Wittgenstein and Scientific Realism (and the Atom Bomb)

In 2012 I gave a seminar on Wittgenstein’s later philosophy at Tel Aviv University. The following is the text of the second of two powerpoints I used as the basis for lectures in that seminar. For the other powerpoint, see the previous post. Each of these powerpoints covers material I dealt with in a number of meetings.

Scientific Realism: “Terms in a mature science typically refer and theories accepted in a mature science are typically approximately true” [I attribute this to Richard Boyd in my Meaning and the Moral Sciences (1978), 20ff]

Moreover, “ realism is the only philosophy  that doesn’t make the success of science a miracle.” [me, in Meaning and the Moral Sciences and more recently “On Not Writing Off Scientific Realism”; all references to my papers in the following are to articles now collected in Philosophy in an Age of Science]

I maintained [and still maintain in 2014!] an allegiance to scientific realism even during my internal realist period [See “From Quantum Mechanics to Ethics and Back Again”]

In chapter 4 of Reason, Truth and History, I even tried to reconcile a physicalist account of qualia like Ned Block’s with “internal realism” and with Wittgenstein by downgrading it to just one more language game.

In my Royce Lectures (Part II of The Threefold Cord: Mind, Body and World), I had given up “internal realism”, but I also gave up the idea of finding correlations between brainstates and qualia, claiming that there is no well-defined relation of identity between qualia (and hence talk of qualia is a confusion—a “Wittgensteinian” moment in my thinking. This is the publication in which the expression “not fully intelligible” made frequent occurrences. I now think both these developments were misguided - as explained in my “Wittgenstein: A Reappraisal” and “Naïve Realism and Qualia” (the latter is forthcoming in a Festschrift for Ned Block).

Where does this put me in relation to Wittgenstein?

Well, Wittgenstein’s views on the relation of science and philosophy are, to put it mildly, a mess. On the one hand, speaking as a thinker but not in his professional philosopher capacity, he had some very negative-sounding things to say about science. Here is an example:

“The truly apocalyptic view of the world is that things do not repeat themselves. It isn’t absurd, e.g., to believe that the age of science and technology is the beginning of the end for humanity; that the idea of great progress is delusion, along with the idea that the truth will ultimately be known; that there is nothing good or desirable about scientific knowledge and that mankind, in seeking it, is falling into a trap. It is by no means obvious that this is not how things are.” [emphasis added-HP]

And again:

“The hysterical fear over the atom bomb now being experienced, or at any rate expressed, by the public almost suggests that at last something really salutary has been invented. The fright at least gives the impression of a really effective bitter medicine. I can’t help thinking: if this didn’t have something good about it the philistines wouldn’t be making an outcry. But perhaps this too is a childish idea. Because really all I can mean is that the bomb offers a prospect of the end, the destruction, of an evil, our disgusting soapy water science.”

On the other hand, in the Tractatus period, he said both that “what can be said” (i.e. all that is cognitively meaningful) is “propositions of natural science”—what has “nothing to do with philosophy”­—and “We feel that even if all possible scientific questions be answered, the problems of life have still not been touched at all.” (Tractatus 6.52) Of course, even this limited privileging of science (even if it doesn’t “touch the problems of life”) disappears in the later philosophy,
In any case, I believe that we can be sure of two things:
First, that the idea that science can resolve or help to resolve any philosophical problem was anathema to Wittgenstein his whole life long.  Recall, for example, PI 109:

109.

It was true to say that our considerations could not be scientific ones. It was not of any possible interest to us to find out empirically that, contrary to our preconceived ideas, it is possible to think such-and-such -- whatever that may mean. (The conception of thought as a gaseous medium.) And we may not advance any kind of theory. There must not be anything hypothetical in our considerations. We must do away with all explanation, and description alone must take its place. And this description gets its light, that is to say its purpose, from the philosophical problems. These are, of course, not empirical problems, they are solved, rather, by looking into the workings of our language, and that in such a way as to make us recognize those workings: in despite of an urge to misunderstand them. The problems are solved, not by giving new information, but by arranging what we have always known. Philosophy is a battle against the bewitchment of our intelligence by means of language.

Second, Wittgenstein would have detested the idea (which I defended at our last meeting) that psychology cum neuroscience can show that talk of qualia does make sense. I believe that the “manometer” passage has that idea as its target.
Here is the passage:

270.

Let us now imagine a use for the entry of the sign "S" in my diary. I discover that whenever I have a particular sensation a manometer shows that my blood -- pressure rises. So I shall be able to say that my blood -- pressure is rising without using any apparatus. This is a useful result. And now it seems quite indifferent whether I have recognized the sensation right or not. Let us suppose I regularly identify it wrong, it does not matter in the least. And that alone shows he turned a knob which looked as if it could be used to turn on some part of the machine; but it was a mere ornament, not connected with the mechanism at all.) And what is our reason for calling "S" the name of a sensation here? Perhaps the kind of way this sign is employed in this language-game. -- And why a "particular sensation," that is, the same one every time? Well, aren't we supposing that we write "S" every time?

I believe that what Wittgenstein would say about the suggestion that discovering the sort of brain processes (in the “work space”, etc., of the brain), and discovering whatever connections you please between those processes and our behavior, reports, etc., would show nothing about Block’s so-called “qualia”. [I assigned Ned Block, “Consciousness, Accessibility, and the Mesh Between Psychology and Neuroscience,” Behavioral and Brain Sciences, 30, (2007), pp. 481-548 in the seminar.]

He would say that the subject  may decide to say that she is having “the same sensation” (in the “qualia sense”) whenever the neuroscientists tell her that a certain process is taking place in her brain, but this is like Wittgenstein’s privateer saying she is have the same sensation whenever the manometer rises. This is just a new (and philosophically irrelevant) language game. And the idea that brain processes may be constitutive of qualia, whereas we know that increases in blood pressure are not, would be dismissed by W. as “language on holiday”.  Of course Block and I don’t think language is on holiday here at all.
Sadly, I am led to conclude that one cannot buy into Wittgenstein’s picture of how philosophy should be done and into scientific realism at the same time. And  I find scientific realism much more persuasive, myself.

A Power Point From a Lecture on Wittgenstein and Rule-Following

In 2012 I gave a seminar on Wittgenstein’s later philosophy at Tel Aviv University. The following is the text of one of two powerpoints I used as the basis for lectures in that seminar (the other powerpoint will be the next post). I am interrupting the flow of this series of posts, but the second of the two powerpoints  - the one I will post next week – talks about qualia, a notion that will come up in future posts on colors and their “looks”.

RULE-FOLLOWING

IN WITTGENSTEIN, KRIPKE, AND MYSELF

Wittgenstein in Philosophical Investigations §195 (re continuing a series, e.g. 2,4,6,8,…..1000, 1002, 1004,….)

“But I don’t mean that what I do now (in grasping a sense)

determines the future use causally and as a matter of experience, but that in a queer way, the use itself is in some sense present.”

I KNOW I AM NOTORIOUS FOR “CHANGING MY MIND”

  Well, upon thinking over what I said about Wittgenstein’s Rule Following argument last week in this seminar left me feeling dissatisfied, and so once again I shall revise my view! So here we go.

Wittgenstein thinks that philosophical problems are only illusions of problems,

 but until we work our way out of the bewitchment, they genuinely do puzzle us. So it will not beg any questions if I speak of a “rule following puzzle”, rather than a “rule-following problem”. Whether it is in the end a real problem or a pseudo-problem, there is a puzzle that Kripke genuinely worries about, and that Wittgenstein responds to in some way

I proposed a response to the puzzle on Wittgenstein’s behalf, which I now think is not Wittgenstein’s, and at the same time I followed Wittgenstein in dismissing the sort of puzzlement Kripke exemplifies as misguided. But it should have been clear to me from my own published criticisms of Wittgenstein’s philosophy of mathematics* that there is a problem with Wittgenstein’s dismissive response.

*For example, “On Wittgenstein’s Philosophy of Mathematics” and “Wittgenstein and the Real Numbers” [collected in Philosophy in an Age of Science, Harvard 2012.]

I shall state the puzzle in my own words, and then present three responses to it.


THE PUZZZLE:

The puzzle is this: when we grasp a rule for generating, say, the decimal expansion of pi, the rule determines what the nth digit of pi is no matter how large n is—for example, it determines whether the trillionth digit is 0,1,2,3,4,5,6,7,8 or 9.

Now, following a rule may not be a scientific concept, as Wittgenstein stresses but, grasping a rule is a mental state in an ordinary sense of “mental state”, and the puzzle is how creatures like us can have mental states that determine such a large number of cases.

3 Responses

I shall present three responses to the puzzle: Kripke’s, Wittgenstein’s, and mine (which I will not call an “interpretation” of Wittgenstein any longer).

Kripke’s response to the puzzle: three parts


Part I: Kripke’s Wittgenstein interpretation (Wittgenstein=Kripgenstein)

Part II: Kripgenstein’s Solution to the Puzzle:

Part III: Kripke’s own view

Part I: Kripke’s Wittgenstein interpretation

(Wittgenstein=Kripgenstein)

According to Kripgenstein, calling a judgment true is simply endorsing that judgment, i.e., “true” is, as Rorty once put it a “compliment that we pay” to judgments we agree with.

Very close to relativism

If people disagree, you can say that one of them is right and the other is wrong, but if you do so you are simply endorsing what one of them says and rejecting what the other says.

According to Kripgenstein

  There is no fact of the matter about anyone “considered in isolation” as to what they she means by the formula for, e.g., calculating the decimal expansion of pi. If someone is able to use the formula well enough (which does not mean she never makes a mistake)—that is, well enough so that others say she understands it as they do, then that counts as her understanding it as they do.

A consequence Kripke does not stress

if the whole community is unable to compute the trillionth decimal place of pi, then there is no fact about the community as a whole which is the fact that the meaning of the formula is such that a certain digit is the one in the trillionth decimal place

Part II: Kripgenstein’s Solution to the Puzzle:


1.      The puzzle assumes that the formula “determines whether the trillionth digit is 0,1,2,3,4,5,6,7,8 or 9.”  But if the community cannot use the formula to determine the trillionth digit, then the way formula is understood does not determine it either.

Apart from the Rortyan relativism about truth

This, I think, is what Wittgenstein thought, and it agrees with the remark in Remarks on the Foundations of Mathematics that “even God’s omniscience” cannot determine anything about the decimal expansion of pi that human cannot determine as well as with the emphasis in PI on the claim that the criterion for understanding is how the speaker applies the formula

Part III: Kripke’s own view


“I can only report that in spite of Wittgenstein’s assurances, the ‘primitive’ interpretation [‘that looks for something in my present mental state to differentiate between my meaning addition or quaddition’] often sounds rather good to me.” [Kripke, Wittgenstein on Rules and Private Language, p. 67.”

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Wittgenstein’s response to the puzzle: two parts

 Part I: Wittgenstein’s “deflationary” attitude to the rule-following puzzle

 Part II: Wittgenstein’s verificationist attitude to mathematical truth

Part I: Wittgenstein’s “deflationary” attitude to the rule-following puzzle

     Following a rule has a normative element. 

   Equally important for our purposes, it implies that a regularity is present;

  

The normative element

if one says that someone followed a rule, one generally means that they followed it correctly; that’s one of the reasons that “he followed the rule for computing the decimal expansion of pi” is not a description of the presence of a mechanism.

The need for regularities

Saying that someone followed a rule implies that a regularity is present. Moreover, the notion “regularity” is not mysterious, I can teach it to someone by means of examples and corrections. [Philosophical Investigations §207]

Even if which sequences of events are “uniform” or exhibit “regularities” is an “anthropocentric” matter, that doesn’t mean that the difference between a regularity (“All emeralds are green”) and a sequence that is not a regularity (“All emeralds are grue”) isn’t a real difference.

[Added for this post: I explained to the seminar that I called this a "deflationary" - as opposed to metaphysically inflated - remark about rule-following, because there is no implication that 'regularities' can extend beyond our ability to recognize them as such]

Part II: Wittgenstein’s verificationist attitude to mathematical truth 


Suppose that people go on and on calculating the expansion of p. So God, who knows everything, knows whether they will have reached '777' by the end of the world. But can his omniscience decide whether they would have reached it after the end of the world? It cannot. I want to say: Even God can determine something mathematical only by mathematics. Even for him the rule of expansion cannot decide anything that it does not decide for us."

[Remarks on the Foundations of Mathematics,V, §34]

In Kripke’s terminology

—In Kripke’s terminology, this says that if the whole community is unable to compute far enough to find 777 in the decimal expansion of pi  or to find a proof that this sequence does not occur in the decimal expansion of pi, then there is no fact about the community as a whole—not just about any one person “considered in isolation” which is the fact that the meaning of the formula is such that 777 does (respectively, does not) occur in that decimal expansion.

Wittgenstein’s response (concluded)

In short, the answer to the “puzzle” is that we don’t have the power to determine the answer in such a large number of cases.

My own view: three parts

Part I: My former interpretation of Wittgenstein

Part II: why I now reject my former interpretation

Part III: My response to the puzzle

Part I: My former interpretation of Wittgenstein


 (in last week’s meeting of the seminar) consisted of the “deflationary reading” of the rule-following discussion plus a “quietist” response to our puzzle, that is, one which denies that there is an intelligible question as whether our grasp of the formula “determines the answer in an infinite [or, alternatively, an enormously large finite] class of cases”.

plus royalistes que le roi

. I now think this response, while Wittgensteinian in spirit, was actually more “Wittgensteinian” that Wittgenstein himself. (“More royalist than the king”, as the French saying goes.)

I distinguished two senses of “determine”

a mathematical sense of “determine” in which it is simply a theorem of mathematics that the algorithm for continuing such series “determines” all the infinitely many members, and an ordinary sense of “determine”, in which it is plainly false that our understanding of the rule “determines” the series so that we can continue it to, say, a trillion places.

It is a theorem of mathematics that the digit in the trillionth decimal place =1, or =2. or =3, or =4, or =5, or =6, or =7, or =8, or =9,

and so this is something we can say. But to ask: but is a particular member of this disjunction the correct one is to attempt to step outside of mathematics, and this “stepping outside” of what we ordinarily say (in this case, say when doing mathematics, as oppose to philosophizing about it) leads to nonsense. Thus the “puzzle” depends on an unintelligible use of “determine”.

Part II: why I now reject my former interpretation

The “quietist” part of my former interpretation amounted to the claim that Wittgenstein would have rejected the question: “Is there is a fact of the matter as to whether the trillionth digit of pi =1, or =2. or =3, or =4, or =5, or =6, or =7, or =8, or =9 [assuming we are unable to find a mathematical answer to the question, even if we try “until the end of the world]. I gave two arguments for this neither of which seems good to me after my rethinking last weekend.

The first argument was that the question assumes that every true judgment must have an “object” which makes it true, e.g. in the case of the judgment “There is nothing red in this room” the “negative” fact” of the absence of red things in the room, and we know from lectures Wittgenstein gave that he rejected this picture—the picture on which this judgment “corresponds” to something.

 But in Remarks on the Foundations of Mathematics, Part V, §34,

Wittgenstein does manage to make sense of the question whether there is a fact of the matter as to whether 777 occurs in the decimal expansion of pi* even if human beings cannot find a mathematical proof one way or the other, by asking whether an omniscient being could know the answer.

* [by the way, it does!]

Saying that even a being who knows everything could not know this clearly implies that there is nothing of this sort to know. The question as to whether every mathematical question actually has a determinate answer was not one that Wittgenstein dismissed as nonsense.

My second argument

My second argument was that it was illegitimate of Kripke to bring in  Remarks on the Foundations of Mathematics in interpreting PI, and that PI is much less extreme on the decimal-expansion-of-pi question than RFM.

But if we don’t bring in Wittgenstein’s philosophy of mathematics,

no reason has been given for rejecting the puzzle as nonsense except the question-begging reason that “if it can’t be asked in ordinary language, it doesn’t make sense.” Evidently Wittgenstein didn’t think that asking whether an omniscient being could know the answer to the question about pi violated ordinary language. (And that violations of ordinary language are what is at stake plunges us into the morass of Baker&Hacker vs. “New Wittgenstein”.)

let us look at the passage in question from PI itself (§516):

 It seems clear that we understand the meaning of the question: 'Does the sequence 7777 [note that the example is slightly different] occur in the development of pi?' It is an English sentence; it can be shown what it means for 415 to occur in the development of pi; and similar things. Well. our understanding of that question reaches just so far, one may say, as such explanations reach.

It is true that

this does not say that there is no fact to be known at to whether 7777 does or does not occur in the decimal expansion of pi; but it is not far away.

No real change in Wittgenstein’s position

The fact that “we know what it means for 415 to occur in the decimal expansion of pi” [=3..14159…] only shows that we can recognize a calculation showing that a particular sequence of digits does occur. But if our “understanding of the question” does not reach farther than our ability to recognize mathematical proofs does, then we have the same picture as in RFM V, §34.

PUTNAM

Part I: My former interpretation of Wittgenstein

Part II: why I now reject my former interpretation

Part III: My response to the puzzle

Part III: My own response to the puzzle


My own response to the puzzle depends on my scientific realism, and goes beyond this seminar to defend it here. [I will post an optional reading about it; part of the position is the criticism of Wittgenstein’s mathematical “verificationism” as presupposing verificationism with respect to physical science (which is widely recognized to be untenable)] 
[Added for this post: The additional reading is ch. 25 of my Philosophy in an Age of Science]

Assuming scientific realism,

Just as we understand what a “regularity” is, even though we can’t explain how to distinguish between regularities and non-regularities except by teaching someone the practice of doing so, we also grasp the fact that a rule determines cases beyond what we can practically calculate, by seeing how that fact ties in with our practice in doing cosmology, atomic physics, etc.

Am I not saying that I don’t know “how creatures like us can have mental states that determine such large numbers of cases”? Well, I don’t know how young children can grasp the idea that there are infinitely many natural numbers, but pace Wittgenstein, many of them do!