I don't agree - with Wittgenstein, not with your exegesis. I'm going with Kripke, in saying that the stick in Paris was used to set a certain length as the referent of "one metre", a sort of baptism ceremony for that length, and that length is now set for all possible worlds.

So it does make sense to ask if the stick is a metre long. — Banno

But we already know that it is a metre long - it was "baptised" as such.

If you proceed to ask the question, then how do you intend to measure it; to check whether or not it really is one metre long?

Or, as Robert J. Fogelin succinctly puts it in his 'Taking WIttgenstein at His Word: A Textual Study', in reference to the sepia example at §50:

What doesn't make sense is to use something as a standard and simultaneously judge its accordance with that standard.

If we're quoting experts, then I like Stephen Mulhall's take in his book 'Wittgenstein's Private Language: Grammar, Nonsense, and Imagination in Philosophical Investigations, Sections 243-315':

When Wittgenstein suggests (in §50) that the standard metre is the one thing of which we can say neither that it is, nor that it is not, one metre long, he characterizes that as marking its peculiar role in the language-game of measuring with a metre-rule. For if we were to try to represent its length as being one metre, and someone were to ask us what we meant by 'one metre', we could only point to the bar itself - thereby implying that what we had claimed amounted only to the empty 'assertion' that 'this bar is as long as it is'.

In other words, Wittgenstein's suggestion reflects the fact that the standard metre is an instrument of that dimension of our language of measurement; in the system of metric measurement, it is a means of representation rather than something that is represented. Hence, in so far as one can intelligibly remark that 'the standard metre is one metre long', that remark will function as an explanation of what we mean by 'one metre' (or perhaps as an explanation of what we mean by 'standard metre'); it will, in other words clarify the meaning of a word rather than conveying any information about the length of that particular rod or bar.

The extraction of language from it's context that Wittgenstein is showing cannot be fruitful is not something that the general population do, it is not a thing which the uneducated need to be taught about so that they can become more knowledgeable, it is something that experts do to manufacture the very body of knowledge about which they are expert.

But that's just my interpretation. — Ciaran

I tend to agree. Thanks for your response.

Okay then. Well, thanks for disrupting the discussion to advise us that we're not discussing it properly, and then leaving without telling us how to discuss it properly.

The analysis would be very different if a person were to approach the text assuming it to be a statement of 'the way things are' to if a person were to approach it as a normative statement of 'you should look at things this way (even though other ways are perfectly possible)'. In the former case, one can critique the text by arguing 'no, things are not that way, here's an example', but in the other, one would critique the text by saying 'looking at things this (other) way has the following use/value'. — Ciaran

As some form of explanation, I take it that you're advocating the latter approach? Could you provide an example? e.g. by saying more about this:

The early points about the role of ostension, for example, seem to hinge entirely on an assumption that Wittgenstein was solely attempting to knock down some kind of straw man version of Augustine's argument which later sections make it clear (to me anyway) that he was not. — Ciaran

Good post. You are right to point out that Wittgenstein is arguing against the view "that "primary elements" are intended by those philosophers who posit them, to be some sort of absolute, as the foundation for all reality,". StreetlightX also notes the importance of these 'ontological primitives' in his latest post, with the elegant description of "a one-to-one mapping between name and primary element". However, I don't consider this to be an entirely new development, since W has been arguing against any presupposed 'occult process' or 'queer connection' between name and object since at least section §37. I maintain that at §47 and §48 he is drawing our attention to the meaning/use of the terms 'simple' and 'composite', but I acknowledge that he is also attacking the deeply ingrained presupposition of a 'queer connection' between name and object in the process.

So, as I said earlier, I thought there was some truth to what you said, but did not agree with your use of the term 'digression'. I also didn't really understand your reference to primary elements being "self-refuting".

Since he says little about "primary elements" and speaks much more about simples and composites from 46-48, then I disagree that it's merely a "digression". If so, it's quite a long digression. Perhaps some of what you say could be deduced from what he says, but you're largely missing the point about meaning being undetermined outside a language-game.

§48. W considers a language-game which conforms to the account from the Theaetetus which is presented at §46, in which names stand for primary elements. "The language serves to describe combinations of coloured squares on a surface" which form a 3x3 matrix or "complex". The squares are red, green, white and black, and the words of the language are (correspondingly) "R", "G", "W" and "B", where "a sentence is a series of these words". The order of the squares has an arrangement like the numbers of a (push-button) telephone, so the sentence "RRBGGGRWW" takes the arrangement of:

RRB
GGG
RWW

(but with the above "words"/letters replaced by their respective colours.)

Wittgenstein states that the sentence "RRBGGGRWW" "is a complex of names, to which corresponds a complex of elements. The primary elements are the coloured squares." Wittgenstein states that it is natural to consider these primary elements (coloured squares) as simple. However, he notes that "under other circumstances" he might call a monochrome square "composite" because it consists "perhaps of two rectangles, or of the elements colour and shape". Or, we might consider a smaller area "to be 'composed' of a greater area and another one subtracted from it". He notes that "we are sometimes even inclined to conceive the smaller as the result of a composition of greater parts, and the greater as the result of a division of the smaller". Wittgenstein now questions whether the sentence "RRBGGGRWW" contains four or nine letters, and whether an element is a type of letter (i.e. a colour) or an individual letter.

Reiterating his message from §47, whether these primary elements are 'simple' or 'composite' depends on how we agree to use those terms; what we mean by 'simple' and 'composite'. As he states lastly: "Does it matter which we say, so long as we avoid misunderstandings in any particular case?"

44. Having previously argued that names do not require a bearer to be used in the language-game, Wittgenstein now changes tack and asks us to imagine a language-game in which names (i.e. "signs which we should certainly include among names") are only used in the presence of a bearer, and therefore "could always be replaced by a demonstrative pronoun and the gesture of pointing".

45. "The demonstrative "this" can never be without a bearer". W suggests that as long as there is a bearer, then the word "this" also has a meaning, regardless of whether the bearer is simple or complex. However, it does not make the demonstrative "this" into a name, "for a name is not used with, but only explained by means of, the gesture of pointing". This is logically similar to his remark at §38 that the word "this" is not defined demonstratively (e.g. [not] "This is called 'this'".)

46. "What lies behind the idea that names really signify simples?" W indicates that this has long been a common philosophical assumption, quoting Socrates in the Theaetetus and noting that the same idea has also been entertained by himself and Bertrand Russell.

47. W asks what are the simple constituents of (e.g.) a chair? Is it the wood, or the molecules, or the atoms of which it is composed? He notes "'Simple' means: not composite. And here the point is: in what sense 'composite'?" He reveals the answer: "It makes no sense at all to speak absolutely of the 'simple parts of a chair'".

W now speaks of his own visual image (e.g. of a tree) and asks of what simple parts it is composed. W considers the question vague: what sense of 'composite' are we talking about? "The question "Is what you see composite?" makes good sense if it is already established what kind of complexity - that is, which particular use of the word - is in question."

W anticipates the counterargument: "But isn't a chessboard, for instance, obviously, and absolutely, composite?" W answers that you are probably thinking of the chessboard's composition as 32 white and 32 black squares, but he notes that you could also say "that it was composed of the colours black and white and the schema of squares". This might sound very similar, but the point is that it has not been established what we mean by 'composite' here. You can't just say that it is composite without first deciding what we mean by that. As W says it is misguided to ask whether an object is composite outside of a particular language-game.

He concludes: "We use the word "composite" (and therefore the word "simple") in an enormous number of different and differently related ways...To the philosophical question: "Is the visual image of this tree composite, and what are its component parts?" the correct answer is: "That depends on what you understand by 'composite'." (And that is of course not an answer but a rejection of the question.)"

I appreciate your remarks upon remarks 36 to 39 as they look at how "corresponding" is assumed so often while not looking at how it is done. — Valentinus

Thanks, Valentinus. Yes, you're right. Wittgenstein is challenging these common philosophical assumptions.

A part of the book that can be overlooked is the way Wittgenstein is teaching a method for doing philosophy. §37 is a case in point. He does not go off theorising about names and the named, but rather draws our attention to a few examples. He want us to look to what is being done here. — Banno

I can't easily tell whether this is a criticism of my post or simply a comment, but some remarks on my method: I am trying to emphasise what I consider to be important and omit what I consider to be less important while trying to retain the overall gist of each section. I'm not sure whether this is adding much value to the discussion, but it's at least helping (or forcing) me to read the text more closely. I expect there to be more divergence and disagreement, and therefore (perhaps) more commentary from me, in the readings to come.

§40. Wittgenstein takes issue with one point of the "sharp blade" argument given at §39: "that a word has no meaning if nothing corresponds to it". Wittgenstein warns against confounding the meaning of a name with the bearer of that name. These are different, W argues, given that the meaning of a name does not die along with the bearer of that name. If it did, then it would make no sense to use the bearer's name after they die, because the name would cease to have any meaning.

§41. W asks us to suppose that "a tool with the name "N" is broken" in his language game at §8 (which is an expanded version of his 'block-slab-pillar-beam' language-game at §2 that also includes numerals and colours). W asks whether the sign still has a meaning when A gives the sign to B, and what will B now do in response? "Well, perhaps he will stand there at a loss, or shew A the pieces". W emphasises that one might say that "N" has become meaningless. W explains what he means by "meaningless": "this expression would mean that the sign "N" no longer had a use in our language-game (unless we gave it a new one)". W notes that this could also happen if the tool was not broken but given another name and therefore the sign "N" was no longer used. However, "N" might retain its use in the language-game if (e.g.) whenever A gives B the sign "N", B shakes his head in reply. "In this way the command "N" might be said to be given a place in the language-game even when the tool no longer exists, and the sign "N" to have meaning even when its bearer ceases to exist."

§42. W indicates that even "a name which has never been used for a tool" in the language-game at §41 could still "be given a place in the language-game", where, for example, B responds to the use of this name with a shake of the head. W states that we could imagine this as "a sort of joke" between A and B.

§43. "For a large class of cases - though not for all - in which we employ the word "meaning" it can be defined thus: the meaning of a word is its use in the language.

And the meaning of a name is sometimes explained by pointing to its bearer."

I would prefer to focus on discussing the text together rather than spend time responding to barely-supported naysaying. But I admire your passion!

§36. As there is no single characteristic behaviour or "bodily action" associated with pointing to a feature (e.g. to shape or to colour), "we say that a spiritual [mental, intellectal] activity corresponds to these words". He returns to comment on this 'queer connexion' or 'occult process' at §38.

§37. Wittgenstein asks us to try and identify "the relation between name and thing named". W says that "you can see the sort of thing this relation consists in" when we look at language games including his 'block-slab-pillar-beam' language-game at §2. W states that the relation "may also consist, among many other things" in the mental picture that is produced when we hear the name, or "in the name's being written on the thing named or being pronounced when that thing is pointed at".

§38. W notes that the words "this" and "that" are not names, and have a different function to names. W states that names are defined "by means of the demonstrative expression"; for example "That is N". However, he notes that the words "this" and "that" are not similarly defined [e.g. by saying "This is called 'this'".]

W states that this is connected with a view of naming which he likens to "an occult process", in which the relation between name and thing named is considered to be a "queer connexion". He states that according to this view "we may indeed fancy naming to be some remarkable act of mind, as it were a baptism of an object". However, he considers this view of naming to be erroneous, as evidenced by his famous phrase from this section that "philosophical problems arise when language goes on holiday". W suggests that attempts to use the demonstrative pronouns "this" and "that" as names is the result of a specifically philosophical confusion and "doubtless only occurs in doing philosophy".

§39. W states that "one is tempted to make an objection against what is ordinarily called a name" and to insist that "a name ought really to signify a simple". This is reminiscent of the logical atomism of his Tractatus. W offers putative reasoning in support of this 'tempting' view, using the example of the sword "Excalibur". He states that the sentence "Excalibur has a sharp blade" makes sense whether or not the sword is whole or broken into parts, but that if the sword is broken into parts then the name "Excalibur" has no referent. Since the sentence about its sharp blade makes sense, then "there must always be something corresponding to the words of which it consists". W says that therefore "the word "Excalibur" must disappear when the sense is analysed and its place be taken by words which name simples".

Just to remind you, at this point in the text there is nothing to indicate that meaning could be private, or "public" (whatever "public" might mean in this context). These terms do not seem to relate. — Metaphysician Undercover

I don't have much time, but I was asked for my opinion of Terrapin's Station's previous post, so I was not speaking to the text there

There clearly is judgement referred to, on the part of the hearer. The hearer must judge the act of the giver, "he pointed to the shape", or "he pointed to the colour", which transposes into "he meant the shape", or "he meant the colour". However, what I was referring to was the need to expose the reciprocal judgement from the giver, "you judged my pointing correctly", "you judged my pointing incorrectly". This reciprocal judgement is not brought out by Wittgenstein, at this point, though you referred to it "...understanding a definition is usually judged by how the hearer goes on to use the word...". — Metaphysician Undercover

Right, I broadly agree with this.

What I interpret as important with this discussion of "characteristic experiences", is the qualification of "not always". — Metaphysician Undercover

Yes, I agree. I should maybe have put more emphasis on this. However, I see 35 and 36 as being a continuation of 33 and 34 and that I mostly covered what's there in my remarks on 33 and 34.

I don't at all believe that meaning is public. It's not at all possible to make meaning public in my view. Meaning isn't the same thing as a definition.

Re the writing thing, I wasn't proposing a definition. — Terrapin Station

Okay.

What do you think of Terrapin Station's reply to me? — Sam26

Terrapin appears to want to have it both ways, appearing to say that meaning can be private even if it's also public. I'm not convinced.

Terrapin speaks of meaning as being "the result of one's private mental happenings". Clearly, there have been individuals who have coined words which are now common in our language, but more is required than just one person making up a word in order for it to gain acceptance and usage in a linguistic community. For example, there is also the linguistic community and whether they adopt the word's usage. Furthermore, there is nothing which compels a linguistic community to preserve the original meaning of a word and use it the same way as the coiner.

On Terrapin's last comment, 'writing' is also a common word of our language which is usually defined more narrowly than simply applying ink to paper. Otherwise, da Vinci's Vitruvian Man would also be considered as writing rather than a drawing.

This is an interesting development. You have used the word "judged' here, and Witty makes no such mention. You seem to be anticipating what will follow in the text. However, do you think that understanding a definition requires being judged as understanding? — Metaphysician Undercover

Yes. Also, I believe that Wittgenstein alludes to judging in section 35 that follows, when he says that it depends "on the circumstances — that is, on what happened before and after the pointing — whether we should say "He pointed to the shape and not to the colour"." [my bolding]

Couldn't one understand the definition, and go away with that understanding, without ever being judged as having understood? — Metaphysician Undercover

Perhaps, but how does one know that one has actually understood unless one tests/demonstrates that understanding? For example, I believe that I have some understanding of the current text, but we'll see...

§35. Wittgenstein continues to discuss what he calls "characteristic experiences" or what I have called "accompanying experiences", which are had in conjunction with pointing or 'attending to' (e.g.) the shape. Wittgenstein offers the example of "following the outline with one's finger or with one's eyes as one points." However, he notes that characteristic experiences do not accompany pointing in every case, but even if they did, it would still depend on what happens before and after the pointing for "whether we should say "He pointed to the shape and not to the colour"."

Wittgenstein notes that characteristic experiences are characteristic "because they recur often (but not always) when shape or number are 'meant'." Wittgenstein notes that there is no characteristic experience which accompanies pointing to a piece in a game as a game piece. Nonetheless, one can still mean that this game piece is called the king, rather than (e.g.) this piece of wood is called the king.

Wittgenstein ends the section with "(Recognizing, wishing, remembering, etc. .)", possibly indicating that characteristic experiences are similarly associated with these activities but, again, not necessarily.

I agree with the first part of this, but the last half raises questions. What could understanding what it means to play chess, be, other than specific behaviors associated within the social context of the game? Are you talking about private behavior? I agree that it depends on the wider social context, but aren't these wider social contexts or surroundings "accompanying behaviors?" — Sam26

I was probably unclear. I was referring to the behaviours which accompany attending to the shape or attending to the colour during the giving/hearing of an ostensive definition. For example, the behaviour of following the perimeter of a shape with one's eyes. As Wittgenstein makes more clear in 34, it is what one subsequently goes on to do with the word in the definition, or how one (later) reacts to the word, which demonstrate one's understanding of the definition. In short, the experiences and behaviours one has during the giving/hearing of the definition do not forge a magical connection between word meaning and object feature.

Otherwise, what do you make of his statement that "a move in chess doesn't consist simply in moving a piece in such-and-such a way on the board"?

Fair enough, I hope you might be able to convince me of your view.

Thanks for the acknowledgement, Sam, which has encouraged me to write some more and provide my own reading of §33 and §34 below. I hope some might find it useful.

§33 Wittgenstein asserts that "you must already be a master of a language to understand an ostensive definition". However, he anticipates the objection that in order to understand an ostensive definition you only need to know or guess what the person giving the explanation is pointing to, e.g., to its shape, colour or number. Wittgenstein invites us to point to a piece of paper, and now to point to it's shape, it's colour, its number, etc. Presumably the physical act of pointing remained the same throughout, so what changed when you "pointed" at these different features of the piece of paper? Wittgenstein anticipates the response that "you 'meant' a different thing each time you pointed", by concentrating your attention on one feature instead of another. But how is the person to whom the explanation is being given supposed to differentiate when you are pointing at one feature instead of another, if the only change in the "pointing" is your (private, mental) concentration of attention.

Wittgenstein then considers whether you always do the same thing, or always have the same accompanying behaviours, when you direct your attention to (e.g.) the colour of an object. After inviting the reader to consider different cases of attending to the colour, he notes that there can be many different behaviours associated with attending to the colour, and that these behaviours occur in conjunction with attending to the colour, but that it is not the behaviours alone which "make us say someone is attending to the shape, the colour, and so on".

Wittgenstein offers the following analogy: "Just as a move in chess doesn't consist simply in moving a piece in such-and-such a way on the board — nor yet in one's thoughts and feelings as one makes the move: but in the circumstances that we call "playing a game of chess", "solving a chess problem", and so on."

On my reading, Wittgenstein indicates that understanding an (ostensive) definition is not something which happens only in the mind of the listener or student, and neither is it something which is only tied to a specific set of accompanying behaviours; rather, it depends on the wider circumstances surrounding the language game.

§34. Wittgenstein asks us to imagine someone who always has the same feelings and behaviours whenever they attend to the shape [of an object]. He further asks us to imagine that this person is giving someone else the ostensive definition of a circle by pointing to a circle and saying "That is a circle". Wittgenstein says that "his hearer" could still interpret this definition differently even if he "sees the other's eyes following the outline, and even though he feels what the other feels". Wittgenstein continues: "That is to say: this 'interpretation' may also consist in how he now makes use of the word; in what he points to, for example, when told: "Point to a circle".

Wittgenstein is again trying to loosen the reader's grip on the view that understanding a definition has anything to do with one's feelings and/or accompanying behaviours while attending to an object, or while giving/hearing the definition. Instead, he indicates that understanding the definition is more about how the hearer "now makes use of the word" and in what he points to when asked to point to a circle.

Even if the hearer and the speaker share identical feelings and behaviours while attending to the object or while giving/hearing the definition, the hearer could still 'interpret' the definition differently. (Also note Wittgenstein's use of scare quotes on 'interpretation' here, indicating that there may actually be no interpretation involved.)

Wittgenstein concludes that: "neither the expression "to intend the definition in such and-such a way" nor the expression "to interpret the definition in such-and-such a way" stands for a process which accompanies the giving and hearing of the definition." Again, understanding a definition is usually judged by how the hearer goes on to use the word and react to the word's use. It usually has little to do with a speaker's intention or a hearer's interpretation.

My only other comment on this section is that I'm a bit baffled by this:"One can also imagine someone's having learnt the game without ever learning or formulating rules." If we're talking about chess a la anything like what conventionally counts as knowing chess, I don't think Wittgenstein's claim there makes any sense. — Terrapin Station

He only suggests that one can imagine it, but even if you can't imagine it, it's a minor detail. The point of this section is in relation to use of the phrase "This is the king". This phrase might be used when explaining to someone who otherwise knows all the rules, or who otherwise knows how to play chess (e.g. only via mimicking the behaviours of others), which piece or shape represents the king. "This is the king" might also be used in the case of teaching someone how to play chess, but Wittgenstein stresses that this is possible only:

if the learner already 'knows what a piece in a game is'. That is, if he has already played other games, or has watched other people playing 'and understood'—and similar things. Further, only under these conditions will he be able to ask relevantly in the course of learning the game: "What do you call this?"—that is, this piece in a game.
We may say: only someone who already knows how to do something with it can significantly ask a name.

This section (31) relates back to his previous remarks on ostensive definition, and also leads into his brilliant summary at section 32 of the problem he has identified in Augustine's description of learning "human language": Augustine describes it "as if the child...already had a language only not this one". Wittgenstein spells out his position in section 33: "you must already be master of a language in order to understand an ostensive definition".

This leads him into a defence of this claim and an attack on the anticipated argument/assumption that ostension (i.e. pointing or "attending to") is only mental, intentional, or even spiritual.

I agree that it may be difficult to imagine someone knowing how to play chess without having learnt the rules of chess, but consider that children learn how to speak before they learn any rules of language, by mimicking the behaviours of others. Also, bear in mind that Wittgenstein is attacking certain prevalent philosophical assumptions of his time, including those of his Tractatus, that language is exclusively a private, mental phenomenon. He is trying to remind us that language is instead (or also?) a shared, public, cultural and behavioural phenomenon.

I beg your pardon, admin?

If you are referring to my account of your argument, then:

P1. Any account of mathematics would need to explain why mathematics is the way it is.
P2. Mathematical Platonism is the view that there is a world M, that contains all possible mathematical objects and truths.
P3. Mathematics is but "an infinitesimal subset" of any such mathematical reality.
P4. Any account of mathematics would need to explain why P3 is the case, in order to satisfy P1.
P5. Mathematical Platonism has no way to explain why P3 is the case.
C1. Mathematical Platonism cannot satisfy P1.

Ergo, Mathematical Platonism fails to have any explanatory force with respect to mathematics.

If you are referring to whether or not your argument implies our interest, it's about our mathematics. Do you claim that we have no interest in our mathematics, or (i.e.) in our infinitesimal subset of M?

What did I insert into the argument that was not there? SX's argument is that MP cannot explain why our mathematics is but "an infinitesimal subset" of M. This again implies our interest. And even if SX's argument doesn't imply this (it does), then the paper of the OP's argument explicitly refers to our interest, anwyay.

I have no motivation to defend MP as I'm not a platonist. I'm just pointing out that the author's supposed refutation fails, or at the very least it fails to convince me. Do you have a knock-down argument to refute the existence of God?

Because that's what the paper answers to, I'd assume. In the referenced work by Penrose, it is stated that: "It may be helpful if I put the case for the actual existence of the Platonic world in a different form. What I mean by this ‘existence’ is really just the objectivity of mathematical truth. Platonic existence, as I see it, refers to the existence of an objective external standard that is not dependent upon our individual opinions nor upon our particular culture".

So, math is the way it is because it can't be otherwise. There's something outside all human practice (a platonic realm where mathematical truths reside, waiting to be discovered, say), which makes math the way it is. The paper tries to refute this. — Πετροκότσυφας

I find the paper's attempted refutation to be unsuccessful.

The author says if M is too large then it is uninteresting. But what the author means to say is that if M is too large then it is mostly uninteresting to us (and perhaps also: at this point in time). Obviously, there are some parts of M that we do find interesting, because "the value is in the selection, not in the totality". The author says that M "contains too much junk", but again, as judged by us (or, alternatively, by the Jovians).

The Jovians might have a different mathematics to us and they might find different parts of M more useful than we do, but presumably we and the Jovians each borrow true theorems and objects from the same universal M. Likewise, we may have discovered how interesting linear algebra is only recently, but it could always have been a part of M, waiting there for us to use it. The same can be said of 2d and 3d (and perhaps 4d) geometry, arithmetic, set theory, logic, category theory, topos theory and whatever mathematics the Jovians might use.

The author says that if M is smaller and interesting then it is not independent. But then neither is it the M of mathematical platonism, I would argue.

The author says that the complete independence of MP "is like the idea of an Entity that created the heavens and the earth, and happens to very much resemble my grandfather."

Here I agree with the author. I think he has as much chance of refuting MP as he would have of refuting the existence of God.

Strictly speaking, according to the argument, it's invalidated because it can't account for why math is the way it is. That an account of mathematics should explain why math is the way it is, is a premise (which MP fails to satisfy). If you don't like the premise, you can reject it and offer another in its place, no? — Πετροκότσυφας

MP posits the existence of a realm of independent, abstract, mathematical objects. Why should this ontology be required to "explain why [our] math is the way it is"?

Put it this way: Why should mathematical platonism be entirely invalidated by its supposed inability to account for an infinitesimal subset of itself?

Mathematics is the way that it is because of its interest or usefulness to us, surely, so interest is still there in your P1.

I don't know. It just sounds a bit like bemoaning the fact that mathematical platonism is unable to tell us which mathematical facts are interesting to us (or "why mathematics is the way it is"), despite mathematical platonism being the view that mathematical facts exist independently of our intellectual activities.

So the argument goes:
1. Mathematical platonism is the view that mathematical reality exists by itself, independently from our own intellectual activities.
2. But what we call mathematics - containing only what is important to us - is but "an infinitesimal subset" of mathematical platonism.
3. Mathematical platonism cannot explain which mathematical facts are important to us.
4. Therefore, mathematical platonism is false.

?

To try and clarify why I remain unconvinced, consider the author's synopsis of his paper:

If there is a "platonic world" M of mathematical facts, what does M contain precisely? I observe that if M is too large, it is uninteresting, because the value is in the selection, not in the totality; if it is smaller and interesting, it is not independent from us. Both alternatives challenge mathematical platonism.

So, M is the "platonic world" of mathematical facts. The author observes that if M is too large then it is uninteresting to us, and if it is smaller and interesting then it is not independent of us.

Perhaps I fail to grasp the dilemma, but can't we just accept both the existence of a very large M and also that we are only interested in a small subset of it? I don't see why our interest in only a small subset of M - the part which we find interesting or useful - should falsify the existence or independence of the much larger M.

If we assume from the outset that M is the "platonic world" of mathematical facts - even those which are of no interest to us - then we cannot also say that M might contain only those mathematical facts that we find interesting (and therefore M is not independent from us). And only one of these resembles mathematical platonism.

I'm not sure if you meant to phrase it how you did, but that... would be a perfectly valid argument ('it is false that the tree is blue because the tree is green - and here is why'). — StreetlightX

Except I found the author to be saying that the tree is not blue, and he did not tell us why. The author appears only to assert, or to assume the truth, that Mathematical Platonism is false. He could have written a shorter paper with the assertion that 'Mathematical Platonism is false'. But I'll take another look regarding the dilemma you mention above.

I'm no expert on the subject, or even a (good) philosopher, but I tend to agree with Pneumenon here.

The author appears to argue that 'Mathematical Platonism...the view that mathematical reality exists by itself, independently from our own intellectual activities' is false, and it is false because mathematics is dependent on our own intellectual activities.

Thanks Posty, and yes, read more Wittgenstein!

Perhaps you will agree, but there's nothing (no thing) to describe.

A study of this statement (and others like it?) can be found here, although I didn't bother to read too much of it.

A possibly more esteemed opinion of the matter is available here: https://www.youtube.com/watch?v=ihuJM8wVJw4.

Who is claiming that time isn't real?

To live, perchance to sleep?

I assume he's talking about attendance records.

I understand your comparison between 'beetle' and 'soul', but, unlike the word 'beetle', the word 'soul' is the name of a thing in our language and actually does have a place in the language-game, whether you think it should or not. As a result, calling this extant use "incorrect" or "neither correct nor incorrect" is inappropriate. It may have incorrect uses (when used incorrectly), but the overall usage of the word is not incorrect as a result of whatever similarities it might appear to have with Wittgenstein's 'beetle'.

As an aside, I think that you might be defining 'soul' a little too strictly to accommodate your beetle analogy, by eliminating any observable behaviour. Google offers several synonyms for 'soul' including 'inner self' and 'inner being', but another is also 'personality', which we know has an outward expression. You said that 'soulful' has a different meaning to the one you intend, but I think your meaning can also be found in describing certain people as 'kind souls' or 'beautiful souls'; descriptions which depend on outward behaviours. Your use of 'soul' also appears restricted only to a post mortem state of the body, whereas the word can equally be used to refer to living bodies, which also fits with your earlier historical definition as that which animates the body.

You appear to consider the use of the word 'soul' as equivalent to Wittgenstein's 'beetle' because one person doesn't know what the next person has in their box (in either case). Is that a fair description of your position?

However, this completely misses the point of Wittgenstein's example. The point is not that it is problematic for us to lack knowledge of what other people have in their box, or in their personal experiences. Rather, Wittgenstein's point is that this lack of knowledge (of what is in another's box) is irrelevant to the use of the word. The thing in the box "cancels out, whatever it is."

This is why I find your specific criticism of the word 'soul' and its lack of sense and/or observable behaviours to be misguided. Christians use the word and make sense of it, so what more needs to be said?

I did say earlier that there is a correct use of the word soul — Sam26

Where did you say this?

One of the reasons it's incorrect is that there is no way to demonstrate that it's incorrect or not. That's also part of the reason the beetle example is also senseless, because there is no way for us to establish a correct or incorrect use of the word beetle. — Sam26

I don't get it. You're saying that it is incorrect because it is neither correct or incorrect?

Think of it in terms of how we learn to use the word pain, we learn based on the rules of use that happen socially, but these rules are rules that have a correction built into them (like mathematics), and it's observable. I can observe if you call someone's joyful acts, painful, that that is incorrect. Let's say that there were no outward signs of pain, would you think it had sense? Would you think it had sense if we attached a definition to it? — Sam26

We already have a word "pain" with particular uses/meanings in our language. If there were no outward signs of pain (as we normally use that word), then we could still use the word in some other way(s) by attaching a different meaning to it.

Furthermore, we learn to use the word 'soul' based on the rules of use that happen socially, and these rules are rules that have a correction built into them (like mathematics), and it [the use of the word] is observable.

so it's not that an individual can't create meaning via their own private sensations, even though that's true, it's that no person or persons can do it. — Sam26

"It's not that an individual can't do it, it's that no individual can do it"? What?

Ask yourself, what would it mean to be incorrect in this particular use of the word soul, it's a kind of self-sealing use of the word. — Sam26

"I soul my car." That is an incorrect use of the word.

Please understand that I originally only took issue with your claim that the use of the word 'soul' by Christians is incorrect on every occasion, tout court. But that's just plain wrong. And now you appear to be vacillating on whether their use is incorrect, or neither correct nor incorrect.

I say the word soul as used by many religious people, has no clear cut meaning that can be said to be correct or incorrect. — Sam26

This is different to your earlier claim, where you said that "Christians generally use the word soul incorrectly". Now you are saying that their use of the word is neither correct nor incorrect. Please clarify your position.

If all of this is true, then it follows that Wittgenstein's beetle example demonstrates that if we talk about something that is totally private, i.e., it not only has no referent, but there is no way for us to establish a rule of use that can be publicly said to be correct or incorrect. — Sam26

Wittgenstein's example has nothing to do with what "we" talk about as a community; it refers to the (mistaken) philosophical assumption that an individual can create sensation terms (or other language) solely via their own sensations. Clearly, the word 'soul' has an established communal usage by more than one person, so it is completely unlike Wittgenstein's beetle.

According to your argument, neither could we establish rules of use for the word 'private'. And you have offered no clear explanation for how we are able to agree on rules of use for the word 'unicorn'.

Moreover, they're saying that there is a something attached to the meaning of the word, viz., the thing that lives on after the body dies, so they're saying it has a referent. [...] How do we know that the thing associated with the word, is a thing at all? — Sam26

Who cares? It doesn't matter. It's only the use of the word that matters. Whether or not there is such a thing, let's agree to use the word 'soul' to mean "the thing that lives on after the body dies", okay? Oh wait, you already were. And now we can use this word correctly or incorrectly.

How is the word soul the same as other inner things that have outward expressions? There are no outward expressions of this thing. All there is, is a definition, but that's not enough to give it sense. No more than giving a definition to the beetle would give it sense. — Sam26

What is enough to give it sense is a public usage, which is precisely what Wittgenstein's beetle does/can not have, in principle.

ETA: Having re-read §293, I may have confused my last response above relating to Wittgenstein's beetle with some other section of the private language argument. The main point as I mentioned earlier and throughout the current post, is that the "thing" or actual referent to which words such as "soul" or "pain" refer, is irrelevant to the language game.

"The thing in the box has no place in the language-game at all; not even as a something: for the box might even be empty.—No, one can 'divide through' by the thing in the box; it cancels out, whatever it is." [PI §293]

Well maybe I wasn't clear in that post. It's not just a lack of a referent, it's lack of any way to be subject to a rule that gives meaning to the word, or any way that we could possibly agree, or not agree, that the thing we are referring to is the same thing. — Sam26

If your concern is that we, as a community, have no way of determining that “the thing we are referring to is the same thing”, then it sounds a lot like it is just a lack of referent. You appear to be saying that a lack of referent is the reason for why we can’t be sure, or can’t find a way to agree, that we are referring to the same thing. But I thought we had already agreed that sense does not require a referent?

Christians do offer a definition of the thing they are referring too, are you suggesting that because there is a definition that that in itself is enough to give meaning to the word? — Sam26

Probably, in most cases. A definition at least offers some direction as to how a word might be used.

We could easily extend Wittgenstein's beetle example into a language-game similar to how Christians use the term soul. We could develop language-games around the use of the word beetle, would that give it sense? — Sam26

Assuming the language games are public, then of course. Meaning is use, right?
 

I think it's exactly like Witt's beetle example. How is it not? — Sam26

Because the word ‘soul’ has a very public use. The beetle example, as part of the private language argument, is designed to show that the meaning of ‘pain’ is not derived from one person’s subjective (private) sensations, but from its public use in the language game. Per Wittgenstein, “if we construe the grammar of the expression of sensation on the model of 'object and designation,’ the object drops out of consideration as irrelevant."

Finally, why would you say that it's inappropriate to say that an entire community is using a word incorrectly? Communities of philosophers and theologians do it all the time. Wittgenstein railed against philosophers for doing this. — Sam26

Which word(s) did Wittgenstein rail against philosophers for using incorrectly?

Even for obsolete scientific terms like ‘ether’ or ‘phlogiston’, I don’t think you would call the users of those words incorrect in their use of those terms, despite the fact that later science found that those words did not actually refer to what it was presumed they did. The obsolete terms had those meanings to those scientists and were used accordingly (and correctly at the time). Even now people (e.g. students) can use those words correctly or incorrectly.

If you trace the use of the word soul, and the way it's been used historically (outside of religion), it refers to the animation of the living body; and the animation of a body doesn't necessarily mean that there's something that survives the death of the body.

Am I saying there is nothing that survives death, no, I'm just saying that the use of the word soul in the Christian context has no sense. — Sam26

I can only see a contradiction in you saying that the word has no sense, and that it refers to the animation of the living body. You appear to be saying that the word both has and does not have a meaning.

The animation of a body might not “necessarily mean that there's something that survives the death of the body,” but that doesn’t necessarily mean that Christians are using the word ‘soul’ incorrectly. You may not believe that the soul survives the body, but this personal view is irrelevant to the meaning of the word or its use by Christians.

I don't have much time to respond, but would you say your criticism regarding the word 'soul' equally applies to words like 'unicorn' or 'if'? Are we all using these words incorrectly? What makes the word 'soul' any different?