The obvious example of a potential misreading is Kripke, Wittgenstein on Rules and Private Language.

Is the "Quus" argument an explanation of Wittgenstein's thinking, or a derivation from it? But more, can such a distinction, between understanding Wittgenstein and extending him, be made?

The supposition here is that there is a something that is the real meaning of Wittgenstein's work, that we might try to understand.

But is that right?

And of course, the answer we give for Witti applies to any other philosophical text. The question is not what did Plato really mean, but does it make any sense to talk of his work as having only one meaning?

Bingo!

In a regulative sense I think it makes sense to talk of the real meaning -- at least somewhat historically grounded, roughly responding to this or that idea -- but then as you try to find the real meaning, so as to say "yes, this is it, for these reasons", especially with the usual philosophical texts which attract us: it is fairly judged as a multiplicity.

The only way forward is to write for an imagined kindred spirit, which will have the secondary effect of alienating a wider audience. — Joshs

An interesting thing about Wittgenstein is that he has always attracted an audience and that audience over time has been quite diverse.

There are various reasons why an author might be or seem to be deliberately obscure. But there is a difference between an obscure writing style and deliberately hiding something.

The supposition here is that there is a something that is the real meaning of Wittgenstein's work, that we might try to understand. — Banno

When Wittgenstein says, as quoted above, that he has been frequently misunderstood, it is clear that there is something that he means, otherwise there could be no misunderstanding. We may never be able to establish a definitive interpretation, but that does not mean we should not attempt to determine what it is he means.

I do not regard interpretation as merely a way of determining what someone else is thinking but as a way of thinking. As Wittgenstein says in the preface to PI:

I should not like my writing to spare other people the trouble of thinking.

And in Culture and Value:

No one can think a thought for me in the way that no one can don my hat for me.

For Wittgenstein philosophy is an activity not a theory or doctrine or set of principles that we must find the meaning of.

Work on philosophy -- like work in architecture in many respects -- is really more work on oneself. On one's own interpretation. On how one sees things. (And what one expects of them.) (Culture and Value)

Thanks. My question was about the sense in which a domain, such as the domain of natural numbers, is real, but not phenomenally existent. I notice that nowadays it is commonplace to say of anything considered real that it must be 'out there somewhere' - but even though such a domain is not anywhere, it is nevertheless real. See this passage. — Wayfarer

From your link:

Cunningham had unwittingly re-ignited a very ancient and unresolved debate in the philosophy of science. What, exactly, is math? Is it invented, or discovered? And are the things that mathematicians work with—numbers, algebraic equations, geometry, theorems and so on—real?

It may be ancient and unsolved, but that doesn't mean it holds the interests of those involved. What appeals to most mathematicians is the exploration and creation (or discovery) of new ideas - new theory. I was a rock climber for over half a century and what compelled me in both math and climbing was finding out what lies around the bend or over the overhang, whether it's creating or discovery - an argument that few in the profession care diddly about - and this seems to be a major difference between what is being said about philosophy in this thread and what is true of mathematics, save for those few in math foundations: Philosophy is concerned with what was said or printed or argued in the past, whereas mathematics (with the exceptions of a few math historians) always looks toward the future, even when analyzing the present lay of the mathematical landscape.

From "what is new is the exception" to "what is new is the rule".

Foundations and set theory, overlapping philosophy and mathematics, are out of my bailiwick. :cool:

It may be ancient and unsolved, but that doesn't mean it holds the interests of those involved..... Philosophy is concerned with what was said or printed or argued in the past — jgill

Not in my view, obviously, but I won't try and persuade you.

Work on philosophy -- like work in architecture in many respects -- is really more work on oneself. On one's own interpretation. On how one sees things. (And what one expects of them.) (Culture and Value)

:100:

Philosophy is concerned with what was said or printed or argued in the past — jgill

Not in my view, obviously, but I won't try and persuade you — Wayfarer

Isn't that what you are talking about? The issue of the "reality" of mathematical objects. Over two millennia have passed with no consensus. When we speak of Platonism isn't that something from ancient times?

However, quantum theory may ultimately bring some clarity as physicists explore the mysteries between mathematical entities and physical reality. Where in a process does actualization occur? Virtual particles appear to be Platonic rather than physically real - they cannot be observed and yet they are convenient in certain procedures. In QT is where I might expect to see progress in understanding the nature of mathematics, here is where the subject may morph into a kind of neophysical existence. Who knows?

Work on philosophy -- like work in architecture in many respects -- is really more work on oneself. On one's own interpretation. On how one sees things. (And what one expects of them.) (Culture and Value)

OK, I'm on board with that. :up: :smile:

When we speak of Platonism isn't that something from ancient times? — jgill

That is what I would describe as a jaundiced view. Platonism one of the wellsprings of Western culture which I think still maintains both relevance and vitality.

Actually I'll hark back to this discussion a couple of weeks ago which I feel ended on a reasonably harmonious note.

Over two millennia have passed with no consensus. — jgill

Jesus. No disrespect, but if this is all you could say about philosophy, then you don't fit in philosophy. People who summarize the thousands of philosophical posts in forums like this with a statement such as above, has not learned anything but cliché.

That is what I would describe as a jaundiced view — Wayfarer

I agree. It is. On rare occasions in my career when the nature of the reality of numbers and math came up amongst a group of my colleagues invariably eyes would roll and the topic would disintegrate shortly thereafter. Had I been among foundationalists reactions might have been different.

Over two millennia have passed with no consensus. — jgill

Jesus. No disrespect, but if this is all you could say about philosophy, then you don't fit in philosophy — L'éléphant

So, you are saying there has been consensus about the reality of numbers and whether math is created or discovered? I'm not addressing other aspects of Platonic philosophy.

As I've often said, I came into this debate not through mathematics, as my school mathematics experience and performance was not very good. It was because I had what I consider a minor epiphany, concerning the reality of intelligible objects. There's a profound issue lurking there, buried beneath the ruins of an abandoned culture. One that used to be our own.

There's no debate, Wayfarer. Mathematical objects are quite real for me, though not like Lake Michigan is real. But I do think it's possible that the mysteries of where math "converts" to physical reality (well, I'm grasping at straws here) in quantum theory may shed light on the subject far beyond what philosophers and mathematicians have thought to this time. That's where I see "the profound issue". :smile:

So, you are saying there has been consensus about the reality of numbers and whether math is created or discovered? — jgill

So, are you saying you did not get the gist of what I just said? Do you really need me to explain to you what I said in english? There are things you could say with depth about the subject besides "Over two millennia have passed with no consensus".

Will you be satisfied with a consensus, just to have an agreement? A population could have a consensus on something and they're still ignorant or wrong. I'd rather read philosophical writings having differing views, but well argued, than seeing a consensus for the sake of stopping all philosophical arguments.

The study of mathematics is not the same as the study of philosophy.

Well, we can agree on that, at least. But if you look at some of the remarks made by the various talking heads in that Smithsonian Institute essay about what they think is wrong with mathematical platonism , the kinds of arguments they cite say something larger about the issue:

Other scholars—especially those working in other branches of science—view Platonism with skepticism. Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago.

Platonism, as mathematician Brian Davies has put it, “has more in common with mystical religions than it does with modern science.” The fear is that if mathematicians give Plato an inch, he’ll take a mile. If the truth of mathematical statements can be confirmed just by thinking about them, then why not ethical problems, or even religious questions? Why bother with empiricism at all?

Massimo Pigliucci, a philosopher at the City University of New York, was initially attracted to Platonism—but has since come to see it as problematic. If something doesn’t have a physical existence, he asks, then what kind of existence could it possibly have? “If one ‘goes Platonic’ with math,” writes Pigliucci, empiricism “goes out the window.” (If the proof of the Pythagorean theorem exists outside of space and time, why not the “golden rule,” or even the divinity of Jesus Christ?)

Why not ‘the divinity of Jesus Christ’ indeed? I think this signifies a deep confusion about the nature of transcendentals. And I think that is because empiricism, as a philosophical attitude, has conditioned us to believe that only what is phenomenally existent, only what science can validate, ought to be considered real. So despite the fact that science in general, and physics in particular, has been so utterly reliant on mathematical reasoning for its discoveries, the philosophical framework in which it operates can’t actually accomodate the kind of insight mathematics represents - hence those declamatory statements!. And that has many vast philosophical implications.

The study of mathematics is not the same as the study of philosophy — L'éléphant

Consensus is vital to mathematics, but from what you say a hindrance to philosophy. When one argues about the reality of numbers, that is not an argument in the realm of mathematical practice. It may have great meaning for philosophers but is seen as incidental to the subject by most math professionals. On the other hand, a philosopher might have difficulty explaining philosophical implications of a theorem picked at random.

Do you really need me to explain to you what I said in english? There are things you could say with depth about the subject besides "Over two millennia have passed with no consensus". — L'éléphant

Maybe in English. And I'm sure you are correct. I suspect most of those things "said in depth" have relevance in philosophical circles rather than in mathematics communities - or anywhere else. It's good to know the limitations of one's reach. I have created and proven perhaps two hundred theorems - but they are virtually worthless, lost in millions more. All said in depth. :cool:

said in depth — jgill

No. I meant to say "with depth" -- meaning, with deeper understanding than the lack of careful thought on your part by saying over 2 millennia and no consensus. Not "in depth" where one demonstrates a comprehensive knowledge of something, such as you and the two hundred theorems you proved.

I hope I've made this clear.

but from what you say a hindrance to philosophy. — jgill

Wrong again. I did not say this. Consensus is not a hindrance to philosophy, but if this is what you think is the pièce de résistance in philosophy; then you've missed the mark by a mile.

Thanks for that link. It's nearly as good as Christmas. But I was thinking that perhaps it was time I read it again, so it is well timed.

We seem to have two quite distinct threads running through this thread. Never mind.

I get quite worried about Wittgenstein's hints that there are things hidden in the Investigations. He does the same thing in the Tractatus in that he says that we cannot speak about the really important things. But at least I understand why. It's less obvious what is going on in these bits of the Investigations.

But then I remember that I'm rarely satisfied with anything I write for longer than about five minutes and if I worry about misinterpretations I get absolutely paralyzed. If Wittgenstein felt the same way, I can understand that.

One has to accept that text (or speech) is never all that we would like it to be. Communication is always subject to noise and distortion - there's no way of escaping from that. One does one's best and that's all there is.

The issue of the "reality" of mathematical objects. Over two millennia have passed with no consensus. When we speak of Platonism isn't that something from ancient times? — jgill

As I see it is, there is really no question about the reality of thoughts, ideas, concepts and abstractions. Very few people would deny the reality of such things. The problem arises from how we talk about these things. The words we use which facilitate such communication often do not properly represent the way that we understand (or fail to understand) these things. Notice for example, I've referred to thoughts as "things". I really do not believe that thoughts are even similar to material objects which I also call "things". With talk like this, we create an environment where ambiguity and equivocation are highly probable.

So, we talk about mathematical "objects" and we also talk about physical "objects". What is implied by this talk is that there are two types of objects, one type having the properties which mathematical objects have, and the other type having the properties which physical objects have. Then we need principles to distinguish one type of object from the other type, and this is where the difficulties arise. When we try to separate two distinct types of objects we employ a reductive analysis, and they end up "converting" into each other.

What is implied by this, is that we cannot maintain a separation between two distinct types of objects. There is not any real principles to separate the two. The separation of two types of objects is not supported by reality and our attempts to create such a separation are fraught with problems because it is a fictional categorization.

Now we are left with a choice, which of the two types of "objects" provides us with a real representation of what an object is. What Plato argued, with the cave allegory, is that the intelligible objects, thoughts, ideas and abstractions, are the real objects. The supposed physical objects are really just the reflections of the true objects which are the intelligible. However, the majority of human beings, the masses, live in a world directed toward fulfilling their bodily desires. Therefore they prioritize their bodily senses, and they refuse to follow what the intellect demonstrates to them. Accordingly, they reject the guidance of "the philosopher", who has come back from his journey into the intelligible in an effort to disillusion them, returning to the cave where the others are imprisoned by their sense inclinations. They refuse to be led toward the truth.

There are various reasons why an author might be or seem to be deliberately obscure. But there is a difference between an obscure writing style and deliberately hiding something. — Fooloso4

Yes, and I think most of the authors people complain about on this site are neither deliberately nor accidentally obscure. They are trying to be as clear and comprehensible as possible in their writing , and it is the inability of many readers to grasp the originality of the ideas that is the source of the mistaken impression of obscurity. The authors are hiding something from these readers, not deliberately but as a consequence of the difficulty of the concepts.

This is true of Wittgenstein’s work. I think that it is a mistake to assume he is deliberately hiding something. Rather than contemplating the ways in which the average reader was likely to interpret him, and then proceeding to craft a style which deliberately hid ideas from them, I suggest he put all his focus into optimally communicating to an idealized kindred spirit, knowing that if he succeeded in doing that it would automatically have the effect of ‘hiding’ his thinking from those who would be inclined misunderstand it under any circumstances.

If you have a room which you do not want certain people to get into, put a lock on it for which they do not have the key.

I take putting a lock on the room that they do not have the key to to be a deliberate act.
It is not that he selects the reader but that the readers are self-selective, they are able to understand it or not. It is for the benefit of these readers who cannot that certain things are kept from them — Fooloso4

Do you think that in my scenario where his focus is entirely on an imagined kindred spirit, the way in which he composed his work would have been different than in your scenario where he not only writes revealingly for such a spirit but at the same time, in a calculated fashion, deliberately hides things from others?

Let’s take ‘On Certainty’ as an example. His main interlocutor here was G.E. Moore. Would you agree his overwhelming focus was on having Moore (and others who agree with Moore) think about certainty in a new way?
if he ‘kept things’ from some other readers, how do you imagine the work would have looked like had he put those thing back into the work? Given that , as he himself admits, he was surprised and disappointed when his earlier efforts were widely misread, do you think he even would have had the confidence to know what to hide from them? How can we choose to deliberately hide things without anticipating ahead of time what things are likely to be misunderstood? I suggest that it is only in hindsight that Witt could know what in fact ended up being ‘hidden’ from readers in specific writings of his.

“I could not help noticing that the results of my work (which I had conveyed in lectures, typescripts and discussions), were in |x| circulation, frequently misunderstood and more or less watered down or mangled.”

The above quote displays a surprised realization in hindsight that his ideas were hidden from many. I think what Witt learned from this disappointment was to no longer expect to reach more than a handful of people with his writing. This preparatory insight is, I believe, the only deliberate thought that pertains to what in hindsight turns out to have been ‘hidden’ and ‘locked’.

the inability of many readers — Joshs

This is often the case.

I think that it is a mistake to assume he is deliberately hiding something. — Joshs

Prior to talking about something hidden he does say in the forward:

The book must automatically separate those who understand it from those who do not.

and then adds:

Even the foreword is written just for those who understand the book.

If those who understand are automatically separated then why go on to talk about locked rooms? He says:

Telling someone something he does not understand is pointless, even if you add that he will not be able to understand it.

But isn't this what he is doing? Doesn't the text tell most readers that something they do not understand? And doesn't he say they will not be able to understand it?

The honorable thing to do is to put a lock on the door which will be noticed only by those who can open it, not by the rest.

I am reminded of something else he said:

A man will be imprisoned in a room with a door that’s unlocked and opens inwards, as long as it doesn’t occur to him to pull rather than push.

Perhaps in his attempt to help the philosopher escape what goes unnoticed is something quite different.

No. I meant to say "with depth" — L'éléphant

And you did. My mistake.

I really do not believe that thoughts are even similar to material objects which I also call "things". With talk like this, we create an environment where ambiguity and equivocation are highly probable — Metaphysician Undercover

Yes, and in the quantum world those distinctions could be imperiled. The problem of actualization of potentia brings science and philosophy forcefully together IMO.

When Wittgenstein says, as quoted above, that he has been frequently misunderstood, it is clear that there is something that he means, otherwise there could be no misunderstanding. — Fooloso4

So it seems. So is Kripke's argument a rendering of Wittgenstein's, or a misinterpretation which is nevertheless philosophically interesting?

Is the Quus argument what Wittgenstein had in mind, or a variation from it?

I'm suggesting that this question need not have an answer.

I don't think Kripke understood Wittgenstein. He took PI 201 and ran with it. He thought it was a new form of philosophical skepticism. In response to Kripke one might ask, given his skeptical solution, why he still maintains that there is a skeptical problem at all? If our ability to follow rules correctly and consistently is not dependent upon the application of a privately held conceptual understanding of the rule (the justified mental fact), but can be explained in terms of training and conformity to standard practice, then what remains of the skeptical problem?

The skeptical problem arises only as a result of the theory that there must be some fact which meets some particular set of conditions to which we must have access in order to justify that we are acting in accord with a consistent meaning for a particular term or rule. Far from introducing a new form of skepticism, Wittgenstein is calling to our attention the fact that in our actual practice of learning and using rules no such demand needs to be met.

Kripke intimates that Wittgenstein deliberately obscures his skeptical position that there is no fact as to whether I mean plus or quus ( On Rules and Private Language, 69-71). What Kripke fails to see is that by denying just such a fact Wittgenstein is not agreeing with the skeptic, but rather calling into question the very assumption that there is such a fact.

:up: