"This seems to abolish logic, but does not do so."

Question

If language is to be a means of communication there must be agreement not only in definitions but also (queer as this may sound) in judgements. This seems to abolish logic, but does not do so. -- It is one thing to describe methods of measurement, and another to obtain and state results of measurement. But what we call "measuring" is partly determined by a certain constancy in results of measurement. (Philosophical Investigations, 242)

I am trying to understand what Wittgenstein meant by "This seems to abolish logic, but does not do so."

My guess is this. Wittgenstein is saying that for words to have a clear meaning a certain degree of agreement in judgement must be present. For example, for the colour "red", although there are certainly cases where people disagree over what is and isn't red there must be other cases where there is overwhelming agreement. And for those who didn't recognise such latter cases as "red" we'd say they hadn't learnt the concept. A similar statement can be made in arithmetic -- the concepts in arithmetic only have clear meaning because of overwhelming agreement in certain calculations. If someone said "2+2=5" we wouldn't say they're bad at calculation, we wouldn't know what they meant at all.

Although this is all true, it is very tempting to draw a "relativist" or "historicist" conclusion here, which would abolish any notion of "universal" logic. Since our meanings rest on merely historically contingent agreements in judgement one might draw the conclusion that logical truths themselves are historically contingent. And Wittgenstein is saying that such an inference is unwarranted. My question is this: do people agree with my interpretation and if so how does Wittgenstein avoid "abolishing logic"?

Answer 1

A pretty interesting case is the blue-green distinction in language. It seems a distinction was not generally made between the colour of leaves and the coloyr of sky, which seems very surprising to us, until certain types of blue pottery provided the reference examples, and economic motivation through their being highly prized, to name blue.

Another interesting case is impossible colours, like magenta which was 'invented' in 1859. There is a theory that it has a particular interest as a colour to tetrachromats, who have an extra cone-cell type in their eyes at the red of the spectrum, and so an extra primary colour. It is fascinating to me that tetrachromacy has only been recently discovered in humans, which I think is philosophically significant about the limited impact of private variances in experience on language.

a certain degree of agreement in judgement must be present

Yes I think that's right, we must look to modes of life.

"In this sort of predicament, always ask yourself: How did we learn the meaning of this word ("good", for instance)? From what sort of examples? In what language-games? Then it will be easier for you to see that the word must have a family of meanings."

-Wittgenstein, in Philosophical Investigations

That is, meanings are embedded in modes of life, the way words are taught and used, like we struggle to privide an exhaustive definition of the word 'game' but feel we somehow know one when we see one. A recent example came up, the language game of 'opposites' Life and Death as one and the same?

I make the case that the Private Language Argument points directly towards intersubjectivity. That is, that in your quoted passage Wittgenstein is talking about the fear relinquishing claims to objectivity opens the door to unlimited subjectivity; but he is pointing to a kind of middle path, by which for instance money exists by agreement and yet embodies it's own reality. Discussed here: Is scientific knowledge personal or general?

Answer 2

I'd like to put this paragraph of Wittgenstein's into the perspective of a relatively recent basis of categorisation, the one that is formed by internalist and externalist positions. As it is the case for most of the items in philosophical vocabulary, it is not an anachronism to apply these terms backwards to the past views.

The main lines of thought for this pair of positions can be roughly given as follows:

Internalist position claims that the mental content (beliefs, intentions, ...) at issue (semantic, epistemic, ...) of a subject (speaker, agent, ...) is localised to the subject's own existence and resides in the subject's inner realm as properly individuated and determined by the subject's capacity alone.

On the other side, externalist position claims that the external (natural and social) world of the subject is an indispensable constituent to some considerable extent; thus, individuation and gaining determinacy of the content requires the subject's interaction with the outer realm.

A typical discrepancy between internalism and externalism arises when a person and her exact twin are considered in divergent environments. While internalism allows both of them to hold the same content regardless of the environment (even without any environment), externalism takes the difference in the environments into account. Notice that, in this respect, Descartes' arguments manifest an internalist character per excellentiam.

It should be remarked that some versions of internalism and externalism tend to trivialise the distinction in their arguments and objections. They take as typical cases, for example, Frege's view of sense (Sinn) that determines reference (Bedeutung) or an intensional definition that precisely specifies an extension in the respect of formal systems. Such cases fall squarely into the internalist scheme. However, they have presuppositions that go unnoticed and here, Wittgenstein, from a philosophical stance, points out one of those presuppositions.

It may be of significance that Wittgenstein chooses the verb 'aufheben' which is translated as 'abolish':

242. Zur Verständigung durch die Sprache gehört nicht nur eine Übereinstimmung in den Definitionen, sondern (so seltsam dies klingen mag) eine Übereinstimmung in den Urteilen. Dies scheint die Logik aufzuheben; hebt sie aber nicht auf.—Eines ist, die Meßmethode zu beschreiben, ein Anderes, Messungsergebnisse zu finden und auszusprechen. Aber was wir “messen” nennen, ist auch durch eine gewisse Konstanz der Messungsergebnisse bestimmt.

The verb 'aufheben' is heavily loaded word of German made famous in philosophical literature by Hegel's use, in which case it is conventionally translated as 'sublate'. Ordinarily, it is thought when we have grasped definitions made clearly and distinctly enough, the rest is an incontrovertible inference from them to their "correct" application (let us call this inference "one-ended" —the internal end). An "incorrect" application could only be a result of some distracting effect (a pathological case, for example). To express in internalist terms schematically, it may be said that we have internal representations and compare these representations to their external (target) designations. If we do not differ in our internal representations, we should not differ in their designations, either.

Wittgenstein says there is still an inference, but that inference is two-ended (internal and external ends), for, to say in externalist terms, the environment is also a constituent of those representations (compare this to Putnam's Twin Earth thought experiment).

Let us carry on with Wittgenstein's example: Suppose we have the required notions and appropriate instruments to measure length; we may say that we have satisfied the internalist criteria, that is, we have got hold of the internal end. But we have to bring off a concurrence of the measurements we perform in different tasks (in a physics laboratory, a civil construction site, a carpenter's workshop, an astronomical observatory, ...) at different times to get hold of the external end, in respect of agreement both of us with ourselves and of us with others. We should be able to make the judgement that we have obtained the same result and the judgement that we have obtained a different result when we think that we should. If such a concurrence were not accomplished, we might need to revise our instruments, our assumptions, our way of rounding numbers, stipulations of standard units, etc., hence, our practice of measurement, but this is in turn to revise our representation of measurement.

Wittgenstein attempts not to take sides in the internalism/externalism dichotomy. To illustrate Wittgenstein's idea alternatively, let us make an analogy to the metaphysical pair of a universal and its instances. Wittgenstein argues that, so to say, to recognise a universal is not enough to recognise its instances, for recognition of instances as instances of that universal is also part of the conception of that universal.

As a side note, those interested in this theme could see that it is not restricted to the debates on semantic and epistemic internalism/externalism, but bears relevance to such other topics as Etchemendy's distinction of interpretational and representational semantics made in connection with the notion of logical consequence and the analytic framework of two-dimensional semantics.