No. You concede that what the sets have in common is the claim of being elements of the set of all sets that have no elements in common. — apokrisis

No. I said the opposite. I said that sets A = {1, 2, 3} and B = {4, 5, 6} do not have "belongs to some other set" in common. Rather, it is your sets, let us call them sets X = {1, 2, 3, belongs to some other set} and Y = {1, 2, 3, belongs to some other set}, that have this element in common. What you're doing here is you are saying that A equals to X and that B equals to Y and that because X and Y are not absolutely different that it follows that A and B are also not absolutely different. This is false because your starting premise, that A is equal to X and B is equal to Y, is false. I have to repeat, once again, that your argument is nothing but sophistry.

All elements are really just sets of elements. — apokrisis

They aren't. Some elements are sets of elements. Some elements are not sets of elements. What you're doing here is called reductionism. But I don't think you can see it.

But there is then your implied promise of being able to cash out the "elemental" at some ground zero level. And that becomes logical atomism. We already know that to be a busted flush. — apokrisis

I don't really think you understand my position. I don't know much about logical atomism but I can't help but have the impression that you do not understand that position either. You are criticizing other people's positions without properly understanding them.

The fact remains that you have yet to demonstrate that there is no such thing as absolute difference or that there are no such things as concrete particulars. You've done nothing so far.

You already concede the principle of indifference as your basis for trying to contest it. — apokrisis

The principle of indifference is common-sense. It does not state anything groundbreaking. It is well known that whenever we look in front of us we do not see what is behind us.

You go well beyond this. Your claim is that if we are not aware of some portion of reality that whatever portion of reality we are aware of is not reality itself. That's nonsense.

It comes down to a judgement that works, not a judgement that is based on some objective "fact of the matter". — apokrisis

We look at objective facts in order to figure out a more effective way to attain our subjective goals. We choose what portion of reality we are going to focus on but we do not choose the content of that portion of reality. You are trying to oversimplify this process by reducing it to "it's all about what works".

Sure, but the issue is to answer this question of whether or not it is. If something appears to us as disordered, this does not mean that it necessarily is disordered, because it may be the case that we just haven't developed the means for figuring out the order. — Metaphysician Undercover

That's true. Similarly, if we have no evidence that God exists that does not mean that God does not exist. Nonetheless, in the absence of evidence that God exists, we have no choice, if we have some intellectual integrity, but to act as if God does not exist.

No. I said the opposite. I said that sets A = {1, 2, 3} and B = {4, 5, 6} do not have "belongs to some other set" in common. Rather, it is your sets, let us call them sets X = {1, 2, 3, belongs to some other set} and Y = {1, 2, 3, belongs to some other set}, that have this element in common — Magnus Anderson

Hilarious. If you are going to invoke set theory formalism, then you have to stick to its rules, not just make up any old shit.

Your claim is that if we are not aware of some portion of reality that whatever portion of reality we are aware of is not reality itself. That's nonsense. — Magnus Anderson

If that was anything like what I said, I agree it would be nonsense.

You are trying to oversimplify this process by reducing it to "it's all about what works". — Magnus Anderson

So you describe the naive realist position and then accuse me of oversimplifying.

Sounds legit. :)

That's true. Similarly, if we have no evidence that God exists that does not mean that God does not exist. Nonetheless, in the absence of evidence that God exists, we have no choice, if we have some intellectual integrity, but to act as if God does not exist. — Magnus Anderson

"Evidence" is a difficult concept. Some people see all sorts of evidence for God, while others will insist that the same things are not evidence at all. What determines whether the things seen are evidence or not? It is the way that the things are looked at. So there might be a group of things, and you point to those things as evidence of X. I just see them as that group of things, and not evidence of any X. You must explain to me how these things are evidence of X in order that I will apprehend them as such. Nevertheless, they are still evidence of X, regardless of how I perceive them, so long as someone else perceives them as evidence of X.

We already discovered that my concept of triangle is not the same as yours. Mine included "three angles", yours did not. We discover these differences, and attempt to correct them through discussion, communication. — Metaphysician Undercover

But what criteria is used to determine that one definition is more correct than the other? I answer that the criteria is the concept, which is the same in all of us. Of course I agree that triangle-ness has the property of "three angles", but as I stated earlier, this is a secondary property which can be deduced from the first property of "three straight lines", and so it is redundant. Similarly, we could add the secondary property that "the sum of all angles equates to 180°", which is also deduced from first properties.

[...] you claim that we could not communicate unless our concepts are the same. See, you have things backward. It is through communication that we establish consistency, and sameness between our concepts, the sameness doesn't exist prior to communication as a prerequisite for communication, it is produced from communication. — Metaphysician Undercover

You are wrong twice. You did not refute my argument that if all words can have different meanings for each individual, then we get infinite regress because all definitions are made of words. It is like speaking completely different languages. My meaning of "yes" could be your meaning of "no", my "flat" could be your "round", etc. Then an agreement could not be attained if there is no common ground or criteria that is shared among all individuals. Therefore, not only could we not communicate, but even if we could, it could not serve to attain an agreement on meanings.

Consider Plato's Symposium. [...] — Metaphysician Undercover

This does not prove that individuals necessarily have different concepts. It could be that some definitions are less correct than others, that is, some definitions less accurately point to the one concept. Do you not agree that if I said my definition of the concept of triangle was "four angles", then it would be incorrect? It is pretty much in the name, that "triangles" have "three angles". And an incorrect definition implies that there exists a correct definition.

The problem is, that definitions do not coincide. We already determined this with our definitions of "triangle", yours is different from mine. [...] — Metaphysician Undercover

Your entire argument depends on the premise that meanings are always different for every individual.
For the sake of argument, let's suppose that our definitions are different to start with. As you said yourself here, "we discover these differences, and attempt to correct them through discussion, communication", thereby making it possible to agree on one definition or meaning for words. Once this is achieved, then concepts become one and the same, by the same law of identity.

Hilarious. If you are going to invoke set theory formalism, then you have to stick to its rules, not just make up any old shit. — apokrisis

You still have to demonstrate that there is no such thing as absolute difference.

So you describe the naive realist position and then accuse me of oversimplifying. — apokrisis

You rely too much on "ism"s.

But what criteria is used to determine that one definition is more correct than the other? I answer that the criteria is the concept, which is the same in all of us. — Samuel Lacrampe

This is very difficult for me to grasp. I have one definition of "triangle", and you have another. We want to determine the correct definition of "triangle". You say that we turn to "the concept" which is already within us, and which is the same within all of us. But I don't see that concept within me, all I see is my inclination to define the term the way I have, and a willingness to make some changes to my definition if necessary. If I believe that I understand the word well, I am only willing to make small changes, accidental changes. But when I recognize that I don't understand the word very well at all, I'm willing to make substantial changes, essential changes. How do I access the concept within me, such that I can determine which changes need to be made?

You did not refute my argument that if all words can have different meanings for each individual, then we get infinite regress because all definitions are made of words. — Samuel Lacrampe

The meaning of words is not necessarily derived from other words. That is a false premise. We can get the meaning of words from physical demonstration. There is a word for this, it's called "ostensive". So your claim of infinite regress is not justified.

This does not prove that individuals necessarily have different concepts. — Samuel Lacrampe

What Plato gave us is a clear, ostensive, demonstration that different individuals have different concepts for the same word. If you are inclined, as I am, you can go onward to discover that there are differences between all individuals, as to how they understand the same word. Some of the differences are very significant, some of the differences are very insignificant.

Since these differences are seen to exist for all words, we can make the inductive conclusion that individuals have different concepts for the same words. Of course, you can choose the position that inductive reason never proves anything "necessarily", and reject this conclusion if that is what you desire. However, I suggest that if you have the will to understand the nature of reality you should accept this as a fact, and move onward. Failure to do so will just put an unnecessary restriction on your mind.

Do you not agree that if I said my definition of the concept of triangle was "four angles", then it would be incorrect? It is pretty much in the name, that "triangles" have "three angles". And an incorrect definition implies that there exists a correct definition. — Samuel Lacrampe

We determine that a particular definition is "incorrect", based on the assumption that there is an ideal definition. The ideal is the best, the most perfect, and need not be something existent, it is simply the assumption of a goal, strive for the best. Assuming that there is an ideal inspires us to always seek a better conception, knowing that we've never actually arrived at the ideal.

In common practise we proceed using a concept which is less than ideal, but adequate for our purposes. So despite the fact that you and I have differences between our individual concepts of triangle, we ignore these differences as insignificant, accidental, and allow that these concepts are both correct. They are "correct" in relation to pragmatic principles, meaning that each one is sufficient to serve the purpose. However, any one of us could appeal to "the ideal", and argue that since the concept which I hold, or the concept which you hold, is not the ideal, it is incorrect.

Your entire argument depends on the premise that meanings are always different for every individual.
For the sake of argument, let's suppose that our definitions are different to start with. As you said yourself here, "we discover these differences, and attempt to correct them through discussion, communication", thereby making it possible to agree on one definition or meaning for words. Once this is achieved, then concepts become one and the same, by the same law of identity. — Samuel Lacrampe

I don't agree with the conclusion here. I think that the ideal is never achieved, and this is what inspires us to always better ourselves in our understanding. We agree because it is pragmatic, and this allows us to proceed with those actions which are dependent on those concepts. Agreement, compromise, and proceeding despite differences, does not necessitate the conclusion that the concepts are "one and the same". If the concepts are one and the same by the law of identity, then the ideal has been achieved. But the nature of the human being, and the imperfections of the material existence of human beings denies the possibility that human beings can achieve the ideal. The fact that we will never reach the ideal need not discourage us, it only encourages us to keep on bettering ourselves.

I have one definition of "triangle", and you have another. — Metaphysician Undercover

Simply not true. You might express it one way, and I another, but there is no room for difference. You’ve been arguing this useless distinction for hundreds of posts.

What Plato gave us is a clear, ostensive, demonstration that different individuals have different concepts for the same word. — Metaphysician Undercover

Where? Plato was hardly concerned with individuation.

Now I gotta add 'phantasms' as part of the terms to understand, on top of 'forms', 'concepts', 'matter', 'mind', 'intellect', and 'nous'. It's times like these I want to go back to simpler theories in which reality is made of 'stuff' out of a mould, and call it a day. — Samuel Lacrampe

Probably, the current author to study is Ed Feser, as he specialises in Aristotelian-Thomist philosophy. But it’s not as difficult as you’re making it sound. ‘Phantasm’ is simply an archaic term for ‘mental image’. As I understand it, the basics of Aquinas’ epistemology is that the senses receive the corporeal image, the intellect perceives the intelligible form, and the mind creates the image/phantasm by synthesising these.

Simply not true. You might express it one way, and I another, but there is no room for difference. You’ve been arguing this useless distinction for hundreds of posts. — Wayfarer

Actually, Samuel and I compared our definitions of "triangle", and they were obviously different. Samuel used "flat surface" while I used "plane". I mentioned three angles and Samuel did not. Therefore it is quite clear that there is a difference here. And despite your insistence that such a distinction is useless, that's just a matter of opinion. So, in your opinion this difference is useless, and in my opinion it is useful. In my opinion the difference is useful because it may be referred to, to refute the premise of your argument. You do not want to accept the fact that your argument is based on an unsound premise so you claim that the difference is not a difference at all, and cannot be a difference because this would shatter your faith. Your opinion amounts to a self-deception of contradiction, that there is a difference which is not a difference. So be it.

Where? Plato was hardly concerned with individuation. — Wayfarer

My example was "The Symposium". Each individual, each member of the group, gives a different account of what the word "love" means. But this same theme is consistent throughout many of Plato's dialogues. You can find a similar discussion of "just" in The Republic, and of "knowledge" in The Theatetus. It is quite clear that what Plato was demonstrating is that different individuals have different ideas which are associated with the same word. You seem very insistent that there is no room for difference here, when in actuality difference is unavoidable.

Actually, Samuel and I compared our definitions of "triangle", and they were obviously different. S — Metaphysician Undercover

IT DOESN”T MATTER. If you were both set an exam, ‘draw a triangle’, then you would both have to do that task. You wouldn’t; draw a square, or play a tin whistle, or bake banana bread. You would draw a figure comprising three lines intersecting in the appropriate way. Otherwise you would fail the test. You have spent thousands of words obfuscating the meaning of ‘the same’.

We would both draw different triangles. I am just clarifying, and adhering to the meaning of "the same" which is stipulated by the law of identity, and which also is necessary to adhere to, in order to produce a sound deductive argument. You are obfuscating the meaning of "the same" appealing to "similar" as if it were "the same", in order to put forth an unsound argument as if it were sound. That's why I accused you of sophistry.

You are obfuscating the meaning of "the same" appealing to "similar" as if it were "the same", in order to put forth an unsound argument as if it were sound. That's why I accused you of sophistry. — Metaphysician Undercover

Where is the difficulty in recognising that "the same" is the idealised limit to "the similar"? Why are you obfuscating the matter with your unsound sophistry?

If things are 100% similar, are they the same? And if things are 99% similar, are they nearly the same?

You seem to be striving after a distinction in language that isn't properly there.

You would both draw a triangle. Your entire (wasted) effort in this thread has been about a completely different subject, namely, the principle of individuation.

Why are you obfuscating the matter with your unsound sophistry? — apokrisis

Sophists generally advance arguments which sound plausible. This argument ‘isn’t even sophistry’ ;-)

Where is the difficulty in recognising that "the same" is the idealised limit to "the similar"? — apokrisis

The "same" and "similar" express two distinct things. One excludes difference while the other includes difference, so the two are logically dichotomous. "The same" is not an idealized limit of "similar", it is a distinct category, the category of no-difference whereas similar refers to things which are different. There are two distinct categories here, different things (similar), and not different (same thing). Notice that the former implies a multitude, more than one thing, while the latter implies one. They are distinct categories.

Why are you obfuscating the matter with your unsound sophistry? — apokrisis

I am adhering to sound principles. Those individuals, such as yourself, who would place "the same" in the category of "similar", when "similar" necessarily implies difference, and "same" necessarily excludes difference, are the ones who obfuscate this issue through category mistake, and proceed to produce sophistic arguments based in this category error.

If things are 100% similar, are they the same? And if things are 99% similar, are they nearly the same? — apokrisis

I really do not know what you mean by "100% similar". Similar implies that there is difference, and same dictates that there is no difference. Therefore whatever you mean by 100% similar, it cannot mean "the same", without contradiction.

Your entire (wasted) effort in this thread has been about a completely different subject, namely, the principle of individuation. — Wayfarer

Your argument, to paraphrase, is that if the same information is conveyed through different physical media, then information is something distinct from the physical medium. So you claim that the same information is conveyed through different physical media, therefore information is distinct from the physical medium.

If it is the case, as I have argued, that similar information, rather than, the same information is conveyed through different physical media, then it follows that your conclusion, that information is distinct from the physical medium, is an unsound conclusion. I believe that I have successfully demonstrated in this thread, that the information is similar, rather than the same. Your response, and apokrisis' response has been that this is an insignificant difference, a difference which doesn't make a difference.

However, it clearly is a difference, and in this case the difference is significant because we must place the thing referred to, information, into the category of things which are "similar" to each other, rather than "the same". Any difference whatsoever necessitates the category of "similar", because "the same" excludes any difference. This is the same category where we place physical particulars similar but not the same. So your argument that information is not physical has been proven to be false. Furthermore, since information is placed in the same category as physical particulars, we should proceed now to consider the probability of information being physical.

One excludes difference while the other includes difference, so the two are logically dichotomous. — Metaphysician Undercover

So you are presuming that dichotomies are dualities and not in fact dichotomies? I see where you are going wrong.

Dichotomies describe complementary limits on being. Thus they talk about the being that lies in-between two opposing limits of the possible.

You are then treating the limits on the possible as the actuality which has the being. Rookie error.

I really do not know what you mean by "100% similar". Similar implies that there is difference, and same dictates that there is no difference. Therefore whatever you mean by 100% similar, it cannot mean "the same", without contradiction. — Metaphysician Undercover

Yeah. That is a question you will really want to avoid having to answer.

You are trying to squirrel out of it by saying similar implies the existence of some difference. Well of course. There's your dichotomy. The similar is that which is the most lacking in any difference. It is formally reciprocal or inverse to difference in being as far from that "othering" limit to itself. It is the least difference you can have - which means accepting difference as the something that sameness is different too.

So back to the 100% similar. Why are you so reluctant to admit that this is no different than any claim about "the same". A complete lack of difference could only be a complete presence of the same.

But you must avoid admitting this otherwise your sophic house of cards collapses.

So you are presuming that dichotomies are dualities and not in fact dichotomies? I see where you are going wrong.

Dichotomies describe complementary limits on being. Thus they talk about the being that lies in-between two opposing limits of the possible.

You are then treating the limits on the possible as the actuality which has the being. Rookie error. — apokrisis

No, A dichotomy is a separation between two things. You are the one making the error assuming that a dichotomy is two limits of the same thing.

Anyway, it's likely the word can be used in different ways, but this is all irrelevant. As I said, what is relevant is that "same" expresses an exclusion of difference while "similar" expresses necessarily, difference. They are categorically different and cannot be "complementary limits" of the same thing, that would be contradiction.

So back to the 100% similar. Why are you so reluctant to admit that this is no different than any claim about "the same". A complete lack of difference could only be a complete presence of the same. — apokrisis

As I told you, I really did not know what you meant by "100% similar". "Similar" implies necessarily, some degree of difference. Therefore 100% similar implies some difference. You only contradict yourself now, when you say that "100% similar" means a complete lack of difference. It is impossible that similarity lacks difference, by way of contradiction. As I suspected, what you mean by 100% similar is nothing but contradictory nonsense. That's why I couldn't answer that question, I was afraid that what you meant was some such contradictory nonsense. Now my fears have been confirmed, what you mean is contradictory nonsense.

But you must avoid admitting this otherwise your sophic house of cards collapses. — apokrisis

Simply put, if I know something as contradictory I will not accept it. However, I know from experience that you have no qualms about accepting contradiction. You seem to believe that reality is fundamentally contradictory, so you readily accept such contradictions, and spout them out at will. I refuse to follow you.

No, A dichotomy is a separation between two things. — Metaphysician Undercover

Bollocks. In metaphysics, the logic of a dichotomy is used to define the complementary limits of any thing-ness or Being.

Anyway, it's likely the word can be used in different ways, but this is all irrelevant. — Metaphysician Undercover

No. It is completely relevant to the matter in hand.

As I said, what is relevant is that "same" expresses an exclusion of difference while "similar" expresses necessarily, difference. They are categorically different and cannot be "complementary limits" of the same thing, that would be contradiction. — Metaphysician Undercover

Keep twisting but you won't wriggle off the hook.

Is "100% similar" saying exactly the same as "the same" or not? Likewise is 0% similar saying just the same as "absolutely different" or not?

You know that they do mean the same yet continue to obfuscate.

It is impossible that similarity lacks difference, by way of contradiction. — Metaphysician Undercover

Well now you are just arguing my point about "the same" being an ideal limit. It doesn't exist. It is just the asymptotic limit on the complementary idea of "the different".

Simply put, if I know something as contradictory I will not accept it. — Metaphysician Undercover

So in your extensive readings of Aristotle, you simply ignored his notion of contrariety?

You seem to be missing the point apokrisis. "The same" implies one thing, the same thing, that's the point of the law of identity, to ensure that we are talking about the one and only same thing, the very same thing, when we designate something as "the same". On the other hand, "similar" implies two distinct things. Therefore "same" does not represent an ideal limit to similarity, it is a matter of indicating one thing, the same thing, while "similar" indicates distinct things. In no way can "same" be reduced to a form of similarity without equivocating to a meaning of "same" which is inconsistent with the law of identity. Give it up, you are only arguing nonsense.

How do I access the concept within me, such that I can determine which changes need to be made? — Metaphysician Undercover

Through a socratic dialogue, either with yourself or with others, which serves as a falsification method. Much like the correctness of a scientific theory is tested through particular experiments, we can test the correctness of a definition through particular examples. Say your first attempt to define triangle-ness is "a plane with three angles". I falsify this by pointing out that this shape is a plane with three angles but is not a triangle. So we must add to the definition that the sides must be straight. Then, I might add the property "red" to the definition, and you falsify this by pointing out that some triangles which are not red remain triangles. So we remove "red" from the definition, and the result is "a plane with three angles and straight sides." If it cannot be falsified any more, then we have obtained the perfect definition.

But... notice that we both seem certain about the correctness of the examples used to falsify the definitions. Where does this knowledge come from? It must come from the concept which we already had. As such, the exercise was never to find the concept, but to express it correctly with words. In other words, we all have the implicit knowledge of concepts, and we just try to obtain explicit knowledge from this. This explicit knowledge is useful to deduce universal truths such as "no triangle can fill up a circle", because we now know that all triangles have straight sides where as no circles do.

We can get the meaning of words from physical demonstration. — Metaphysician Undercover

This sounds more like a method to learn a new language than to obtain a concept; but for the sake of argument, let's suppose you are correct. Well, you and I did not go through this process of physical demonstration before having a discussion; and so according to you, it is possible that, despite using the same language, my words have significantly different meanings than yours. So why would to decide to have a discussion with strangers if there is a possibility that none of the words used have the same meaning?

We determine that a particular definition is "incorrect", based on the assumption that there is an ideal definition. The ideal is the best, the most perfect, and need not be something existent, it is simply the assumption of a goal, strive for the best.[...] — Metaphysician Undercover

Actually, inasmuch as a 'better' implies a 'best'; and a 80% mark implies a 100% mark, then a 'more correct' implies a 'fully correct' or 'ideal'. This is necessary. If the ideal does not exist, then neither does the 'more correct' in any objective sense. As such, if you believe that no ideal definition for triangle-ness exist, then it follows that the definition "three angles" is no more correct than "four angles", which is absurd.

I think that the ideal is never achieved, and this is what inspires us to always better ourselves in our understanding. — Metaphysician Undercover

This claim sounds ad hoc. Can you back it up? If I obtained a 100% mark on a math exam, then my answers have reached the ideal, and I cannot better myself on that exam.

Does a 100% similar = the same? And if not, how not?

We are talking about a similarity with a lack of any actual difference. So don't just keep asserting that there remains some difference. You can't wriggle out of it that way.

The same" implies one thing, the same thing, that's the point of the law of identity, to ensure that we are talking about the one and only same thing, the very same thing, when we designate something as "the same" — Metaphysician Undercover

So, in the case of 'the triangle', you are denying that a triangle is the same for you and Apokrisis - that because your idea of a triangle, is different from his idea of a triangle, that they're not two instances of the same thing? Because that is what you seem to keep saying, again and again and again, so it seems to me that you're the one participant in this debate who is 'arguing nonsense' which you have accused him of doing. The fact that two persons might have different ideas of what a triangle means, or form a different image of it, is immaterial to the fact that 'a triangle is a triangle' - a fact which is central to this whole debate, but which seems to be eluding only yourself at this point.

I have this dread that by saying the above I've triggered another cloud of obfuscation.

When I was a kid, I used to snorkle. Every so often I would approach a squid underwater. If you disturb a squid, it shoots off very quickly using its water jet, but it leaves a puff of ink in its place, which looks just like the squid, which, if you're a predator, you will then lunge at.

It's like that. ;-)

Where is the difficulty in recognising that "the same" is the idealised limit to "the similar"? Why are you obfuscating the matter with your unsound sophistry? — apokrisis

@Metaphysician Undercover has already answered your question. Nonetheless, I will proceed to answer it myself, and more or less repeat what MU said, because it appears to be necessary to do so.

"The same" is a relation between two sets where every element that belongs to one set also belongs to the other set. "The similar", on the other hand, is a relation between two sets where most of the elements that belong to one set also belong to the other set. If "same" means "identical" then "similar" means "nearly identical". Thus, it would be incorrect to say that 100% similar = the same. The very concept of "100% similar" makes no sense. Similarity is not a percentage of elements that two sets have in common. However, you can redefine the word to mean precisely that. Defined in this way, you would be right to say that 100% similar = the same. Still, it makes no sense to say that "the same" is the idealized limit to "the similar". The concept of limit, as defined in mathematical analysis, refers to a value that is approached but never reached. Sameness isn't something that is only approached.

"The same" implies one thing, the same thing, that's the point of the law of identity, to ensure that we are talking about the one and only same thing, the very same thing, when we designate something as "the same". — Metaphysician Undercover

Where I might disagree with MU is with his apparent claim that "the same" means "the one". If two things are the same that does not mean they aren't two things. Sameness is a relation and as such it exists "between" two things and not within a single thing. In order to say that two things are same they must first be two things i.e. distinct things.

As I told you, I really did not know what you meant by "100% similar". "Similar" implies necessarily, some degree of difference. Therefore 100% similar implies some difference. You only contradict yourself now, when you say that "100% similar" means a complete lack of difference. It is impossible that similarity lacks difference, by way of contradiction. As I suspected, what you mean by 100% similar is nothing but contradictory nonsense. That's why I couldn't answer that question, I was afraid that what you meant was some such contradictory nonsense. Now my fears have been confirmed, what you mean is contradictory nonsense. — Metaphysician Undercover

He's defining similarity to mean "the percentage of elements the two sets have in common". Thus, "100% similarity" means "the percentage of elements the two sets have in common is 100%" or in plain terms "the two sets have all of their elements in common". But that's not the standard definition. The standard definition of similarity, as Google can tell us, is "having a resemblance in appearance, character, or quantity, without being identical". Similarity, in other words, implies difference. But even if we accept his definition, it does not follow that "the same" is "the limit of the similar" or in plain terms "the value similarity can approach but never attain". The problem is created by his inability to fix his attention.

Defined in this way, you would be right to say that 100% similar = the same. — Magnus Anderson

Great. Glad you agree.

Still, it makes no sense to say that "the same" is the idealized limit to "the similar". The concept of limit, as defined in mathematical analysis, refers to a value that is approached but never reached. Sameness isn't something that is only approached. — Magnus Anderson

I dunno. Why not check out actual set theory concepts like measure theory, almost surely and negligible sets. You might find out that this is in fact exactly how it works.

I dunno. Why not check out actual set theory concepts like measure theory, almost surely and negligible sets. You might find out that this is in fact exactly how it works. — apokrisis

Sameness isn't something that can only be approached. It is something that is regularly attained. This is, in fact, why sameness is a perfectly meaningful term. The fact that we can think of infinite series where a value, such as sameness, is approached without ever being attained does not mean that every infinite series is of that kind.

Sameness isn't something that can only be approached. It is something that is regularly attained. — Magnus Anderson

Heh, heh. Almost surely!

Anyone interested is more than welcome to argue in defense of the claim that there is no such thing as sameness (or what @apokrisis calls "100% similarity".) If you're going to say that there is no such thing as sameness then you should be able to explain what you mean by sameness. This is in order to make sure that we're talking about the same thing. Note that I expect you not to define sameness in the way @apokrisis does i.e. as a value a sequence of similarities approaches but never attains. This is because he thinks that's the only form in which sameness exists. What I am asking you is to define the form of sameness that you, and most of all @apokrisis, claim does not exist. Once you do so, I will take a look at it, and if I think there is evidence that such a thing exists, I will show it to you. It is unfortunate that I have to do this because it is one of the most evident truths that there is such a thing as sameness. It should be something we already agree upon.

The standard definition of sameness is "lack of difference". When you take a look at two different portions of reality and see that there is no difference between their contents then we say that these two portions of reality are the same. (It apparently has to be emphasized that the fact that these two portions of reality are not one portion of reality does not determine whether they are two same or two different portions of reality. Whether they are two same or two different portions of reality is determined entirely by their contents.)

Some people in this thread are trying to argue with a definition.