So I think the distinction you are trying to draw between physical universals and non-physical universals is not a tenable one. — Andrew M

You seem to be misunderstnding; it is the incoherence of such a distinction that I have been arguing for both in this thread and the other. The reference to incoherence is right there in the OP.

You are employing a very narrow sense of 'observe' here. Natural regularities and patterns are observable, but obviously not in the sense that you can look at one like you might look at a tree.

To address your other objection: if there is some "aspect of reality" that we cannot observe, and that cannot be explained in the language of physics, it can only be daid that it is non-physical in the trivial definitional sense that 'physical' is taken to mean 'unobservable' and/or 'not capable of explanation in terms of physics'.

Any other sense of 'non-physical' implies dualism...or what else?

You seem to be misunderstnding; it is the incoherence of such a distinction that I have been arguing for both in this thread and the other. The reference to incoherence is right there in the OP. — Janus

OK, then I'm not clear on what we would be disagreeing about. Do you agree that information, gravity and mind (as universals) are all physical? Which is to say, aspects of the natural world that we empirically investigate?

Math are grounded in certain human actions; sorting, arranging etc. These actions are performed with a certain amount of regularity by most humans. These performances are then re-enforced by schooling and "hardened" into rules. These rules then, are the basis of math — Πετροκότσυφας

We've invented nuclear weapons, and calculated the age and size of the Universe, by such 'sorting and arranging.' On the basis of what is quoted, I don't find Wittgenstein's philosophy of mathematics at all compelling, it amounts to basically rejection of Platonic realism, without any real account of an alternative.

If you can only convey the mental imagery in your head to others by converting it into a physical format, like the screen with letters on it that you see before you, for others to then receive, then doesn't that show that information is physical? How do you get the information in your head to others, and before anyone reads your post does your post contain information? — Harry Hindu

Again - the representation is physical, but ideas are a different matter. Notice that in physics, computer science, and many other fields, new symbols, codes and languages have been invented specifically to communicate ideas that have been discovered. At the time those insights are first glimpsed, quite often they emerge in quite incommunicable ways, or even ways that can't be articulated, and then first they have to be described, and then communicated. That is what it takes to translate them into physical representations. What does that, is the human intelligence, the mind. I am saying it is the unique ability of the mind to discern meaning - likeness and unlikeness, greater than, less than, equal to - and central to that, is the ability to recognise universals.

I see nothing to comment on. It is as it is, could have been otherwise. Whatever.

Seeing flags being waved is necessary but not sufficient to know what information is being conveyed. It also requires the ability to think abstractly. — Andrew M

How did you even know that flags are being waved if a flow of information (that flags are being waved) didn't happen? It seems to me that you thinking abstractly isn't necessary for information flow. You simply need to have eyes and brain to process sensory information.

It did require using physical means to convey it. There is no other way. — Andrew M

Thank you.

Again - the representation is physical, but ideas are a different matter. Notice that in physics, computer science, and many other fields, new symbols, codes and languages have been invented specifically to communicate ideas that have been discovered. At the time those insights are first glimpsed, quite often they emerge in quite incommunicable ways, or even ways that can't be articulated, and then first they have to be described, and then communicated. That is what it takes to translate them into physical representations. What does that, is the human intelligence, the mind. I am saying it is the unique ability of the mind to discern meaning - likeness and unlikeness, greater than, less than, equal to - and central to that, is the ability to recognise universals. — Wayfarer

So what if the representation is "physical"?! Ideas can be representations too. You are still caught up in this false dichotomy of "physical" vs. "non-physical". I have said numerous times that this distinction is unnecessary as the "physical" and "non-physical" still interact and are causally influenced by each other. By this same token, information is both "physical" and "non-physical" as information is the relationship between cause and effect (which I have said numerous times as well).

The ability to discern meaning is not unique to the human mind. Do not other animals discern the meaning of what they are smelling - is it predator, food, a female in heat, or the scent markings of a competing male?

You are employing a very narrow sense of 'observe' here. Natural regularities and patterns are observable, but obviously not in the sense that you can look at one like you might look at a tree. — Janus

It is necessary to employ such a narrow sense of "observe" in order to understand the nature of the things which you call regularities, and invariances. These things are not perceived by the senses, they are produced by inductive reasoning, as conclusions.

To address your other objection: if there is some "aspect of reality" that we cannot observe, and that cannot be explained in the language of physics, it can only be daid that it is non-physical in the trivial definitional sense that 'physical' is taken to mean 'unobservable' and/or 'not capable of explanation in terms of physics'.

Any other sense of 'non-physical' implies dualism...or what else? — Janus

Doesn't this sense of "non-physical" imply dualism to you? If there is an aspect of reality which cannot be sensed, nor understood by physics, then we ought to conclude that there are two distinct aspects of reality, that which is sensed and understood by physics, and that which is not. Doesn't this seem like dualism to your?

From this premise, of the two distinct aspects of reality, we can proceed using the mind, rather than the senses and the principles of physics, toward understand this other aspect of reality. If you deny the dualist premise, and the premise is in fact true, then you will never have an approach to this non-physical aspect of reality, always falsely believing that it will eventually be understood by empirical science. The non-physical will forever remain obscured to you, because you will deny the premises required to understand it, and you will act like a monist materialist, continually making false assumptions concerning this aspect of reality.

As explained in this article:



Thus, interestingly, there is a sense in which Wittgenstein actually agrees with the line taken by Hardy, Frege and other Platonists insisting on the objectivity of mathematics. What Wittgenstein opposes is not objectivity per se, but the ‘philosophical’ explanation of it. The alternative account he proposes is that arithmetical identities emerge as a special codification of these contingent but extremely robust, objectively verifiable behavioral regularities. (Yet, recall that although the arithmetical propositions owe their origin and relevance to the existence of such regularities, they belong to a different order.) So, what Wittgenstein rejects is a certain “metaphysics of objectivity” (Gerrard [1996, 173])



A closer look at the contingent regularity relevant in this context – behavioural agreement – is now in order. (At PI §206 and 207 Wittgenstein suggests that these regularities form the basis of language itself.) This type of agreement consists in all of us having, roughly, the same natural reactions when presented with the same ‘mathematically’ related situations (arranging, sorting, recognizing shapes, performing one-to-one correspondences, and so forth.) Its existence is supported by the already discussed facts: (i) we can be trained to have these reactions, and (ii) the world itself presents a certain stability, many regular features, including the regularity that people receiving similar training will react similarly in similar situations. (There surely is a neuro-physiological basis for this; cats, unlike dogs, cannot be trained to fetch.)



So, it is simply not the case that the truth-value of a mathematical identity is established by convention. Yet behavioural agreement does play a fundamental role in Wittgenstein’s view. This is, however, not agreement in verbal, discursive behaviour, in the “opinions” of the members of the community. It is a different, deeper form of consensus – “of action”



The specific kind of behavioural agreement (in action) is a precondition of the existence of the mathematical practice. The agreement is constitutive of the practice; it must already be in place before we can speak of ‘mathematics.' The regularities of behaviour (we subsequently ‘harden’) must already hold. So, we do not ‘go on’ in calculations (or make up rules) as we wish: it is the existent regularities of behaviour (to be ‘hardened’) that bind us.



While the behavioural agreement constitutes the background for the arithmetical practice, Wittgenstein takes great care to keep it separated from the content of this practice (Gerrard [1996, 191]). As we saw, his view is that the latter (the relations between the already ‘archived’ items) is governed by necessity, not contingency; the background, however, is entirely contingent. As Gerrard observes, this distinction corresponds, roughly, to the one drawn in LFM, p. 241: “We must distinguish between a necessity in the system and a necessity of the whole system.” (See also RFM VI-49: “The agreement of humans that is a presupposition of logic is not an agreement in opinions on questions of logic.”) It is thus conceivable that the background might cease to exist; should it vanish, should people start disagreeing on a large scale on simple calculations or manipulations, then, as discussed, this would be the end of arithmetic – not a rejection of the truth of 2+3=5, but the end of ‘right’ (and ‘wrong’) itself, the moment when such an identity turns into a mere string of symbols whose truth would not matter more than, say, the truth of ‘chess bishops move diagonally.' (Note that this rule is not grounded in a behavioural empirical regularity, but it is merely formal, and arbitrary.)



The very fact of the existence of this background is not amenable to philosophical analysis. The question ‘Why do we all act the same way when confronted with certain (mathematical) situations?’ is, for Wittgenstein, a request for an explanation, and it can only be answered by advancing a theory of empirical science (neurophysiology, perhaps, or evolutionary psychology).



Related to Platonism, ‘mentalism’ is another target of Wittgenstein, as Putnam [1996] notes. This is the idea that rules are followed (and calculations made) because there is something that ‘guides’ the mind in these activities. [...] The mind and this guide form an infallible mechanism delivering the result. This is a supermechanism, as Putnam calls it, borrowing Wittgenstein’s own way to characterize the proposal. [...] Moreover, if we try to take these super-mechanisms seriously we fall into absurdities. — Πετροκότσυφας

The problem with Wittgenstein's approach is that he misunderstands, and therefore misrepresents the nature of these "behavioral regularities". Behaviour regularities are represented as something which is naturally comes to us from society, rather than as something which comes about as the result of the individual's willingness. He represents it as the institutions of society naturally pass their conventions to the individual in the process of learning, as if the teacher is the agent, and the student is passive, in the process of learning. This is a misrepresentation of what is really the case, and that is that the individual through the means of intention, will, ambition, and effort, is the agent who is actively learning.

This is clearly exposed in his Philosophical Investigations, where he defines "rule-following" as observed activity which is in accordance with some standards set by society. With this definition of "rule-following" he excludes the true nature of rule-following, what really happens in a case of rule-following, which is that an individual holds a principle within one's own mind, and adheres to that principle with one's actions. The exclusion is demonstrated in the so-called private language argument.

The difference between these two representations of "behaviour regularities" has very significant ramifications. The Wittgensteinian way completely misses the role of intention and will in the act of learning. It is as if Wittgenstein gets a glimpse of intention and sees it as a vast and incomprehensible subject to approach, so he defines his terms in such a way as to completely avoid it. But the difference is this. Right and wrong, under Wittgenstein are determined by social conventions. The problem is that sometimes human knowledge is faulty and social conventions are actually wrong. In this case, then individuals need to determine the real truth, and rectify the social conventions. But this is impossible under the Wittgensteinian principles because right and wrong can be nothing other than what is determined by the social conventions. If we allow that the individual can produce a right, or a wrong, which is contrary to those of society, the whole epistemological system is undermined as contradictory.

So in Wittgenstein's system the description of how right and wrong is determined is inherently faulty. There is no way to judge the principle from which an action proceeds, as right or wrong, because we can only judge the action itself as right or wrong, in reference to the principles accepted by convention. Since only the judgement of actions is possible, and there is no way to judge principles, then the principles of convention cannot be judged as right or wrong.

I have said numerous times that this distinction is unnecessary as the "physical" and "non-physical" still interact and are causally influenced by each other. — Harry Hindu

As I've told you already, the fact that two things interact is not reason to deny that there is a useful distinction to be made between those two things. If you want to claim that the distinction between physical and non-physical is unnecessary, you need a much better argument than that.

Do not other animals discern the meaning of what they are smelling - is it predator, food, a female in heat, or the scent markings of a competing male? — Harry Hindu

Stimulus and response are different to language and abstraction.

It has been said that ‘intelligence is the ability to make distinctions’. There are some fundamental distinctions you’re failing to grasp here, although it is habitual nowadays to ignore the distinction between h. Sapiens and other animals (which is ‘sapience’, the Latin equivalent of ‘sophia’, which is wisdom, which is what philosophy is named for.)

OK, then I'm not clear on what we would be disagreeing about. Do you agree that information, gravity and mind (as universals) are all physical? Which is to say, aspects of the natural world that we empirically investigate? — Andrew M

I have not been clear that we have been disagreeing from the beginning. In our initial exchange I had thought that you were suggesting that we should think of information as non-physical, and that you were treating gravity as a mere abstraction analogous to information; but perhaps I misunderstood you.

I don't agree, though, that it makes sense to say that information, gravity and mind (as universals) are all physical. We can think of universals as either physical or non-physical, but I think such thinking is poetic, metaphorical rather than propositional. To say that universals are physical or non-physical is like saying the air is green or red. We might say in a poetic context that the air is green or red, but the question of whether it is green or red is meaningless.

In other words I don't think that the idea that universals are physical or non-physical is a proposition that could be correct or incorrect; but merely more or less useful or fruitful in different contexts. This is why I have been criticizing Wayfarer on this; because he seems to think there is some higher, unimpeachable truth of the matter regarding universals; that universals point to some 'higher, supernatural order". I don't believe any of that; I don't think there is anything like an ultimate authority or power beyond nature that could hold sway over us and our investigations.

Also I don't believe that our investigations and judgements are restricted to the merely empirical and/or propositional; I think this would be a very narrow, reductive view of human enquiry.

These things are not perceived by the senses, they are produced by inductive reasoning, as conclusions. — Metaphysician Undercover

No, this is wrong. If you see your cat coming in every morning for her food; this is something you have observed. This habit of hers is not 'directly' in-the-moment-observed, like the cat herself is, but it also not an inference; you know she regularly comes in and eats the food you provide for her.

Doesn't this sense of "non-physical" imply dualism to you? If there is an aspect of reality which cannot be sensed, nor understood by physics, then we ought to conclude that there are two distinct aspects of reality, that which is sensed and understood by physics, and that which is not. Doesn't this seem like dualism to your? — Metaphysician Undercover

It might imply an inherent dualism in the way we think about things; but I don't think it implies an ontological dualism. Actually I think reality is pluralistic; there are infinitely many aspects to reality, but no two totally distinct types of aspect as you are suggesting; so I don't think as a monist would, but as a non-dualist.

The term "behavioral regularities" does not even refer to the process of learning and its institutions. It refers to acts of sorting and arranging and W. does not hypothethise about its origin. Regarding the rest,
at least what of it is not irrelevant, it does not sound like W. I'm not sure where you've found that. It actually sounds more like you when you were replying to Samuel about school. — Πετροκότσυφας

Have you read Wittgenstein's "Philosophical Investigations", or "On Certainty". If so you ought to recognize what I'm talking about. Your whole quoted passage completely obscures what Wittgenstein actually wrote, with terminology like "behavioural regularities" and "behavioural agreement". Wiittgenstein wrote about following rules, learning how to follow rules, what constitutes following a rule, and consensus, not about behavioural agreement.

What is "behavioural agreement", supposed to mean, that we can describe numerous people as behaving in a similar way? Wittgenstein proposes a principle for distinguishing correct from incorrect, but "behavioural agreement" implies no judgement of right or wrong. To say "2+2=4" is correct, to say "2+2=5" is incorrect. To say that Wittgenstein represents 2+2=4 as a "behavioral agreement" rather than as "correct", is simply a misrepresentation of Wittgenstein.

It may be the case, that what Wittgenstein calls "correct", (which is derived from how he defines "rule"), is reducible to a form of behavioural agreement, but that is exactly the point I made in my last post. Under Wittgenstein's epistemology correct and incorrect, right and wrong are defined by behavioral agreement. This eliminates the possibility that behavior which everyone is doing, and everyone agrees upon (behavioural agreement), might in fact be wrong. That possibility is eliminated because "right", "correct", is defined by what everyone is doing. So if an accepted behaviour turns out to be, in fact, a bad habit which everyone is doing, it is impossible to rectify this bad habit, because it is by definition, right, correct.

No, this is wrong. If you see your cat coming in every morning for her food; this is something you have observed. This habit of hers is not 'directly' in-the-moment-observed, like the cat herself is, but it also not an inference; you know she regularly comes in and eats the food you provide for her. — Janus

You have noticed that your cat comes for food. That it comes "every morning for food" is an inference. Your sense observations, along with your memory, can only tell you that you have observed your cat coming time and again. That there is some sort of pattern, or regularity to your cat's activities is an inference.

It might imply an inherent dualism in the way we think about things; but I don't think it implies an ontological dualism. — Janus

Either the dualism is inherent in reality, in which case it is ontological, or it is just a feature of the way that we describe things. Our discussion has been such that we have assumed that it is inherent within reality, therefore it is an ontological dualism. If you want to change your position now, and say that it is just a feature of how we describe things, and that it is all in our heads, imaginary, then that's a different matter completely.

That there is some sort of pattern, or regularity to your cat's activities is an inference. — Metaphysician Undercover

No, you still have it wrong: that there has been a pattern or regularity to your cat's activities is a matter of observation: that there will be such in the future would be an inference.

Our discussion has been such that we have assumed that it is inherent within reality, — Metaphysician Undercover

What have I said that entails that I must think that? I don't agree with any notion that any way we might be able to think is just "all in our heads". Nature (including us) is such that we can think dualistically (among other ways of thinking); and from that it certainly does not follow that nature is, in some purportedly absolute ontological way dualistic (or monistic). I think what follows is that nature is non-dualistic or pluralistic; it has infinite, and infinitely many, aspects.

No, you still have it wrong: that there has been a pattern or regularity to your cat's activities is a matter of observation: that there will be such in the future would be an inference. — Janus

Consider that every time your cat comes for food you look at your clock, and calendar, and make a note. After some duration you have a lot of notes. You can look over your notes and state specific times that the cat came, but you cannot claim that the cat's appearance is a pattern, or regular, unless you apply some principle of what it means to be regular, and deduce, from your notes that the cat's appearance fulfills these conditions of regularity. Clearly it is a matter of inference.

What have I said that entails that I must think that? I don't agree with any notion that any way we might be able to think is just "all in our heads". Nature (including us) is such that we can think dualistically (among other ways of thinking); and from that it certainly does not follow that nature is, in some purportedly absolute ontological way dualistic (or monistic). I think what follows is that nature is non-dualistic or pluralistic; it has infinite, and infinitely many, aspects. — Janus

What we have been discussing is the premise that one aspect of reality is physical, and another is non-physical. You claimed that this was a trivial form of dualism. I demonstrated how it is an ontological dualism. Now it appears like you want to reject the premise, saying that it is not the case that one aspect of reality is physical and another non-physical, that this is just one way of thinking about reality, and that there is an infinite number of ways to think about reality, each just as likely to be true as any other.

Consider that every time your cat comes for food you look at your clock, and calendar, and make a note. — Metaphysician Undercover

No, all I have to do is remember seeing the cat come in each morning, or the sun set each evening, to know that those things have happened with an observed regularity.

What we have been discussing is the premise that one aspect of reality is physical, and another is non-physical — Metaphysician Undercover

No, what I have been discussing is the fact that we call some things physical and others non-physical, for certain reasons and in particular contexts; and whether that fact should lead us to posit ontological dualism or some other (as yet unspecified) position to the effect that there really are things which are real and yet non-physical in the sense of being ontologically independent of nature.

Nope, it's not correct by definition, because there's nothing in place to make it right or wrong. — Πετροκότσυφας

What is in place is the definition of what it means to follow a rule, provided by Wittgenstein in the Philosophical Investigations. Acting in a way which is judged to be in accordance with a rule, is to be right, correct. To say that two plus two equals four is to act in a way which is judged as being in accordance with a rule, and therefore is to be right, or correct.

Nope, it's not uniform practice itself that makes it right or wrong. It's not the criterion, it's the presupposition for the emergence of the criterion itself. It's the rule, which is based on uniform practice, which makes it right or wrong. — Πετροκότσυφας

This resolves nothing. Even if you represent the rule as "emerging" from uniform practise, my criticism is still relevant. Once a rule emerges, if right and wrong are relative to the rule, the rule itself cannot be wrong, because right and wrong are judged relative to the rule. If a further uniform practice emerged which was contrary to the rule, it would necessarily be wrong. So it is impossible that one rule could come to replace another rule, such that rules might evolve. Clearly, the Wittgensteinian description of the relationship between these three things, "rules", "uniform practise", and "right and wrong", does not correspond with reality at all because we observe the evolution of rules.

Based on that, it's only natural to harden this basic mathematical practice, inherent in this situation, into a rule. Three kids = split food in three. — Πετροκότσυφας

My objection is not concerning the relationship between "uniform practice" and "rule" if there is no ambiguity with "rule", and "rule" is understood as a descriptive rule. It is when a descriptive rule, which emerges from uniform practice, is suddenly claimed to be a prescriptive rule, through some sort of equivocation, that I call foul. So I'll reiterate my claim. We have a uniform practice. We have a descriptive rule which emerges from that uniform practise, "things are done this way". There is no principle here by which we can proceed to claim "things ought to be done this way". Therefore, there is no principle by which we can say that acting according to this descriptive rule is "right", or acting in a discordant way is "wrong". This is a false representation of what right and wrong are. Right and wrong are based in acting according to certain principles which have been judged, they are not based in acting according to a description of uniform practise.

It appears like we have been talking about completely different things.

How did you even know that flags are being waved if a flow of information (that flags are being waved) didn't happen? It seems to me that you thinking abstractly isn't necessary for information flow. You simply need to have eyes and brain to process sensory information. — Harry Hindu

That's true, but I'm not just referring to seeing the flags and that they're being waved (which, as you say, also involves a flow of information). Seeing the flags waving is presumably automatic and instinctual for humans and animals alike.

I'm instead referring to the higher-level information that is being communicated via the flag waving, namely, the ship arrival details.

Now that information is in the world as well. But to interpret and understand it requires the ability to think abstractly, it is not just an automatic sensory process.

In other words I don't think that the idea that universals are physical or non-physical is a proposition that could be correct or incorrect; but merely more or less useful or fruitful in different contexts. — Janus

A different way to state my basic claim is that universals (such as information, gravity and mind) are aspects of the natural world. This distinguishes it from Platonism, which posits a non-natural realm for universals, and Nominalism, which denies that there are universals.

Is that also your view of universals?

Yes I believe universals are more than merely names and I don't believe there is anything over and above the natural.

That could well be so.

This distinguishes it from Platonism, which posits a non-natural realm.... — Andrew M

Do you think ‘the domain of natural numbers’ is ‘a realm’? Because, I’m inclined to believe that it is a realm or a domain - but that those descriptions are metaphorical, as they are not in a literal place or domain. Nevertheless I think ‘the domain of natural numbers’ is a perfectly intelligible expression, even if it’s not something that exists in a spatial or temporal sense. Some things, like the integers, are included in that domain, and other things, like the square root of -1, are not.

So again, a Platonic realist view, as I would understand it, is not that natural numbers are existing things in an existing place, but that they’re real, insofar as they’re the same for anyone capable of counting. It’s possible to be wrong about maths (as I nearly always was, and failed the subject).

Furthermore, numbers are not ‘aspects of the natural world’, if by that we mean the world that is perceptible by sense, as they are only perceptible by means of reason. Given the ability to count and measure, then numbers have a wide range of application, but they’re not empirical objects. That was why I mentioned the ‘indispensability argument for mathematics’ earlier in this thread, which attempts to justify the sense in which mathematical objects are real, without appealing to traditional rationalism. The very fact that such an argument is deemed to be necessary supports the view that rational objects such as numbers are not empirical but purely intelligible in nature.

I don't believe there is anything over and above the natural. — Janus

I don’t think we know enough about nature to know what might be ‘over and above’ it. Some things we take for granted now might once have seemed supernatural. In any case, the Kantian argument from such faculties as mathematical reasoning, is that reason is indispensable for the understanding (otherwise we couldn’t even pose an argument) yet the nature or source of reason is not disclosed in the facts of experience, which is what he means by ‘transcendental’; and to this extent, reason itself can’t necessarily be said to be ‘natural’, in the sense of having a natural explanation. (I do note however that nowadays it is widely assumed that reason can be explained with recourse to evolutionary biology, however I think this is highly dubious.)

I think a good deal of the resistance to that argument, is the fact that anything deemed supernatural is deemed by many out-of-bounds for philosophy. Yet that road only leads to positivism.

Kant, Spinoza and Hegel all reject the supernatural and modern metaphysics in general has no truck with it; so to say that the only alternative to the supernatural is positivism is nonsense.

I think it is far too sweeping to say that Kant, Spinoza and Hegel 'all rejected the supernatural'. There are books on 'Hegel the mystic'; Kant said the purpose of his philosophy was to 'find the limit to knowledge so as to make room for faith'; the high point of Spinoza's philosophy was 'the intellectual love of God'. It is also the case that the rejection of metaphysics, in a general and broad sense, was the defining characteristic of positivism. And you yourself have on numerous occasions in this thread, and elsewhere, said that anything you regard to be 'supernatural' is out of bounds for philosophy; I seem to recall your quoting Biblical verses in support of that argument in this very thread.

What I’m trying to do in this thread is to develop an argument for non-material realities, by appealing to the nature of reason, mathematics, and logic.

That image imparts no information. — Wayfarer

Nevertheless, we agree that the container of info is physical, even if the info it contains is not. But I think that a mental image is also nothing but a container of information. After all, 'mental image' is synonymous to what I called earlier 'physical visualization', even according to Edward Feser's article.

If information is the arrangement of physical parts, then there must be a reason for that particular arrangement being the particular arrangement which it is in order that we can say that it is "information". It must have the capacity to inform us of something. — Metaphysician Undercover

To clarify, I was referring to information pointing to no concepts, that is, meaningless raw data, like statics from the tv set, perceived by the senses but unintelligible to the mind. Otherwise, I agree that meaningful information must be non-physical, for the reason you pointed out.

What different symbols represent is not unchangeable, and this is evident in evolving language. So if for some reason the ordering of the symbols which represent numbers gets changed, and this all agreed upon, such that the order is 1,3,2,4, and the symbol 3 starts to mean the same thing as 2 does now, then 1+1 would equal 3. — Metaphysician Undercover

You are once again confusing the symbol or word, with the concept it points to. Yes, we can change the symbols 1, 2, 3, ..., but we cannot change the concepts I, II, III, ... As such, we can make 1+1=3 if we change the symbols, but cannot make I+I=III <-- As you can see, there is one too many bar on the right side of the equation, which makes it unbalanced.

And as it is with concepts of numbers, so it is with other concepts. E.g., we can change the word "red", but the concept of red-ness will remain unchanged.

The point is that there is no necessity between the symbol and what it represents. It doesn't necessarily represent what it does, and this is because what it represents was somehow decided upon. Therefore the relationship between the symbol and what it represents is dependent on the existence of subjects. Since the existence of concepts seems to be dependent on this relationship between symbols and representation, we cannot simply assert that concepts are "objective" if you define objective in this way (independent of subjects). — Metaphysician Undercover

I agree with your first three sentences. This is why there are different languages and writing symbols. However, I still disagree with your last sentence, that concepts or universal forms are dependent on that relationship. A rock participates in the form of rock-ness, even before a subject observes it or find a word or symbol for it for the first time.

Wittgenstein would agree they're objective. Yet, he (rightly, in my opinion) denied that math are discovered and unchangeable. Rather, they're invented. The world is a certain way. But it could be otherwise. This means that the way the world is, is contingent. Although, it is also a fact that people most of the time perform certain tasks the same way. It is not just the world that exhibits regularities, it is us as well. Math are grounded in certain human actions; sorting, arranging etc. These actions are performed with a certain amount of regularity by most humans. These performances are then re-enforced by schooling and "hardened" into rules. These rules then, are the basis of math. Had the world been otherwise, had we been otherwise, then our practices would be different and math would be different as well (if they would have been invented at all). — Πετροκότσυφας

Not gonna lie, I did not read your quoted paragraphs (tl;dr O:) ), but I read the above. Let's make the distinction between three kinds of reality: (1) potential, that is, not actual and contingent, (2) actual and contingent, and (3) actual and necessary. I claim that math concepts fit into reality (3). We can use Chesterton's Test of Imagination to demonstrate this.

• (1) Unicorns don't exist, but I can image them. They are therefore potential.
• (2) Horses exist but I can imagine a world without them. They are therefore actual and contingent. Same for laws of physics. These may be unchangeable in our universe, but sci-fi writers imagine universes with different laws all the time, like a flat Earth carried by elephants on a giant turtle.
• (3) The concept I+I=II is actual (we can test this with objects), and I cannot imagine any other results, such as I+I=I or I+I=III. E.g., try to imagine 1 apple, and then 1 other apple, and yet imagine 3 apples in total, without adding a third apple in the mental image. It cannot be done. Math concepts are therefore actual and necessary.

Sure, there are the books that contain the definition and the people that know it. The definition, while abstract, is not something ontologically separate from those physical books or people. (It is also implicit in the natural world which means it is discoverable by anyone with the requisite intelligence and skills.) — Andrew M

If by definition, you mean quite literally the description of the concept, and not the concept in itself, then I agree with you. (man this topic is hard).

we agree that the container of info is physical, — Samuel Lacrampe

But in this example there's no 'info'. A random squiggle doesn't convey anything, it literally has no information content. So whether you can form a mental image of it or not, it is meaningless. The only context in which it might be meaningful, is if you found it in a place where you were looking for traces of human habitation. But even then, the content would contain no information - only the fact of its existence.