that exists between objects, that is being measured when we measure distance, an aether o something? In other words, you might insist that we ought not reify space, but this is irrelevant to the fact that the model you use actually does reify space.

And as I explained, that's the same as saying that a binary star is full of empty space, rather than simply saying that it is two stars orbiting one another. Just because we call two stars orbiting one another a "binary star" and can treat it as one whole, does not suddenly imply that space is a substance that can curve or expand and that it refers to anything more than the unoccupied volume between things. — leo

That analogy doesn't provide a solution to the problem. The problem is that not only is there space between objects, but objects also occupy space. You might say that the only real objects are point particles, which occupy no space, but then you rob objects of their reality, only to hand it to space.

Well on the one hand we have the space that we do see, the unoccupied volume between tangible objects, that's where our very notion of space comes from. — leo

I think you have this wrong, not only do we not "see" space (it is conceptual), our notion of space comes from measuring objects, and this means it is derived from the "space" occupied by things, not the space between things. Consider the development of ancient geometry, the right angle was developed for the purpose of measuring land for example, and the principles of a "circle" are the principles of a thing.

But history has shown that when we apply these principles produced for the purpose of measuring things, to measuring the "space" between things, there is a problem. That problem is that things are moving in relation to each other. This adds another "dimension" to the problem of "space", because "space" is now not the static area occupied by a thing, it is the changing distance between things.

The issue, as I pointed out earlier is that the "space" occupied by a thing is fundamentally different from the "space" between things. The two concepts of "space" are incompatible because the space occupied by a thing is static and the space between things is changing. When we move to allow that the thing is changing, and therefore the space occupied is not static, we describe the changing thing, as parts moving relative to each other. But then we're not talking about the original "thing" anymore, as the parts are now things in themselves, the subjects of discussion.

So I'd reverse your order of space 1 and 2

So what I was doing, is that I used the notion of space1 to explain that when the shape of space1 changes, it's merely that the tangible objects (which define the very shape of space1) are moving, so we don't need to say that space1 is a substance that curves or expands and that is responsible for making the objects move. When we talk of space1 curving or expanding, we're not doing anything more than describing the motions of the tangible objects, there is no need to reify space1 as a substance. — leo

You can't do this with "space 1" though. In space 1, space is the thing measured, so if the distance between objects changes, then the measurement changes, therefore space, as the thing measured, changes.

Then usually the notions of space1 and space2 are conflated, that is usually we imagine that the tiny invisible particles that make up a tangible object are real things and not just theoretical entities, so in that context we can apply the same reasoning as in the paragraph above to say that the space between these particles refers merely to the unoccupied volume between them, that it is not a substance that has any causal influence on the motions of these particles. — leo

So this is false too. You are actually removing "substance" from the things, making them point particles, and making space, as the thing measured, into the substance. Since space is the thing measured, you cannot interpret this model as saying that space is not substance.

Streetlight thinks we ought to change the topic of the thread to discuss politics rather than character. But we're the peanut gallery here, and we like to think we're judging the politician's character, not the politician's policies. There's no fun in the latter.

- points at which one might actually intervene to make a difference i.e. engage in politics and attempt to excercise agency. — StreetlightX

That takes character, to jump in and intervene, make a political difference. Trump did it, he's got character. The reasons for doing it define the character, good or bad.

You can also talk of the center of gravity of two distinct bodies such as binary stars, and treat them as one cohesive body, but it's not necessary, you can simply model the motion of each star individually without referring to a center of gravity, which is a tool of thought and not a tangible thing. So I don't agree that talking about the center of gravity of a body implies that space is a tangible substance that can curve or expand, in principle we could also model each part of the body individually and never talk of a center of gravity. — leo

As I explained, a body is full of empty space, and that empty space is treated as part of the body, and therefore substantial. You might model the motion of a body without referring to its centre of gravity, but it is implicit within the way that the multitude of parts which compose "the body", is treated as one whole.

If we define space as the unoccupied volume between tangible objects, then when the shape of that volume changes it's simply that the tangible objects are moving, we don't need to say that the volume is made of an underlying substance that is changing shape and dragging the objects with it. — leo

This is not an acceptable definition for physicists though, because physics deals with objects which are very tiny and therefore not tangible. A tangible object is made up of parts which are not tangible. And even if you define "tangible" in such a way that all these tiny parts are said to be tangible, there is the issue of having to deal with the "space" within a large tangible object. The "space" within an object allows its parts to be moving.

The "space" within tangible objects is outside your proposed definition of "space". If we say that when we are talking about its constituent parts, the "space" within the whole is "space", and when we are talking about the object as a whole, it is not "space", then the same area is treated in one context as "space", and in another context not as space, and this is contradictory. So we cannot define "space" in that way without the consequence of contradiction. .

You can have contact action without assuming space to be a concrete substance. As an analogy, if I throw a ball at you and it hits you there is no spooky action-at-a-distance, the contact action occurs when the ball hits you. In the case of gravity we can assume there are things traveling between bodies attracting one another, which have an influence when they reach the bodies. — leo

The problem is not so simple though. One object hitting another is nothing but a transferal of force or energy from on solid body to another. But when we look at what constitutes a solid body, it is tiny parts, with space between them. So we need to account for how the tiny parts of one body interact with the tiny parts of another body, as if the two bodies are each a coherent, massive whole, instead of the tiny parts simply interacting with each other, as independent bodies.

Now, since the space occupied by a massive whole is mainly empty space, with tiny parts precisely positioned to make a whole massive body, all that "empty space" must be modeled as part of the body. This is why the centre of gravity (or, centre of mass) is an important concept in physics, it allows that numerous particles with various spatial relations, can be treated as one cohesive body. However, this way of modelling things necessarily reifies the space within that body, as part of the body. and clouds the issue of how the parts of the body interact with the parts of another body, in the transferal of force. The concept of placing the force at a point has literally been abused by physicists to produce nonsensical things like point particles.

But it is wrong to say that just because we can model what we do observe as perturbations of an underlying space, then that implies that space really is a substance curving or expanding or stretching, it's a theoretical model out of many possible, it's not something we actually observe or detect, and it's not the only way to explain what we do observe. — leo

I believe that this is an incorrect assumption, and that there is really no way to adequately or accurately model motions and interactions of bodies without representing "space" as a real underlying substance. As described above, there is no way to even account for the existence of a body without representing its internal "space", as part of the body, and therefore substantial.

Clouds are lonely?

You deliberately re-quoted exactly the line that I apologized for, explained as a typo, and corrected in my previous post. Why? You do know you're strenuously arguing against a typo for which a correction has already been issued, don't you? — fishfry

It couldn't have been a typo because you continued afterward, to make the same mistake. Look:

I know of no instance in which mathematical equality is anything other than set identity and logical identity. — fishfry

You claimed that in ZFC they misuse the law of identity in some way — fishfry

No, I said that equality in ZFC is not based in the identity of the law of identity. I explained why this is the case.. You insisted that the equality of ZFC is based in identity, so I asked you for a citation of a law of identity which ZFC is based in. I'm still waiting.

It's not a matter of what people " think they know" but of the common understanding that meanings of terms are based upon. — Janus

It is exactly a matter of what they think they know. The problem is that we take some things for granted, because they are assumed to be "the common understanding", locked up into the way that we use the words. But the common understanding is often misunderstanding. it's almost like a fashion, we accept something as true because others do. This is evident in phrases like "the sun rises", and "the sun sets". These are phrases which used to represent the common understanding, things which people took for granted thousands of years ago, which we now know as misunderstanding, because we recognize that the earth rotates.

This is the important point of Plato's cave allegory, the philosopher sees beyond the common understanding (which is really misunderstanding) to the true reality.

The point is that human knowledge is grounded in things which we take for granted. But in reality these "things", (Wittgenstein's bedrock or hinge propositions) are the extreme limits of human knowledge, and they actual mark off, or even represent the unknown. When there appears to be a limit to what can be known about something (beyond this point appears to be beyond our intellectual capacity), we establish a principle which marks that limit, and allows us to work around that unknown element.

So we find these principles in examples like Aristotle's "matter", and Newton's first law of motion. Notice that we do not at all understand what matter is, or what inertia is, but these principles allow us to work around this area of the unknown, that aspect of reality which appears to be beyond our intellectual capacity. These principles are very useful, and lend themselves to "the common understanding". However, we know from quantum mechanics that Newton's law of inertia does not properly represent the temporal continuity of physical existence. So this principle, Newton's first law, is something we take for granted, and it has become the common understanding, but it really is a misunderstanding, because it creates the illusion that we think we know what we do not really know, as the unknown lurks behind this principle.

Interestingly, 'matter' (hyle) is derived from the same root as 'mother', with the connotation of it being the passive component. The 'active' component is, on the one hand, the 'active intellect', when individuated, or intellect in general. — Wayfarer

We may have discussed this briefly before. Plato makes this reference to the female aspect, in Timaeus, referring to ancient myths. He might be criticized for being sexist when he describes matter or "the receptacle", in this way, but he is really just referring to this ancient wisdom, citing myths, to support what he is putting forward as the relationship between universal forms, and particular material objects.

In their discussion in the Timaeus they find it necessary to posit "matter" as a principle of individuality. However, the matter is necessarily passive, as being merely a receptacle for the active form which will in-form the matter, determining what type of thing will be generated. It's really just an analogy using the ancient understanding of sexual reproduction, but it's not a very good analogy because it portrays the mother as completely passive in determining the traits of the off-spring, and even the ancient Greeks, though they gave priority to a good sire, knew by this time that this was not true.

So two meals can't be identical? It is called qualitative identity rather than quantitative identity. — Bartricks

If we're talking about qualitative identity, then only one quality need be the same in order that we call it "the same", the same colour, the same weight, the same length, etc. Or even if two things appear similar we might say that they are the same. But you said that everything describable about the supposed "two" acts are the same, so you clearly weren't talking about qualitative identity.

Face the facts Bartricks, you're trying to put forward an argument which fails, as unsound, because it begins in an impossible premise.

Whether or not there can be anything real apart from any observer's perspective is not a question I am attempting to answer. My concern was with what is commonly meant by "real", and what is commonly meant just is something indepedent of any observer's perspective. So, who is not listening, eh? — Janus

This is what you said:

For me the real is what is, not (necessarily) what we experience. — Janus

You were clearly associating "what is" with something independent of any observer's perspective

What I pointed out is that it doesn't make sense to speak of the real as "what is", and try to separate "what is" from what we experience, because for something to be, (and this is what "what is" refers to), requires an experiential perspective. Furthermore, there is a large body of evidence, and philosophical arguments, which demonstrate that if anything did, or could, exist separate from any experiential perspective, it would be completely different from, and incompatible with, what we refer to with "what is".

All of that supports the conclusion that it is unacceptable metaphysically, to speak of "the real" as "something independent of any observer's perspective", whether or not this is common parlance. Common parlance is often inconsistent with what is acceptable within a field of study. Logic shows that there couldn't be anything without an observer's perspective, so it really doesn't make sense to define "the real" as that which is independent of any observer's perspective, because this would just be like saying that there is nothing real, no such thing as reality. That's why I said your claims are just an attempt to make the illusion (that there could be something independent of an observer's perspective) into reality.

Physicist Victor Toth answered the question, "What is a quantum field?" in this manner :
"But no, quantum fields do not interact with matter. Quantum fields are matter." ___ https://www.forbes.com/sites/quora/2017/12/20/what-is-a-quantum-field-and-how-does-it-interact-with-matter/#6c0495928c4a

That would also be my answer to "What is an Information Field?" : the information field does not interact with matter, it is matter. — Gnomon

The problem though, is that matter itself is just an idea, a concept. It was introduced by Aristotle as an attempt to substantiate logic, being faced with the scourge of sophism. In more modern times, physics has replaced matter with energy, which substantiates its logic. Perhaps it now turns to "fields". Aristotle however, laid down strict conditions, metaphysical principles, concerning the use of "matter" (as an idea). These were derived from a logical treatise on the nature of "change", his Physics. Those conditions have long ago been ignored, and have been superseded by metaphysical principles which do not adhere to such strict principles.

The issue being that "matter" was introduced into physics as necessary to account for the unintelligible aspects of change. These unintelligible aspects allowed sophists to argue the reality of absurdities But "matter" is defined metaphysically (because it is of the unintelligible). Under the direction of Aristotle, it is a concept formulated with specific logical rules, intended to keep physics "real", grounded. If we move away from these rules, without introducing new rules which are at least as rigorous as the old, there is nothing to keep physics real, or grounded.

Omg, this is just too painful. No, there can't be 'other factors'. The whole point is that the two acts are identical in every way apart from that one is right and the other wrong. — Bartricks

How can you not see that you're talking nonsense? If they are identical then they are not two acts but one and the same act. You are starting with an impossible premise.

Now, imagine two actions. These two actions have the same consequences (they both result in an innocent person's death, say). They are both performed with the same intentions. Now, do they both have to have the same morality? That is, if one is wrong, must the other be wrong too? — Bartricks

Good and bad are measured by degree, that's why there are differing punishment sentences for "the same" criminal act. It is the fact that each of these acts in your example, results in an innocent person's death which makes them both wrong. But the degree of wrongness may vary such that one is worse than the other.

Now, given that they are identical in terms of their intentions and consequences, must they have the same morality? — Bartricks

No, there could still be other factors specific to the circumstances which makes one worse than the other, therefore they would not have the same morality.

Virtually everyone - I mean, virtually everyone - gets the rational intuition that they do. — Bartricks

So this is false, by the argument above. I think virtually everyone would get the idea that one act would be worse than the other, depending on the circumstances.

But we can't do that in terms of moral properties. We do not seem able coherently to say that two acts can be identical in every way apart from that one was right and the other wrong. — Bartricks

Just as you did before, you are misrepresenting morality. Morality is based in judgements of degree, so it is not the case that every good act is morally equivalent to every other good act, nor is it the case that every morally bad act is morally equivalent to every other morally bad act. So the fact that two similar acts are both morally bad doesn't imply that they are morally identical.

In conclusion, just because two acts are bad doesn't mean that they are morally identical.

So, if act A is right and act B is wrong, then either act A was performed with a different intention or it had different consequences - and that explains why it is right whereas B is wrong. — Bartricks

But act A may differ morally from act B even if they are both bad. So you start from a false premise, that if two acts are bad, they are morally identical.

Now the point I was making to Janus is that if we divide events up, or put events together, which is what we have to do to say "this is a rock", or "that is a proton", this is just a human construct. So it makes no sense to talk about "what is", independent of human experience, because "what is" is a human construct, and there is no such thing as what is, without the human consciousness which constructs it.

That would be a fair point if I was speaking in terms of temporality, but I was speaking generally about what I think the common meaning of the term 'real' is. What is real is what is...what was real is what was...what will be real is what will be. The point is that I think we have a common understanding that what is real, as such, does not depend on us, or on our experience. — Janus

See this is evidence of what I said, you don't listen. Instead of addressing my point (that "is" necessarily implies temporality present, now) directly, you simply side step the issue.

If "what is real" , is what "is", and the existence of the present depends on us, as it appears in modern scientific theory that the present (now) is a subjective perspective (the observer's point of view), then how can there be a "what is real" independent of an observer's perspective? And an observer's perspective requires an "observer". All we have here is a glorified form of the relativism presented by the sophist Protagoras. You claim that "what is" gives you a perspective independent reality, but "is" requires a perspective.

I'll tell you, that this position of yours (concerning what "is") is denied by many modern metaphysicians who attempt to maintain consistency with relativity theory. In physics we describe reality in terms of motions, assuming that all is moving, and this is conducive to a philosophy of process, everything is changing, there is no rest, or what "is". in any absolute sense. This means that any description of "what is" is just that, a description, artificial, produced by the observer, and that which is supposed to be independent, being described, is incompatible, and therefore completely different and unlike any description, of "what is". Furthermore, this metaphysical position is strongly supported by Hegelian dialectics, which also supports dialectical materialism, and dialetheism. These positions accept violation of the contradiction law, such that reality must accept what is and what is not. That's because "becoming", change, motion and activity, which is what reality consists of for these metaphysicians, cannot be adequately described in terms of is and is not.

You may understand this incompatibility from the discrepancies between the ancient philosophies of Parmenides and Heraclitus. Parmenides described reality in terms of being, what is and is not, and this position supported the idealism of the Pythagoreans and others. Heraclitus described reality in terms of becoming, motion and change. Plato considered both of these perspectives, and found them to be incompatible.

From the Platonic/Aristotelian tradition, dualism is the solution to this problem. Reality must be described with reference to two distinct and incompatible aspects, the passive (what is), and the active (what is changing). The monist simplification which you propose, "the real is what is", only reintroduces this problem of incompatibility. So it is very easily demonstrated as unacceptable, inadequate, as a return to presocratic confusion.

I really really want to find fault with any or all of these insights ... Maybe Gnomon, Metaphysician Undercover, et al are up to that challenge. But damn, J, well done — 180 Proof

It's very easy to find fault with Janus' principles. But Janus doesn't listen, so I've given up on that. Here's some examples:

For me the real is what is, not (necessarily) what we experience. — Janus

There is no such thing as "what is". "Is" refers to what is "now", present tense, and time passes so fast, that by the time the future is present, it is past. One cannot say "what is", because by the time this is done, it is past. "The present" is an illusion, as is "what is", because all is future and past. So Janus' claim, that "the real is what is", is nothing other than a claim that what is an illusion "the present", is what is real.

It makes no sense to me to say that something could "exist" beyond the bounds of reality. — Janus

Reality, according to what it has been claim to be, above, is already an illusion, as nothing "is". Therefore everything must be beyond the bounds of reality, as defined. So it is not only the case that something "could" exist beyond the bounds of reality, it is necessary that if anything exists at all, it is beyond the bounds of reality, when reality is defined in that way.

But Janus only pretends to listen to reason, until it gets too difficult to maintain the principles which Janus holds in the face of reason which demonstrates the deficiencies of these, then Janus let's go and slips back into the unreasonable principles, and refuses to listen.

Two acts - A and B. They are the same in every non-moral respect. — Bartricks

Problem is, these are not two acts. You are referring to one and the same act, and calling it "two acts". That's why your premise is self-contradicting.

I honestly see that for one to decipher those hard subjects, then one must read at least some of the conventional work done by foundational mathematicians on that. — Zuhair

OK, I've reconsidered. I recognize that making stupid comments about conventions which one is totally ignorant of is not good for a person's integrity, so I think I will take some time to educate myself on some of those basic conventions you've referred to. Thanks Zuhair.

Answering questions is not in the interest of spreading pro-Trump propaganda. — Echarmion

That is done by making statements of fact. That's all NOS4A2 does, states "the facts" over and over again.

If you put two cows on the commons, we should all move away from you when you go to the Pub for a beer after work — Banno

The real problem with the commons was not from the greed of the individual, who wants more than one's fair share of cows, it's a problem of too many individuals sharing the same resources. That's overpopulation. Overpopulation seems to be a natural tendency for any living species which is capable of dominating the others. Have you ever grown a culture on a petri dish? The thriving species will run rampant, rapidly overrunning and using up all the choice nutrients, then it dies because it hasn't the capacity to adapt: some might go into suspended animation (seeds or spores) waiting for another chance to dominate.

That's why the third option won't work. We haven't the capacity to adapt. I'd propose a fourth option, vegetarianism or something like that, and I think Plato suggested something like this in his Republic (which was supposed to be a communal society), saying that meat ought to be given up, as a relish. But again, I don't think we have the capacity to adapt. "Taste" might be the strongest of all instinctual motivators. We take oxygen for granted and don't need to taste it out, but food is not only fundamental to subsistence, it supports growth, loco-motion, and all the higher level activities like sensing and thinking. The variations between individual highly organized living beings, like the human, are probably closely related to taste.

Again: imagine two acts that are identical in every way apart from spatially and or temporally. Not hard. — Bartricks

Yes it is hard. I find it to be impossible. This is like saying imagine two people who are exactly alike except they are different. It's nonsense.

I mean, if I ask you to imagine a car identical to yours in every way apart from it is in another location, would you find that difficult? Would you say "er, but then it is not the same car" - yes, I know. Not the same car. But similar in every way - apart from it is over there. — Bartricks

Cars don't have intention. Anyway, I'd say that the two cars were not exactly alike, they have a different serial number to begin with, and they've both been used in different ways with different wear and tear.

Imagine two acts - two, not one, two - that are identical in every non-moral way apart from spatially or temporally. — Bartricks

Sorry, but I find that you are asking me to imagine the impossible, like a square circle. It's nonsense, it can be said, but not imagined.

OK, what you are saying in this last posting is understandable, I in some sense agree with most of it.
There is something nice in your conception about 'equality', you view the substitution schema to mean 'equal' treatment given by the theory to the related objects, and not as indiscriminability which is the synonym of identity. — Zuhair

OK, let's say equality is a "qualified" identity. This means that it is a relative identity. In relation to the specified theory, the two objects are identical when they are said to be equal. But we all know that they are not really identical, that's an artificial simplification which is theoretical only.

But again I would consider such a kind of "equality" relation far stronger than just being an "equivalence" relation, i'd consider it as some kind of quasi-identity relation, i.e. some equivalence relation that is the nearest possible relation to identity that the theory in question can describe. — Zuhair

What would be the point of this though, really? Let's say that this "quasi-identity" relation is "the nearest possible relation to identity that the theory in question can describe". How near this equivalence relation actually is to true "identity", would be completely dependent on the theory's capacity to describe. And unless we had some way of determining true identity, and comparing the identity produced by the theory, we would never know the theory's capacity, or how close the quasi-identity is to true identity. And if we had a way of determining true identity why would we be using the theory which employs quasi-identity.

The real issue I think, is what I explained to fishfry earlier. The purpose of equations in mathematics is to compare similar things in an attempt to determine the differences between them. So we find all the ways in which they are the same, "equal", and we are left with the differences. If the right and left side of the equation both represented the very same thing, then there would be no difference between the things represented, and the equation would be useless.

So I don't think that equality even aims for identity. If the two equal things were really identical, then we wouldn't be employing equality to determine this. We employ equality when we know that the things are different and we want to understand the differences between them. That's why the principle of identity is actually completely different from the principle of equality. But if we had some way to quantify the difference between "identical" and "equal", then we'd have the basis for accurately determining the difference between equal things.

Also you not discriminating between a predicate (relation) symbol and a constant symbol, so you thought that 0,1,2,.. are held conventionally as PREDICATE symbols (although one can indeed make a formalization that can interpret them as such, but this is not desirable, and definitely not the convention) — Zuhair

Let me refresh your memory. I didn't say that apprehending those symbols as predicate symbols is conventional, I said it's what I think, meaning it's the way that I see them. That's my interpretation, not the conventional interpretation. As you may have noticed, I don't see things in the conventional way.

those aspects of your response were really very poor, and reflects great shortage of knowledge regarding the common conventions held by foundational mathematics regarding the main logical language which is first order logic and one of the most formal languages that are directly connected to mathematics, that is the first order language of arithmetic. Anyhow your account on equality was very good, I hope your knowledge increase one day about the syntax of first order logic, and of Peano arithmetic and set theory, etc.. so that we can have correspondence would be by far more fruitful and productive. — Zuhair

Thanks for the encouragement Zuhair, but following common conventions is really not what I enjoy, I find that rather boring. So I like to look for those bits of meaning which are omitted by the conventions. Generally, they are omitted because they are what's taken for granted. But what's taken for granted, is left as an unknown, like when the religious take God for granted. So for instance, Newton's laws of motion take inertia for granted, so what inertia is, its nature, is left without an approach, and it remains in the realm of the unknown. Here, in set theory, identity is taken for granted, so what it means to be "the same" is left in the realm of the unknown.

No! Unless these differences are indescribable by formulation of the language. — Zuhair

That's the key point, the limitations of the language. The law of identity puts identity of the thing within the thing itself, such that even if the human being cannot discern the differences (due to deficiencies of sense, language, whatever), but can still recognize two things as distinct, we can say that the two are distinct. Therefore the law of identity represents a recognition of the limitations of the language system, the inability of the human being to adequately identify certain objects.

When we approach mathematical axioms with the recognition that equality is not identity we uphold this principle which represents the limitations of the language. If we ignore this principle, and insist that equal things are identical we become ignorant of the limitations of the language, and we will start to believe that mathematics is capable of doing what it is not capable of doing. Belief that a tool is capable of doing what it is not capable of doing is a dangerous belief.

Once you are in a logical theory then what decides identity of something in it should be in relation to what the theory can describe. Indescribable difference are immaterial inside the theory, and the two objects would be considered identical by the theory because it cannot discriminate between them by its language, so it considers them "IDENTICAL", it sees them as identical (not just equal). — Zuhair

Sure, within the theory there is no difference between the two objects. But in application, and theories are useless unless applied, there is a difference between the objects which the theory is applied to. Because of this, within the theory the two objects are said to be "equal". Therefore the rules of the theory recognize that the two objects are not actually the same, and express this recognition by using the word "equal" and not "identical". But within the theory, the objects are treated as if they are identical and this is a deficiency of the theory. If we ignore, or even deny this deficiency, we are in a world of self-deception.

The substitution scheme says that if we have x = y then whatever is true about x is true about y and whatever is true about y is true about x, which mean that "all equals are identical"! — Zuhair

Whichever things that are said by the premises to be true about x are also true about y. But that does not mean that the two are identical, it just means that they are treated equally by the theory.

. But if we are thinking of equality as indiscernibility and thus "identity" from the inner perspective of the theory, then we'd add such a strong principle. — Zuhair

Of course you add a strong principle, but a strong principle which is false (as yours clearly is) is a deceptive and dangerous principle.

just wanted to add, that first order identity theory does not allow adding to it objects that can obey the substitution principle and yet be non-identical. — Zuhair

You see why I claim there is contradiction in the very first principles? What point is there in making exceptions to the first principle, because you know it is wrong? Why not just admit that the principle is not a principle of identity, but a principle of equality, it doesn't have the strength which you desire it to have, and get on with the use of the system, understanding that it has its weaknesses, instead of trying to hide its weaknesses and disguise them to create the illusion of strength?

A similar act in different circumstances cannot be called the same act. They may have different intent. Therefore it is possible that they could differ morally.

Doesn't your reason tell you that the two acts must be morally identical? — Bartricks

No, because the acts are carried out on different planets with differences between them so reason tells me that they are not identical. If they are not identical acts, then why say that they are morally identical?

It's not just humans though, each individual animal has its own way of being.

What do you mean by "numerically distinct"? If there are differences, what are the difference between them? These differences could amount to the act being morally unacceptable on one and morally acceptable on the other.

But it's the Republicans who really hold his fate in their hands. Several, including Romney, are saying that 'this is serious, it's an impeachable offense'. If that takes root amongst more Republicans and begins to snowball, then things could develop very quickly. — Wayfarer

The election is not far off. The Republicans need to seriously consider who their candidate for presidency will be.

Now imagine there is another planet exactly like this one - I mean, exactly like it in every physical respect. — Bartricks

If the planets were exactly the same, then by the principle of the identity of indiscernibles, they would be one and the same planet, and everything which is the case on one would also be the case on the supposed "other", because it wouldn't be "other", it would actually be the very same planet. So your question doesn't make any sense because you are talking about one and the same planet as if it were two distinct planets.

disagree because as I said different kinds of beings have different ways of being. — Janus

How would the difference between the different ways of being, which are proper to the different kinds of beings, be fundamentally different from the difference between the different ways of being which are proper to the different kinds of human beings? For example, beavers make dams while birds make nests, and engineers make dams while homemakers make nests. Each individual being has a different way of being.

That criticism is that if moral norms and values are the prescriptions and values of a subject (be they a god, gods or us) then they would not be immutable. They could vary over time.
Yet, in Plato's day as today, moral norms and values appear to be fixed. They are represented to be by our reason. Hence a problem. — Bartricks

I don't agree that moral values appear to be fixed, not today, nor in Plato's day. The criticism appears to be way off base.

Just engage with the actual criticism. — Bartricks

I did engage with the actual criticism. I pointed out that you were using "necessary" in a way which is inconsistent with the way that it is used in moral philosophy. You insisted that "necessary" means "cannot not be the case", which is some sort of logical principle that has nothing to do with morality, which deals with how people ought to behave. Then you went off on some tangent talking about different worlds with identical features.

If two worlds are identical in all non-moral respects, then necessarily they are identical in all moral respects? — Bartricks

You know that if they are two worlds, then they must differ in some way, or else they would be one and the same world. If they do not differ in non-moral respects, then they necessarily differ in moral respects.

"Consider yourself owned."

Otherwise the discussion would be really very poor. — Zuhair

Then why did you waste so much of your time discussing this with me?

However when logicians are speaking about equality in the sense of satisfying the substitution schema, then in reality they mean "identity", — Zuhair

I know enough but the substitution axiom to know that it deals with equality not identity. The difference is that two distinct things may be equal, but they cannot have the same identity. The substitution axiom allows that one thing may be substituted by another equal thing, so it clearly accepts that these are two distinct things, not one and the same thing, with one identity. The substitution axiom allows that two distinct things, with differences between them, which don't make a difference to the purpose of the logician, may be substituted as equals. But clearly, that there are differences between them means that they are not one and the same thing, as required by the law of identity.

Judging by the op, I'd say you haven't read The Euthyphro. In it, Plato relates morality to the gods, not to Reason, or to worlds which are identical in some aspects (whatever that means).

Trump does not seem to be able to see beyond his own experiences. Hunter Biden made millions of dollars in the Ukraine therefore he must be corrupt.

Now there are some second order logic theories that can interpret arithmetic in a manner that 2, 1, etc.. are predicate symbols, but those do have equality of predicates axioms in them. — Zuhair

Are you still unwilling to accept a difference between equality and identity? I thought we agreed to that difference a long time ago.

You need to read some foundation of mathematics book, then you can come a speak about it. — Zuhair

Why would I want to waste my time doing that, when I find inconsistencies and contradictions in the conventional interpretations of the very first principles?

If two worlds are identical in all non-moral respects, then necessarily they are identical in all moral respects? — Bartricks

How does that make any sense?

No, it is exactly how it is used in moral philosophy. You're the one using it incorrectly. — Bartricks

It seems you haven't read any moral philosophy. Do you recognize a difference between "is" and "ought". "Necessary" in the sense of "cannot not be the case" is based in what "is". "Necessary" in the sense of what is needed for some purpose is based in what ought to be done.

Or do you think that moral values are not invariable across time and space?

if so, what do you do with all those widely corroborated rational intuitions that represent it to be? Just reject them? — Bartricks

How could moral values be invariable across time and space when "ought" refers exclusively to future acts?

I am using 'necessary' to mean 'cannot not be the case'. — Bartricks

The point though, is that this is not how "necessary" is used in morality. It is used to indicate what is needed, what ought to be done for some purpose. If something is "necessary", there is a reason why it is necessary, it is deemed as needed for some purpose. So you are taking the wrong sense of "necessary", one not applicable to morality, and trying to make a moral argument out of it. That's nothing but equivocation.

You mention the Platonic form of the good - okay, so if this strange obelisk values things (a notion I can make no sense of whatsoever), why is it the case that it could not disvalue the things it values? — Bartricks

That's not what I said about 'the good", nor is it what Plato said about 'the good".

already wrote that explicitly it is the reflexive and substitution axiom schema, those are the identity theory of first order logic, and ZFC is *usually* formulated as extension of the rules of first order logic and those axioms of identity theory. — Zuhair

All the information I've seen shows that the reflexive axiom and the substitution axiom are equality axioms. Why do you think they that are identity axioms?

It seems you didn't read it well, the expression 2, 4 are called zero placed function symbol, or simply constants, and those are TERMS of the language and they denote objects. — Zuhair

I saw no such rule, to dictate that "2" and "4" are "zero placed function symbols", on the page you referred. I think you're making this up. Any way "zero" would indicate an absence of objects.

However, we CAN formalized 2 and 4 as predicates that's not a problem at all, this can be done. But it is not the usual thing. — Zuhair

We agree then, that there are no objects denoted by "2+2=4"? On what basis would you claim that "2+2" is identical to "4" then?