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Measuring Belief | "Absolute Certainty"

These are "logic of language" questions, and sometimes replies. The expression 'logic of language' comes from Wittgenstein, but in my jargon it means: a way of distinguishing between sense (language with meaning) and nonsense (language without meaning) in the context of philosophy. Wittgenstein's way is set by the meaning of 'meaning' he chose for his later work.

Topics on this page ...

Common names and non-answers. Frank Ramsey and measuring belief. Absolute certainty. Wittgenstein, Malcolm and 'national character'. Socrates, freedom, injustice and the rule of law.

Wittgenstein's criticism of Socratic Logic

Query: why Socratic logic is damaging.

But the philosophical question is not "Why is it damaging?" but instead "Is it damaging?" because in philosophy the conclusion comes at the end not at the beginning of the investigation. (The word 'logic' as used by Socrates and in Wittgenstein's later work.)

The requirements (PI § 107) Socrates sets for language meaning, as found in Plato's early dialogs and according to Aristotle: (1) a common name names the common nature of the thing it names -- the common nature is the name's meaning; and (2) if we cannot say what common nature a common name names, we do not know the name's meaning (namely, the essential nature of the thing the word names). (This is the basis of Plato's early theory of Forms.)

The idea that in order to get clear about the meaning of a general term one had to find the common element in all its applications has shackled philosophical investigation; for it has not only led to no result, but also made the philosopher dismiss as irrelevant the concrete cases, which alone could have helped him to understand the usage of the general term. (BB p. 19-20)

Socrates' picture of how our language works, of what gives it meaning, does "wound the human understanding" (Kant) -- whether it is used (1) as a definition of the word 'meaning' (because if we look we very seldom find common natures, and therefore most common names are "meaningless"), or (2) as a "theory of meaning" in the context of concept-formation (as if to say: it must be that if we have these concepts -- i.e. if our language has these common names -- they are dictated to us by nature's reality. That is metaphysical speculation about the origin of language, about what "must be" despite what "appears to be"), giving birth to the "theory of abstraction", a theory that makes language meaning something hidden ("I know even though I cannot say"), and thus the irresolvable unclarity of philosophical discussions: "If I say that a sentence has meaning for me, no one has the right to say it is senseless", because if meaning is not objective, what could give anyone that right?

The Socratic definition of the word 'meaning' contrasts sharply with the definition of the word 'meaning' that Wittgenstein used (cf. the distinction between nature and convention: Socrates asks about nature, which is natural in the context of his view of ethics): Wittgenstein asks simply for the conventions (rules) for using the words of our language, conventions that are public and therefore objective (Thus language meaning in Wittgenstein's definition of 'meaning' is objective).

But is Wittgenstein's logic, specifically his account of the meaning of common names, any less damaging to philosophy? Because (1) it does not answer the Platonic question of why we have the concepts (common names) we have (Is there any compelling reason to classify badminton, cribbage and fetch together as games?), much less the Socratic search for an absolute standard in ethics (Plato, Euthyphro 6d-7d).

Since Wittgenstein does not show that either Socrates or Plato is talking nonsense, it seems that all Wittgenstein's account of common names does is to side-step these questions in logic, metaphysics and ethics. He simply tells philosophers to stop asking them, since in any case philosophy cannot answer them (Metaphysical speculation is not an answer).

On Absolute Certainty

It seems there are things we know with complete certainty (for which we can use the expression 'absolute certainty' if we like), that is, unless we've all gone mad, including the one who writes these words, which is, as we normally use the word 'madness', nonsense [if everyone is mad, then no one is mad; antithesis and meaning], despite its being logically possible if we introduce a god who can see what we cannot see. However, within our normal frame of reference -- i.e. the human frame of reference -- it is nonsense to say that everyone is mad.

We know with certainty (or "absolute certainty") that it is a rule of arithmetic that 1 + 1 = 2 [Note: the rule that 1 + 1 = 2, not "the reality" that 1 + 1 = 2 (whatever, if anything, it might mean to know that)]. Although I as an individual can be mistaken about that, just as I can be mistaken about what my own name is and about where I live and which language I speak, if I have gone mad, that is, or suffered some illness. However, in the normal case I know that 1 + 1 = 2 is a mathematical rule with certainty; there is no possible doubt about it -- even though a doubt is logically possible if we introduce a god who sees what we do not see, or if I were able to step outside myself and see [with the eyes of that god] that I have gone mad.

However, within my frame of reference -- the shared-in-common human frame of reference (if there is such a Kantian-like thing) -- I know such things with certainty, and not with "the highest certainty", but with complete certainty.

Or I should say 'we know' rather than 'I know' because I make these statement within a "community of ideas", and further, because belief belongs to the individual, but knowledge belongs to the community, to its way of life. (Remember that the word 'knowledge' is a tool belonging to a particular community of language users.)

Look at the word 'certainty' as a tool we use to accomplish some work or other (PI §§ 421, 360; cf. the word 'know') -- and not as an existential boast about what we (whether I, or G.E. Moore, or anyone else) "really know".

Measuring the Degree or Strength of a Belief

I remember one characteristic example (like Wittgenstein's strange tribes) when he told the class, 'There's a lion on the landing' and had us discuss in what sense it was true of false or nonsensical. (Michael Wolff's Cambridge Recollections of John Wisdom, a professor of philosophy at the university)

There is a way to verify the proposition 'There's a lion on the landing', namely to open the door and look. However, if we believe there to be a lion on the landing outside our classroom (We might be in Africa), we will not want to open the door. Perhaps we hear what appears to be growling or clawing outside, but can those sounds be explained in one way only. But the philosophically-logically interesting question is, if we are in Cambridge, England ... We certainly don't believe that there is a lion on the landing. And here is the question Frank Ramsey asked: we talk about "degrees" or "strength of belief", but how do we measure a belief?

The odd thing about the proposition 'There is a lion on the landing': we're not going to verify it by opening the door. Does that belong to the "language-game" -- is it a rule of the game? It doesn't look like a rule of the game. And yet, there it is.

Because the rule for verification is open the door -- i.e. look and see --, but no one is going to open the door (Of course there are other rules that don't require the door be opened).

Contrary to Ramsey's assumption, however, "How can we measure the degree of belief?" is not a psychological -- but instead a grammatical-logical question (a question about the "grammar" of the word 'belief' rather than about any phenomenon called "states of mind") -- just as the question of whether we can imagine an imperceptible lion on the landing is. It is not here a question about our powers of imagination, but about the logic of our language ("logical possibility" = what can be described, because it is described).

We believe there is not a lion outside our door at the moment - but do we know there is not, even without verifying that there is not?

Question (a bit different from John Wisdom's question): Do we know there is not a lion on the landing outside the door? And we can, Well, we can look and see. But the interesting question is: Can we know there is not a lion on the landing without opening the door and looking -- i.e. do we know even without looking? We certainly believe that there isn't a lion on the landing. And so there is the question Ramsey asked: How do we measure belief, that is to say, the strength of belief? Because some propositions we hold fast to more strongly than others.

There are lions in Britain; one might have escaped from the zoo and found its way even to Cambridge University. That is, it is not only logically possible for there to be a lion outside on the landing. We say, "Come, come, what is the likelihood of that?" And when we say this, we are not talking about "odds", a percent expressed as a ratio; what we mean is that the combination of circumstances needed for a lion to be outside on the landing is a possible combination no "reasonable person" would take seriously (It would be like someone seriously preparing contingency plans for an invasion of Cambridge from the planet Mars). Nonetheless, if there is a real possibility that something may happen, then we do not know that it is not happening without verification -- isn't that simply how we use the words 'know' and 'believe'? Even if no one believes it in the least likely, nonetheless no one knows that there isn't a lion outside on the landing without looking.

Well, if everything speaks for an hypothesis and nothing against it -- is it then certainly true? One may designate it as such [i.e. apply the word 'true' to it]. -- But does it certainly agree with reality, with the facts? -- With this question you are going round in a circle. (OC § 191)

F.P. Ramsey: 'degree of belief' is nonsense unless a method of measuring belief is specified

Note: there is an earlier, related discussion of this topic: "Belief is measured by willingness to take risks" (Frank Ramsey).

I shall try to argue later that the degree of a belief is just like a time interval; it has no precise meaning unless we specify more exactly how it is to be measured. (Truth and Probability (3. Degrees of Belief) (1926), in The Foundations of Mathematics and other Logical Essays, ed. Braithwaite, 1931, p. 167)

Note: Sadly for me, due to the time limits of Interlibrary loan, I do not have Ramsey's essay past page 167. The last sentence of that page ends:

... what is peculiar is that it is difficult to form any idea of how the measurement [of a belief] is to be conducted, how a unit is to be obtained, and so on.

The subject of our enquiry is the logic of partial belief, and I do not think we can carry it far unless we have at least an approximate notion of what partial belief is, -- (ibid. p. 166)

Comment: but the philosophical question is not: What is partial belief? (-- Note that 'full belief' doesn't mean 'knowledge'; 'knowledge' and 'belief' are different concepts: it is not possible to both believe something and to know it; knowledge is not a degree of belief: 'absolute certainty' ('full belief', 'complete belief') doesn't mean 'absolute knowledge'. --) The question is: How do we use, or want to use -- i.e. define for our special purpose --, the combination of words 'partial belief'?

Thus this is not a question of forming an hypothesis or theory about what some phenomenon named 'partial belief' is (if there is such a phenomenon or phenomena), but about stating rules for using the combination of words 'partial belief'. Or is it? Well, it is possible to be interested in a phenomenon from a variety of points of view (PI § 108), but not all those points of view belong to philosophical investigations, and what Ramsey is indeed asking is a philosophical-conceptual question, not a psychological-factual question. [Ramsey's presupposition about language meaning seems related to the TLP's definition of the word 'nonsense', where the meaning of a word (a "sense datum") was to be determined by an investigation by the natural science of psychology].

-- and how, if at all, it can be measured. It will not be very enlightening to be told that in such [and such] circumstances it would be rational to believe a proposition [or, declarative sentence] to the extent of 2/3, unless we know what sort of a belief in it that means. We must therefore try to develop a purely psychological --

Comment: Wittgenstein's philosophy of psychology treats of the language of feeling and the language of mind, but has nothing to do with the epistemological concepts 'belief' and 'knowledge', which are concepts of logical justification (i.e. asking the for the grounds for belief, the sufficient grounds for knowledge, as a grammatical investigation) rather than of mental states (as if the word 'belief' shared the grammar of the word 'anger', which it does not; only the bare sign 'strength of' is shared). Belief may be a variable in the calculus of probability, but it is not a psychological variable because 'belief' is not a concept belonging to psychology.

-- method of measuring belief. It is not enough to measure probability; in order to apportion correctly our belief to the probability we must also be able to measure our belief.

It is a common view that belief and other psychological variables are not measurable, and if this is true our inquiry will be vain; and so will the whole theory of probability conceived as a logic of partial belief; for if the phrase 'a belief two-thirds of certainty' is meaningless, a calculus whose sole object is to enjoin such beliefs will be meaningless also. Therefore unless we are prepared to give up the whole thing as a bad job we are bound to hold that beliefs can to some extent be measured. (ibid.)

Frank Ramsey and measuring belief = certainty

How much is someone willing to risk ("the cash value"?) that a proposition is true? How much would someone be willing to bet that e.g. the sun will rise tomorrow? The answer presumably is 100%. On the other hand, in contrast, something like "Which horse is going to win a race", it would only be a lesser percent of that 100% that a person would be willing to risk. (But I need more everyday-ish examples than a horse race.)

If you are going to measure belief, it seems to me what you are measuring is (the amount or degree of) certainty of (the) belief. And so we can go from 0% to 100% or $100 and imagine that the person is a gambler who always gambles to win and always wants to gamble to win. And so he will bet $100 or 100% that the sun will rise tomorrow.

Is "what a reasonable person believes" a measure of belief?

But the question of the degree or strength of a belief is not the same as the question of whether or not that belief is "reasonable". (Has the word 'reasonable' any meaning in the context of "measure of belief" (beyond that word's being an English word with uses in our language, obviously)?)

If we were offered a wager where if we wager 3 dollars and win we get 103 dollars back, this might look like a good wager; but if the risk of losing involved losing a child rather than losing money, it might not be an attractive wager. For example, if a mother's daughter has been bitten by a poisonous snake of which only 3 out of every 100 of its bites are fatal, that mother might well say "Then if I had a hundred daughters, I would only lose three ... But I only have one daughter". And the mother suffers anxiety because of her belief that her child may well die, whether or not this belief is "reasonable" or "rational" according to the wager's odds (which is not a question that enters into her thinking). The degree to which she believes that her child may die is surely shown by her inability to eat or sleep and pacing up and down, back and forth, behavior like this.

If you say that, "If there is only 3 in 100 chance, then it is not reasonable to worry", what are you saying? Ramsey thought that nothing useful could be done with the notion 'reasonable' in the context of partial belief. And if, when told that the snake's bite is only fatal in 3% of cases, the mother replies, "But I only have one daughter", is that not true? Or is she being unreasonable if she suffers from worry and sleeplessness and so on?

"Is it not true?" If 3 out of 100 die, then someone's child must be one of those three, and why shouldn't one of those children be her child? The meaning of saying that we 'believe' something [i.e. a proposition] surely is shown by what we do if we believe it, e.g. is we believe that there is hazardous ice covering the road we don't drive an automobile on it; if we believe Columbus discovered the Americas in 1492, we do not intentionally write "1493" on our test paper. (On the other hand, in the context of religion, Wittgenstein said "I would not ask if he would take his coat", as he would do in the normal language-game, because in religion belief is measured in a different way.) If belief is measured at all, that is, for what are we calling 'measurement' here: what connection, if any, does the grammar of 'measure' have with the grammar of 'believe'? or is talk of "measurement" here only a seeming metaphor?

(We don't measure the strength of belief by how tightly a preacher can squeeze his eyes shut when he publicly addresses the Lord in prayer. Why not? Are an actor's tears used to measure his sincerity -- "What's Hecuba to him or he to Hecuba that he should weep for her?" and yet he does weep.)

(Even in law 'reasonable' means no more than 'community standards' or 'what all right-thinking persons think'. It indicates consensus. But philosophical questions are not questions of consensus; they are not answered by taking a vote; the truth is not democratic, as it were.)

"National character"

Deutsche Welle reported (2 November 2009) that according to the president of the Republic of France:

"France has a particular identity which is not above the others but which is its own," Sarkozy told farmers in eastern France. "I don't understand how anyone could hesitate to say the words 'French national identity'."

What did Mussolini say the "Italian national identity or character" was? Something about a "warrior race" ..... And Hitler -- what did he say was the "German national character" and the "Jewish national character"? Why was Wittgenstein angry and upset with Norman Malcolm in autumn 1939 for using that expression?

You & I were walking along the river towards the railway bridge & we had a heated discussion in which you made a remark about "national character" that shocked me by its primitiveness. I then thought: what is the use of studying philosophy if all that it does for you is to enable you to talk with some plausibility about some abstruse questions of logic, etc., & if it does not improve your thinking about the important questions of everyday life, if it does not make you any more conscientious than any ... journalist in the use of the DANGEROUS phrases such people use for their own ends. (Memoir, Letter No. 9)

According to the French historian cited by Deutsche Welle, "The expression "national identity" was imported by the extreme-right National Front party in the 1980s". (Compare the expressions "our values as a nation" and "our values as a people" and "what it means to be British".)

"We must reaffirm the values of national identity and pride in being French," Eric Besson, the Minister for Immigration and National Identity, said in November [2009]. (ibid. 11 February 2010)

"National identity" Updates

Guardian News and Media Limited reported (17 November 2010):

Nicolas Sarkozy has admitted that he was wrong to create a ministry of immigration and national identity and that his nationwide debate on what it means to be French had led to tension and misunderstanding. Sarkozy said he had given up on the terminology "national identity" ... [But he] said even if he had "given up on the wording 'national identity'", he would not give up on the principles of his crack-down on immigration.

Even third- and fourth-generation children of immigrants (from North Africa and Africa, especially Moslems) are still referred to as French people "of immigrant origin". (ibid. 16 November 2010)

From the "Comment is free" section of Guardian News and Media Limited, by Michael Burke (20 June 2011) titled "Greek mythology, by Boris Johnson":

If the Greeks would only change their national character, and suddenly discover a Scandinavian faith in government combined with German habits of industry and thrift -- then, or so we are told, the catastrophe could be averted.

The London mayor is a canny enough politician to distance himself from a xenophobic rant against the Greeks by an artful "so we are told". But to repeat myths without debunking them ...

Johnson used the expression "national character" writing as a journalist in his column for Britain's Daily Telegraph. Johnson studied Classics at Oxford's Balliol College, including Classical Philosophy. He is a Tory politician.

Socrates and the rule of law: Can man be free if he is subject to arbitrary rule?

To the extent that it is unpredictable, it is doubtful (as a logical possibility) that he can, because, as I asked earlier, what would it be like if we lived in a world where there were no laws of nature, where there was no regularity we could count on (but everything constantly subject to the variable will of gods or demons) -- and thus no predictability. It is difficult to know what it would mean to be free under those circumstances, i.e. what we would call 'being free' in those circumstances.

Is it better to suffer an injustice rather than undermine the rule of law? Socrates believed that it was. For can you be free if you are subjected to arbitrary rule, in a society where there is no rule of law and you are subject to arbitrary rule? Or is your freedom conditional on the rule of law -- (but not as if the rule of law does not impose unjust as well as just laws) -- so that you always know where you stand -- (even if a law is unjust, you nonetheless know where you stand; the law does not change like a weather vane in the breeze)?

If freedom is dependent on the rule of law, then it is not an institution you will want to undermine -- i.e. that it is indeed better to suffer an injustice than to undermine it. Not every society, civilization, is ruled by law, but it was Socrates' belief that Athens was. The question is not whether the Athenian court had the legal authority. Of course it had. But because laws come and go, the question is whether the court had the moral authority. If you judge that a court has the moral authority, because it indeed -- (more or less impartially) -- enforces the rule of law, then you must accept its decisions. I think.

Does the rule of law have anything to do with justice in the sense of 'justice' = 'equity'? Only if jury or judge are willing to set the law aside and reach a decision based on what they regard as fairness in a particular case. But then wouldn't we have arbitrary rule rather than the well-defined rule of law?

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