Wittgenstin on the “odd resemblance” between a philophical investigation and one in aesthetics

Aesthetics ‒ Wittgenstein’s Paradigm of


Simo Säätelä

Consider the following two appraisals of Wittgenstein’s philosophy:

It might be argued, however, that broadly understood there is a great deal of aesthetics in Wittgenstein’s works, and that aesthetics as he conceived it is the paradigm of philosophy, also as he conceived it. (Barrett [1967]: 158)

But what I wish to underscore is how tightly Wittgenstein draws the parallel between […] features of the Übersichtlichkeit of mathematical proof and features of «perspicuous presentations [Übersichtliche Darstellungen]», in philosophical investigations ‒ for this indicates one way in which Wittgenstein’s discussions of mathematics come to epitomize all his philosophy. (Floyd [2000]: 237)

Surely this sounds contradictory: how could both aesthetics and mathematics be thought of as paradigms of philosophy? Or perhaps Barrett and Floyd are talking about quite different aspects of Wittgenstein’s philosophy? However, Wittgenstein himself seems to have thought there is some kind of important similarity here, as we can see from this notebook entry from 1937:

The strange resemblance [die seltsame Ähnlichkeit] between a philosophical investigation (perhaps especially in mathematics) and an aesthetic one (E.g. what is bad about this garment, how it should be, etc..). (Wittgenstein, MS 116,56; Wittgenstein [1998]: 29)[1]

Why did Wittgenstein make this remark? I take that it is uncontroversial to assume that he is here not reflecting upon philosophy in general, but that the remark shows how he thought about his own work. Wittgenstein evidently wants to point to a similarity in «method» or approach between what he calls aesthetics, and philosophy, i.e. a similarity in the investigation itself ‒ he wants to say something about the nature of philosophical activity, as he understands it, or at least point to important aspects of it. The remark can be supplemented by an observation from 1949, where Wittgenstein points to a similarity in the questions the investigation is supposed to resolve:

Scientific questions may interest me, but they never really grip/intrigue me. Only conceptual & aesthetic questions have that effect on me. At bottom it leaves me cold whether scientific problems are solved; but not those other questions. (MS 138,5b; Wittgenstein [1998]: 91)

Wittgenstein thus wants to compare conceptual (philosophical) questions with aesthetic questions, and distinguish them from scientific questions. But what are aesthetic questions, and what sort of investigation can deal with them? And why is it specifically the investigation of conceptual issues in mathematics that Wittgenstein wants to compare to «an aesthetic investigation»?

The fact that Wittgenstein himself attached importance to the remark is shown by the fact that we can find a similar, but longer and sketchier version in another notebook from the same period. This variant is probably a rough draft that Wittgenstein, in his usual manner, worked on and revised:

The strange resemblance between a philosophical investigation (maybe especially in mathematics) and an aesthetic one, for instance, what is bad about this garment, how it should be, etc.

Also here it is said: »What still does not fit here?» and also here the less sensitive person [das stumpfere Gefühl] says: »Everything is already in order». Nor must one in this case throw away the falseexplanation, because it is useful when you want to find the correct one/ it leads a bit on the way towards the right one.

The similarity reaches very far. (MS 119, 88v-89r)

What is an Aesthetic Investigation?

In spite of the extensive discussion concerning Wittgenstein's conception of philosophy this particular remark has received relatively little attention. For instance Peter Winch ([1995]: 97) mentions it in passing, only to note that «it is clear that [Wittgenstein] has had something technically methodological in mind» with this remark. However, Winch seems to downplay the difficulties involved in understanding this comparison. In what sense is the remark «technically methodological»? What aspects of the philosophical investigation is it supposed to highlight? In addition, Winch does not address the perhaps most perplexing feature of Wittgenstein’s remark, i.e., the parenthesis about mathematics.

To make sense of Wittgenstein’s comparison between a philosophical investigation and an aesthetic one (hereafter called «the aesthetic analogy») we must first try to understand what he might have meant by an «aesthetic investigation». It should be clear that he cannot have philosophicalaesthetics or the philosophy of art in mind when using this expression; he is not talking about an investigation in aesthetics (i.e. referring to aesthetics as a subject matter), but about an aesthetic investigation (i.e. characterising a certain kind of investigation). Wittgenstein also gives a brief example ‒ but in what sense are appraisals of dresses and how they should be, what fits, etc., «aesthetic investigations»? We can turn to the lectures on aesthetics Wittgenstein gave in Cambridge the following summer for an answer. Wittgenstein’s take on the subject in these lectures is quite unorthodox, and he devotes at least as much time to the discussion of suits, fashion, and other examples of «everyday aesthetics» as to art. He also used the word «aesthetics» in a rather peculiar sense:

I know exactly what happens when a person who knows a lot about suits goes to the tailor, also I know what happens when a person who knows nothing about suits goes ‒ what he says, how he acts, etc. [Taylor’s notes:] That is aesthetics. (Wittgenstein [1938]: 7)

It would of course be ridiculous to take this as a definition of «aesthetics» or as an illustration of an investigation in philosophical aesthetics. «Aesthetics», as Wittgenstein uses the word here, does not refer to a subject matter or branch of philosophy: instead, it has to do with seeing that something fits or does not fit, that something is pleasing or displeasing, beautiful or ugly ‒ or noticing that a picture, a melody, or an architectural detail «has the right expression» or «makes the right gesture», or fails to do these things (Wittgenstein [1938]: 31). It also has to do with understanding why something is right or wrong, and giving reasons for this, and thus possibly changing a person’s way of perceiving things. This is what Wittgenstein calls an «aesthetic investigation». For instance, if someone «less sensitive» says that something is all right (cfr. MS 119, 89r, quoted above), then a person with a more developed sensibility might try to get him to see that something is still missing or wrong.

But what is an «aesthetic investigation» more exactly? It can have to do with an attempt to locate the source of what Wittgenstein often calls «aesthetic perplexity» or «aesthetic puzzlement». By an «aesthetic puzzle» Wittgenstein means for example situations where I feel dissatisfaction, unease or even disgust at something but am uncertain why I have such a reaction, or cases where a melody, a picture, a building, etc. has a certain effect upon me but it is not clear for me why. Consider the following example: an architect is designing a door by letting someone else sketch its outline on a wall. The architect is looking at it and saying: «Higher, higher… oh, all right». Here, the initial discontent as well as the eventual satisfaction with getting it right, Wittgenstein said, may be called «aesthetic reactions» (see Wittgenstein [1938]: 13; for a more detailed discussion of  why Wittgenstein wants to emphasize the importance of «aesthetic reactions», see Säätela [2002]). The situation also gives an example of a solution of an «aesthetic puzzle». The architect feels discomfort with the door, because it is too low. This means that he has solved the puzzle by locating the reason for his discomfort. What is central for Wittgenstein is that we are not looking for causes here, instead, what we are interested in are reasons. The reaction is «directed» ‒ it has an object (the door); Wittgenstein says there «is a “Why?” to aesthetic discomfort not a “cause” to it» (Wittgenstein [1938]: 14-15). A reason entails one’s agreeing with it, whereas a cause is found out experimentally. An «aesthetic investigation» has to do with understanding and describing this kind of reasons. Wittgenstein also thought that psychoanalytic explanations should be compared with such aesthetic investigations instead of being misunderstood as scientific, causal explanations: 

The success of the analysis is supposed to be shown by the person's agreement. There is nothing corresponding to this in physics. Of course we can give causes for our laughter, but whether those are in fact the causes is not shown by the person's agreement that they are. A cause is found experimentally. The psychoanalytic way of finding why a person laughs is analogous to an aesthetic investigation. For the correctness of an aesthetic analysis must be agreement of the person to whom the analysis is given. (Wittgenstein [1932-1935]: 14)

«A Synopsis of Trivialities»

What, then, is the point of comparing this kind of investigation with a philosophical investigation? Does Wittgenstein's own approach give examples of how he perceived this «strange resemblance»? He did not explicitly take up this analogy in his lectures on aesthetics in 1938 or his lectures on the foundations of mathematics the following year. However, he did compare aesthetics both with mathematics and philosophy earlier, during his 1930-1933 lectures, and here the «methodological» dimension of the analogy is quite explicit. We can assume that he is alluding to this kind of similarities in his 1937 remarks as well. What is very clear in the 1930-1933 lectures is his insistence upon that he had found a new, revolutionary method in philosophy. He even talked about it in the same terms as a revolution in science. But as G. E. Moore points out, Wittgenstein was not very clear as to what this «new method» amounted to, though he «gave some hints as to its nature»:

He also said that he was not trying to teach us any new facts: that he would only tell us «trivial things ‒ Things we all know already»; but that the difficult thing was to get a «synopsis» of these trivialities, and that our «intellectual discomfort» can only be removed by a synopsis of many trivialities [....] I imagine, that it was in this respect of needing a synopsis of trivialities that he thought philosophy was similar to Ethics and Aesthetics. (Moore [1955]: 114)

Since this kind of «synopsis of trivialities» is to be understood in the light of aesthetics we can assume that at least one important aspect of it has to do with the kind of reasons Wittgenstein thinks are given in aesthetics. Indeed, Moore reports:

Reasons, he said, in Aesthetics, are «of the nature of further descriptions»; e.g. you can make a person see what Brahms was driving at by showing him lots of different pieces by Brahms, or by comparing him with a contemporary author; and all that Aesthetics does is to «draw your attention to a thing», to «place things side by side». He said that if, by giving «reasons» of this sort, you make another person «see what you see» but it still «doesn’t appeal to him», that is «an end» of the discussion [...]. And he said that the same sort of «reasons» were given, not only in Ethics, but also in Philosophy. (Moore [1955]: 106)

This is an important clue to how to understand the aesthetic analogy: Wittgenstein hints that both aesthetic and philosophical (as well as ethical) puzzlements can be dissolved or explained by certain kinds of reasons, by drawing attention to certain features or placing «things side by side». Also in the 1938 lectures he said that «what we really want, to solve aesthetic puzzlements, is certain comparisons ‒ grouping together of certain cases» (Wittgenstein [1938]: 29), and (again referring to Brahms) he developed a similar example of an «aesthetic investigation» that is supposed to give us the kind of answer we want when we are «puzzled about aesthetic impressions», e.g. «Why do these bars give me such a peculiar impression?»:

As far as one can see the puzzlement I am talking about can be cured only by peculiar kinds of comparisons, e.g. by an arrangement of certain musical figures, comparing their effect on us. When the written notes or the played notes are spread out, then you say: «If we put in this chord it does not have that effect; if we put in that cord it does». (Wittgenstein [1938]: 20)

It is such a surveyable or perspicuous representation, achieved in this case quite literally by «spreading out» the different versions that are to be compared, that Wittgenstein wants to call a «synopsis» or, in German, eine übersichtliche Darstellung[2].

An «aesthetic investigation», according to Wittgenstein, can thus give us reasons for why e.g. a particular word is used in a particular place in a poem, or why a particular door should be precisely so-and-so high (or why there is something wrong with these details).These reasons do not give us new information, but make us notice aspects we have neglected. This means that an aesthetic investigation, in Wittgenstein’s sense, bears a close similarity to a philosophical investigation (also in Wittgenstein’s sense): both aim at putting things «side by side» and change one’s way of perceiving.

An example of an «aesthetic investigation» that is particularly interesting from this perspective is art criticism, which demands that the critic expresses his own aesthetic reactions, and attempts to formulate reasons for what he wants to say about a particular work of art. The point of an «aesthetic investigation» is often to change a person’s way of looking ‒ you want to get him to see what you see, to appreciate what you are appreciating. In order to do this, he has to notice what is there, in plain view (cfr. aspect-change and the duck-rabbit). What is important is that I cannot prove that I perceive the object correctly, but I can, by giving different kinds of reasons, try to get somebody to see it in the same way as I do. According to Wittgenstein something similar also characterizes a philosophical investigation and its results. Stanley Cavell in particular has stressed the similarity in «grammar» between aesthetic judgements and the kind of philosophical claims that appeal to «what we would say when». Cavell also wants to connect this to the Kantian idea that the aesthetic judgement postulates a «we», it has a claim to universality, but cannot demand agreement (like a logical judgement). We can often formulate reasons for why we think something is beautiful, but the reasons come to an end if you cannot get a person to «see what you see». Something similar is, according to Cavell, the case in philosophy of the type Wittgenstein is practising, and which appeals to «what we would say when» (see e.g. Cavell [1969]: 73-96).

Summing up, the most salient points of comparison between investigations in philosophy and aesthetics are that:

- patterns of argument and possibilities of achieving agreement are similar.

- the investigation looks for reasons, not causes, and the reasons that can be given are similar.

- the idea of a «synopsis of trivialities» or «surveyable representation» applies to both kinds of investigations.

- the nature of questions in aesthetics and philosophy are similar; we do not have to do with problems (that have a substantial answer and that can be solved by new information and/or appealing to theory or experiments) but puzzles (where you have all the information you need, but you must «get» the point; for a further discussion of this point, see Säätelä [2011]).

- the result of the investigation (e.g., locating the reason for one’s puzzlement) can be the changing of one’s perception, and this kind of change in perception or aspect also has the potential to remove our discomfort, and free us from misleading pictures (so it can be in a sense therapeutic).

The Context of the Aesthetic Analogy

My claim so far is that Wittgenstein’s notion of eine übersichtliche Darstellung can be understood as an «aesthetic» one (in Wittgenstein’s sense of the word), and that it is this kind of «strange resemblance» that Wittgenstein is alluding to. Now that we have given a partial interpretation of the analogy, the next thing to ask is why Wittgenstein formulated it in late autumn of 1937. It is tempting to read this remark as a kind of free-standing aphorism on philosophy, and understand it as a description, or «constative» utterance, the truth value of which we can discuss:  Is it true of all of philosophy? – Hardly; Is it true of Wittgenstein’s own way of proceeding in philosophy? – In that case, does it apply to his philosophy as a whole, or certain parts of it?; etc.  However, if we want to be true to the spirit of Wittgenstein’s way of doing philosophy, we should realize that such questions are not answerable unless we place the utterance in a context, and look at the reasons for, and circumstances in which it was actually produced, i.e., take note of what could be called its performative aspects.

It is, of course, quite possible that Wittgestein wanted to make a general statement about (his) philosophy. Indeed, when G.H. von Wright decided to publish the remark in Culture and Value, he obviously thought that this is a remark of a general nature, that can be separated from the text surrounding it (see von Wright’s preface in Wittgenstein [1998]: IX). However, even if the analogy at a first glance seems to be quite self-contained, there are no clear indications in the manuscripts that Wittgenstein would have wanted to mark it off from the rest of the text. We must also take note of the fact that Wittgenstein made this remark in two different manuscripts, and that the surrounding philosophical discussion is more or less the same in both (so this part of MS 116 seems to be a reworking of the corresponding passages in MS 119). This indicates that the analogy, in spite of superficially being a self-sufficient aphoristic reflection upon philosophy, is indeed a direct commentary to the matters under discussion in these particular notebooks.

Thus we should take a closer look at the immediate context of the utterance in the manuscript texts in which it occurs. A part of the discussion surrounding the analogy reoccurs in Zettel (§§ 258-273), but the remark about the «strange resemblance» is not included in that fragment. The discussion revolves around making sense of concepts, and the limits of sense. Wittgenstein writes here, among other things, that in order to understand the sense of a sentence, we must look at how the sentence is used. What do the surroundings of the sentence look like? Grammar, he says, can be viewed as «the account books of language», and the interpretation of a sentence «is its surroundings in the grammar». The important thing to take note of is how you use language; «What you do with a word teaches me how you understand it» (MS 116,47 ; MS 119,82r). He also considers how one could argue against the use of wrong concepts, especially in discussions about mathematics:

I could say: Your concept is wrong. ‒ However, the issue does not get cleared up by fulminating against your words, but only by investigating how you use your words and by trying to turn your attention away from certain words, illustrations, images, and towards the use of the words. (MS 116, 53-54 ; MS 119, 90r;  cfr. Wittgenstein [1929-1948]: §463)

The discussion in these passages is quite interesting in itself, but here we must concentrate on Wittgenstein's possible reasons to interpolate the aesthetic analogy into it. The connection is not immediately obvious, but I want to claim that the aesthetic analogy must be seen in relation to a discussion of a quotation from Hardy, that immediately precedes it in both manuscripts:

Hardy says in the paper Mathematical Proof: «That “the finite cannot understand the infinite” should surely be a theological and not a mathematical war cry». It is true that this expression is infelicitous. But what people using it want to say with it is: «We have to deal with the right things here. Whence this leap from the finite to the infinite?». Nor is this a completely nonsensical expression ‒ only the “finite”, that is not supposed to be able to think the infinite ‒ is not “the human being”, or “our understanding”, but the symbolism, the calculus. And precisely how this conceives the “infinite” is well worth an investigation. And such an investigation should be compared to the thorough investigation and clarification of the management of a business by a chartered accountant. The goal is a surveyable and comparative presentation [eine übersichtliche vergleichende Darstellung] of all applications, illustrations, and conceptions of the calculus. An all-sided lighting (because a one-sided lighting also throws a shadow). A complete overview [Übersicht] of everything that might produce unclarity. And this overview must cover a wide domain, because the roots of our ideas reach far. Such a distinction is difficult. ‒ «The finite cannot understand the infinite» means: it cannot work in the way you, with characteristic superficiality, present it. (MS 116, 55; cfr. MS 119, 84v-85v; Wittgenstein [1929-1948]: § 273)

But if this reflection prompts Wittgenstein to formulate the aesthetic analogy, does he really want to claim that this kind of investigation in the philosophy of mathematics exhibits a «strange resemblance» to an aesthetic investigation? The kind of philosophical investigation he alludes to here is a kind of investigation that aims at a «surveyable representation» or «overview». However, here Wittgenstein seems to present a more systematic and «non-aesthetic» understanding of this notion, comparing it to the going through of the account books or management of a business. But does not the comparison of the philosopher’s activity to that of a «chartered accountant» undermine my interpretation of the aesthetic analogy rather than support it? As a reply to this, I would venture to claim that Wittgenstein formulates the aesthetic analogy as an alternative view of how to understand the notion of «eine übersichtliche Darstellung» – not as a systematic «overview» aspiring to completeness and an «all-sided lighting», but rather as the kind of «aesthetic» way of seeing things together, opening up new aspects through close attention to particulars that we outlined above. I think this interpretation can be supported if we take note of Wittgenstein’s own philosophical activity at the time. The remarks containing the aesthetic analogy are especially interesting because they are written in late autumn of 1937 when Wittgenstein was working on an early version of what we now know as the Philosophical Investigations[3].

The Aesthetic Analogy and the Method of the Investigations

Let us, then, take a closer look at the relation between the aesthetic analogy and Wittgenstein’s philosophical work in the period surrounding its formulation.  As we noted, the connection between aesthetics and the idea of a «synopsis of trivialities» or «eine übersichtliche Darstellung» as important for philosophical investigations is not new to Wittgenstein; indeed, he develops it, as we saw, already in the early 1930’s. However, in his work up until 1936 the notion of surveyable representation or synopsis of trivialities is indeed connected to a more systematic notion of an «overview» of the rules of grammar, or different language games, and the systematic presentation of examples that give us a kind of «birds-eye view» of the uses of a concept or a «segment of grammar pertinent to a given philosophical problem» (Glock [1996]: 280). The comparison between philosophical clarification and the systematic going through of the account books of a business that we quoted above corresponds to this systematic idea of Übersichtlichkeit. However, this notion is understood in a new way in Wittgenstein’s «investigations-philosophy», beginning in the autumn of 1936, when he abandoned his attempt to recast the Brown Book, simultaneously abandoning the systematic book form and starting instead to work in a radically new way, the result of which is the first version of the first part of the Investigations (see Pichler [2004])[4]. It is possible to claim that in fundamentals, Wittgenstein’s view of philosophy did not change; what changed was the way he chose to present it. It was not until he let his thoughts «travel freely» according to their «natural inclination», trying to not «force them in any single direction», that he found a Darstellungsform that fitted the kind of investigation he wanted to make:

The best that I could write would never be more than philosophical remarks; my thoughts were soon crippled if I tried to force them on in any single direction against their natural inclination. ‒ And this was, of course, connected with the very nature of the investigation. For this compels us to travel over a wide field of thought criss-cross in every direction. (Wittgenstein [1953], preface, first version written in August 1938)

So I would claim that Wittgenstein in MSS 116 and 119 gives voice to two, partly conflicting inclinations he has regarding the notion of übersichtliche Darstellungen: the «systematic» and the «aesthetic» one. When formulating the aesthetic analogy, he is reminding himself about the «aesthetic» Darstellungsform he has recently developed; i.e. he is reflecting upon his new «investigations-philosophy», where his way of presenting his philosophical thoughts is characterized or «earmarked» by the concept of eine übersichtliche Darstellung. However, he has now abandoned the idea that this means aiming at some kind of complete overview and systematic description of grammar. Instead, the emphasis is on a making something übersichtlich rather than on a representation that is in itself «surveyable» (Pichler [2004]: 183-184). It is a way of representing that allows us to see things together, and helps locate the reasons for our puzzlement in particular cases. In this sense the übersichtliche Darstellung is less a result than an attitude or activity (Pichler [2004]: 183), a way of viewing things rather than a view of things (Hallett [1977]: 217), an opening up of new aspects and alternative ways of seeing. It is a method for «dissolving philosophical problems by effecting changes of aspect», as Baker ([1991]: 48) puts it in his interpretation of the locus classicus for the discussion of this notion, Wittgenstein (1953): §122 (this passage can be found both in the Urfassung and the Frühfassung of the Investigations):

A main source of our misunderstanding is that we do not have an overview [übersehen] of the use of our words. ‒ Our grammar is deficient in surveyability [Übersichtlichkeit]. A surveyable representation produces just that understanding which consists in “seeing connections”. Hence the importance of finding and inventing intermediate links. The concept of a surveyable  representation is of fundamental significance for us. It characterizes the way we represent things [unsere Darstellungsform], how we look at matters (is this a “Weltanschauung”?).

The way of «looking at matters» that Wittgenstein talks about here is intimately connected to the form of presentation of the Investigations, that he himself characterizes in the preface as a kind of «criss-cross» philosophy. This view is also reflected in his abandonment of the traditional linear book form in favour of the «album» of the Philosophical Investigations. With it he finds a form of presentation that suits this methodological ideal, i.e. a kind of investigation that bears a «strange resemblance» to an aesthetic investigation. Compare this to what Wittgenstein says in a later discussion about aspect perception:

In conversation on aesthetic matters we use the words «You have to see it like this, this is how it is meant»; «When you see it like this, you see where it goes wrong»; «You have to hear these bars as an introduction»; «You must listen out for this key», «You must phrase it like this» (which can refer to hearing as well as to playing). (Wittgenstein [1953]: 202)

So what kind of reasons can we appeal to in such cases? As noted earlier, one possibility is to use different comparisons or analogies, to make certain connections appear by means of a «synopsis of trivialities» or a «surveyable representation». This kind of reasons, if persuasive (i.e., accepted as the reason for my puzzlement), can lead to a shift in perception, to the dawning of a new aspect. In the Frühfassung (that Wittgenstein was working on when he formulated the aesthetic analogy) this connection between the notion of a surveyable representation and changing our way of thinking, and the changing of an aspect of a picture or a way of talking, is even stronger than in the final, printed version (see TS 220, §§98 ff.; cfr. Baker [1991]: 48).

Why Mathematics?

So why does Wittgenstein single out a philosophical investigation especially in mathematics when formulating the aesthetic analogy? A trivial answer is that he was quite preoccupied with themes belonging to the philosophy of mathematics at the time[5], and that the «strange resemblance» struck him when reflecting upon such a theme (i.e. the concept of the infinite). But why does he think that precisely a philosophical investigation in mathematics should be conducted in a manner strangely reminiscent of an «aesthetic investigation»?

We must first and foremost note that the analogy is not about some putative resemblance between aesthetics and mathematics, but a note on the «strange resemblance» between an aesthetic investigation and a philosophical investigation especially in mathematics. We should, that is, be careful to distinguish between a mathematical investigation and a philosophical investigation in mathematics[6]. The investigation Wittgenstein is talking about in connection to the quote from Hardy is undoubtedly what he means by a philosophical investigation in mathematics. But what is the object of such an investigation? It is not mathematics, but what we are tempted to say about mathematics, that is the «raw material» for philosophy:

Thus, for example, what a mathematician is inclined to say about the objectivity and reality of mathematical facts, is not a philosophy of mathematics, but something for philosophical treatment. (Wittgenstein [1953]: §254)

Wittgenstein formulated a similar idea already in the early 1930s:  «Philosophy does not review the calculi of mathematics, but only what mathematicians say about these calculi» (MS 113, 108r). Philosophy will not interfere with the mathematical theory or calculus, but is rather concerned with what we (especially mathematicians and philosophers) tend to say about mathematics, what kind of pictures, analogies and conceptions of the symbolism our use of words reveals. These pictures and analogies can, in turn, tempt us to formulate philosophical statements about mathematics that can be severely misleading. Thus, «the finite cannot understand the infinite» is not (yet) an example of philosophy of mathematics ‒ however, for instance such ways of speaking about infinity are the raw material for Wittgenstein’s philosophical reflections about mathematics and his treatment of the philosophical questions such ways of talking can give rise to.

Any attempts to understand Wittgenstein’s general pronouncements about philosophy’s aims and methods should of course be supplanted by close attention to his actual philosophical practice. A more detailed look at different concrete examples of his investigations would therefore be needed at this point. However, we will here have to be content with a few glimpses of ways in which the aesthetic analogy can illuminate Wittgenstein’s philosophical investigations in this area.

Even though he does not explicitly discuss philosophical investigations in his lectures on aesthetics, where he gives several examples of «aesthetic investigations», he does in fact in passing (at the end of his third lecture) touch upon an issue relating to the philosophy of mathematics. Interestingly, this occurs when he characterizes his own way of philosophizing as a kind of «persuasion», in which he wants to «draw attention to certain differences» and get his interlocutors to «look at things in another way.» Here, he considers Cantor’s statements about transfinite set theory as an example of a way of thinking he wants to combat. He says that he is, in a sense, making «propaganda for a style of thinking as opposed to another» and that he is «honestly disgusted with the other», i.e. Cantor’s. Cantor’s proof and manner of expression has «no charm» for him—he «hates it», and he wants to put for instance an expression like «the Cardinal number of all Cardinal numbers» in a way «in which it will lose its charm». This means that he wants to show how misleading such expressions are:

If we explain the surroundings of the expression we see that the thing could have been expressed in an entirely different way. I can put it in a way in which it will lose its charm for a great number of people and certainly will lose its charm for me. (Wittgenstein [1938]: 28)

I would like to claim that the form of expression Wittgenstein is referring to here is precisely a kind of «synopsis» that will help us to see the matter in another light. And I would argue that it is such an «aesthetic» form of presentation that Wittgenstein himself uses, both in his manuscripts from the late 1930s[7] and especially in his lectures on the foundations of mathematics in 1939, when he deals for instance with the concept of infinity. This kind of investigation can be contrasted to one aiming at a «complete overview» and «all-sided lighting».

According to Wittgenstein, what leads to philosophical problems or «puzzlement» is Cantor's statements about his «discovery». We do not have to do with a mistake (i.e., that Cantor would say something false), but with a way of thinking and talking which lends the concepts of set theory a false and misleading, or even (Wittgenstein claims) dangerous charm. The problem he wants to point out is that what is said about mathematics (numbers, calculations, proof, etc.) can help create a mythology that gives a charm to the numbers or calculi but also contributes to obscure their use in mathematics, i.e. what actually determines their significance. Wittgenstein's treatment aims at freeing us from such misleading pictures, which requires that we ourselves realize that we were misled and could not see clearly. Therefore it is not enough to dogmatically proclaim that something is misguided or that someone uses a wrong concept. Wittgenstein says repeatedly in his lectures on the foundations of mathematics that he does not try to persuade anyone to change opinions. Opinions have to do with facts, and he does not want to bring forward new facts: «I am only trying to recommend a certain sort of investigation» (Wittgenstein [1939]: 103). It is this kind of investigation which exhibits a «strange resemblance» to an «aesthetic investigation», and it does often consist of introducing different types of comparisons and analogies. But it is not the case that Wittgenstein would argue that his own pictures and analogies are necessarily true, or more accurate than those he believes are misleading. Instead, they provide an object of comparison that can function as contrast, or an «antidote» that can counter the misleading analogies and pictures we have created for ourselves. Neither is he claiming that this kind of investigation results in a «complete» overview or an «all-sided lighting». Instead, Wittgenstein is explicit about being engaged in a kind of persuasion, or even «propaganda for a style of thinking as opposed to another» (Wittgenstein [1938]: 28).

A similar aim can be seen in his treatment of another central theme in the philosophy of mathematics, i.e. mathematical proof. When Wittgenstein maintains that in mathematics «surveyablity [Übersichtlichkeit] belongs to proof» (TS 221, §243; cfr. Wittgenstein [1939]: I, §154)  this clearly does not refer to some kind of systematic and «complete» overview; indeed, in his discussions of proof Wittgenstein especially criticizes the logicistic idea that mathematical proof is a process of step-by-step reasoning, ultimately reducible to a logical structure. When he insists on the «surveyability» of mathematical proof, he means that a proof shows us something in a convincing way. By a mathematical proof one is brought to see something; it must show us how to reach a solution, not simply that a problem has a solution. So it is for instance in this sense that Übersichtlichkeit in mathematics bears a close resemblance to Übersichtliche Darstellungen in philosophical investigations (as Juliet Floyd notes in the quotation adduced at the beginning of this paper; cfr. Floyd [2000], and Mühlhölzer [2005]). The aim of the philosophical investigation is to locate and describe the reasons for our accepting something proffered as a proof. This discussion of proof also allows us to glimpse a «strange resemblance» between the nature of mathematical rules and the nature of «aesthetic rules» (that Wittgenstein discusses in his lectures on aesthetics).

My conclusion is that Wittgenstein calls special attention to mathematics in the aesthetic analogy partly because he was, at the time, preoccupied with themes in the philosophy of mathematics, partly because he obviously thought (for reasons discussed above) that it is in particular when it comes to themes in the philosophy of mathematics that the «strange resemblance» between a philosophical investigation and an aesthetic one becomes evident[8]. And indeed also Wittgenstein’s later remarks on mathematics display the «criss-crossing» nature that he thinks is essential for his way of thinking.

The Aesthetic Analogy and Wittgenstein's Later Philosophy

In the preceding sections I claimed that the aesthetic analogy can be understood as Wittgenstein’s reflection upon the kind of «criss-cross philosophy» and the Darstellungsform appropriate to it that he was developing at the time. I also claimed that the parenthesis «(perhaps especially in mathematics)» can be explained by looking at his philosophical activity at that time. From this perspective it is interesting to note that he still in late 1937 presents the systematic way of understanding eine übersichtliche Darstellung as an alternative to the «aesthetic» way. However, I also think that scope of the aesthetic analogy can be understood in a broader sense, i.e. not just as a reflection upon the work in philosophy he was involved in at precisely that time, but as having in addition a forward-looking or programmatic dimension: it is conceivable that Wittgenstein wants to remind himself about the importance of this «strange resemblance» in order to carry on this kind of in investigation when continuing his work. Thus the analogy could be seen as a kind of declaration of intent regarding the future, and not just as a reflection on his current philosophical work in 1937.

So I would like to claim that both the Investigations and the post-Investigations philosophy can be profitably understood in the light of this analogy, and in this sense the aesthetic analogy can be seen as describing a Leitmotiv for Wittgenstein’s later philosophy. In this work he moves more and more away from the view of a surveyable presentation as a kind of complete, systematic mapping of «the account books of language», towards a conception that can be characterized as aesthetic (in the sense discussed).

Therefore it is not an exaggeration to say, with Cyril Barrett, that aesthetics can be viewed as Wittgenstein’s «paradigm of philosophy» ‒ as he conceived it. In fact, we can find that Wittgenstein, in some of his very last writings (MS 172, written in 1951, published as part of On Certainty), gives a new version of the aesthetic analogy, this time comparing a philosophical investigation with art criticism (which, as we noted, can be understood as a central example of «an aesthetic investigation»):

But is it an adequate answer to the scepticism of the idealist, or the assurances of the realist, to say that «There are physical objects» is nonsense? For them after all it is not nonsense. It would, however, be an answer to say: this assertion, or its opposite is a misfiring attempt to express what can't be expressed like that. And that it does misfire can be shown; but that isn't the end of the matter. We need to realize that what presents itself to us as the first expression of a difficulty, or of its solution, may as yet not be correctly expressed at all. Just as one who has a just censure of a picture to make will often at first offer the censure where it does not belong, and an investigation is needed in order to find the right point of attack for the critic. (Wittgenstein [1950-51]: § 37; my emphasis)

Saying that it makes no sense either to deny or affirm that there are physical objects is not an adequate response to the sceptic’s challenge. Instead, it must be shown that such an expression will «misfire» in different ways, and this has to be «correctly expressed» in order to be efficient. It is this kind of investigation (which involves real or imagined examples, «intermediate cases», and so on) by means of a «perspicuous representation», that Wittgenstein wants to compare to an «aesthetic investigation», in this case the activity of an art critic attempting to find «the right point of attack» for her assessment of a picture, i.e., formulate the reasons that are persuasive. We can also note, that he repeats the point (from MS 119, 89r) about a «false explanation» being useful when you want to find the correct one. So it is not the activity of a «chartered accountant», but that of an art critic, that remains as Wittgenstein's paradigm for a philosophical investigation.

Finally, a caveat: when considering these similarities we should remember that we have to do with an analogy, so we should not look for exact one-to-one identity. Wittgenstein is not claiming that «a philosophical investigation (in mathematics)» is «an aesthetic investigation»; we do not have to do with a scandalous «aesthetisation» of philosophy or mathematics ‒ there is a resemblance, but it is seltsam: it should strike us as something odd or peculiar, i.e., something out of the ordinary, something we did not expect to find. This also means that we should not be oblivious of the differences between these kinds of investigations, and that we should not look at these particular examples as the prototype for all cases. After all, there is «an extraordinary number» of different cases of aesthetic appreciation (Wittgenstein [1938]: 7). There is no essence to aesthetics; what belongs to aesthetics is an «immensely complicated family of cases» (Wittgenstein [1938]: 10) ‒ we should not expect there to be any single common denominator to everything we call for instance «aesthetic appreciation» or «aesthetic investigations». Indeed, it is precisely in this sense also that aesthetics resembles philosophy: there is not a single method of philosophy; neither is there a clearly delimited set of problems that makes up the subject matter of philosophy.

So how are we to sum up the importance of the aesthetic analogy? It should be clear that we do not have to do with theses about (the essence of) mathematics, aesthetics, or philosophy. Neither is the later Wittgenstein’s aim to introduce an alternative theory or new methodology (this can be contrasted to the fairly ambitious notion of method he seems to have had when he first introduced this comparison in the 1930-33 lectures). The point of comparing a philosophical investigation and an aesthetic one is, instead, to free us from some potentially misleading ways of looking at philosophy and its methods by giving a new, unexpected and surprising perspective, and thus help to battle the danger of dogmatism in philosophy.


Baker, G., 1991: Philosophical Investigations Section 122: Neglected Aspects, in R. Arrington and H.-J. Glock (eds.), Wittgenstein’s Philosophical Investigations: Text and Context, Routledge, London, pp. 35-68.

Barrett, C., 1967: Symposium: Wittgenstein and Problems of Objectivity in Aesthetics, “British Journal of Aesthetics”, 7 (2), pp. 158-163.

Cavell, S., 1969: Must We Mean What We Say?, Cambridge University Press.

Floyd, J., 2000: Wittgenstein, Mathematics and Philosophy, in A.M. Crary and R. Read (eds.), The New Wittgenstein, Routledge, London, pp. 232-261.

Glock, H. J., 1996: A Wittgenstein Dictionary, Blackwell, Oxford.

Hallett, G., 1967: A Companion to Wittgenstein’s Philosophical Investigations, Cornell University Press, Ithaca.

Kant, I., 2000: Critique of the Power of Judgment, ed. by P. Guyer, Cambridge University Press.

Moore, G. E., 1955: Wittgenstein’s Lectures in 1930-33, III, “Mind”, New Series, 253, vol. 64, pp. 1-27.

Mühlhölzer, F., 2005: «A Mathematical Proof Must Be Surveyable»: What Wittgenstein Meant by this and what it Implies, “Grazer Philosophische Studien”, 71, pp. 57-86.

Pichler, A., 2004: Wittgensteins Philosophische Untersuchungen: Vom Buch zum Album, Rodopi, Amsterdam.

Schulte, J., 2001: Einleitung, in L. Wittgenstein, Philosophische Untersuchungen: Kritisch-genetische Edition, Suhrkamp, Frankfurt a.M., pp. 12-50.

Säätelä, S., 2002: «Perhaps the Most Important Thing in Aesthetics» – Wittgenstein on «Aesthetic Reactions»,  “Revue Internationale de Philosophie”, 219, vol. 56, pp. 49-72.

Säätelä, S., 2011: From Logical Method to «Messing About»: Wittgenstein on Under­standing «Open Problems» in Mathematics, in O. Kuusela and M. McGinn (eds.), The Wittgenstein Hebook, Oxford University Press, pp. 162-182.

Winch, P., 1995: Discussion of Malcolm's Essay, in N. Malcom, Wittgenstein: A Religious Point of View?, Cornell University Press, Ithaca, pp. 95-135.

Wittgenstein, L., 1929-1948: Zettel, ed. by G.H. von Wright and G.E.M. Anscombe, Basil Blackwell, Oxford, 1968.

Wittgenstein, L., 1932-1935: Wittgenstein’s Lectures: Cambridge, 1932-1935: From the Notes of Alice Ambrose and Margaret Macdonald, ed. by A. Ambrose, Basil Blackwell, Oxford, 1982.

Wittgenstein, L., 1938: Lectures and Conversations on Aesthetics, Psychology and Religious Belief, ed. by C. Barrett, Basil Blackwell, Oxford, 1968.

Wittgenstein, L., 1939: Remarks on the Foundations of Mathematics, ed. by G.H. von Wright, R. Rhees and G.E.M. Anscombe, Basil Blackwell, Oxford, 1979 (3rd ed.).

Wittgenstein, L., 1939(b): Wittgenstein’s Lectures on the Foundations of Mathematics, ed. by C. Diamond, Cornell University Press, Ithaca, 1976.

Wittgenstein, L., 1950-51: On Certainty, ed. by G.E.M. Anscombe and G.H. von Wright, Basil Blackwell, Oxford, 1969.

Wittgenstein, L., 1953: Philosophical Investigations, ed. by G.E.M. Anscombe and R. Rhees, Basil Blackwell, Oxford, 1958 (2nd edition).

Wittgenstein, L., 1998: Culture and Value, ed. by G.H. von Wright and A. Pichler, Basil Blackwell, Oxford.

Wittgenstein, L., 2000: Wittgenstein’s Nachlass, ed. by The Wittgenstein Archives at the University of Bergen, Oxford University Press (electronic publication).

Wittgenstein, L., MS: Manuscripts, in Wittgenstein [2000].

Wittgenstein, L., TS: Typescripts, in Wittgenstein [2000].

[1] I have modified Winch’s translation from the second edition of Culture and value, since it is important that Wittgenstein does not write «one in aesthetics» (i.e. an «investigation in aesthetics») as Winch has it, but «an aesthetic one» («einer ästhetischen»), i.e. an «aesthetic investigation». This means Wittgenstein is not talking about aesthetics as a subject matter, but about the characteristics of the investigation. When quoting form the Nachlass, I have, when possible, used existing translations (sometimes amending them). Otherwise, translations are my own.

[2] It is worth noting that the translation of «übersichtliche Darstellung» that Wittgenstein himself favored was «a synopsis» or «a synoptic view» (see  Pichler [2004]: 183). Indeed, this translation avoids some of the problems we get if we use the translation «perspicuous representation», established by  Anscombe ‒ we do not have to do with the «mirroring» or representation of something that is already there, to be represented; in addition, a Darstellung has the connotation of activity, of something carred out (I’m indebted to Klaus Puhl for stressing this point).

[3] Regarding the dating: the remark containing the analogy in MS 119 is (in the manuscript) dated «1.11 (1937)». MS 116 is from the same period, but from purely stylistical consideration it is possible to say that the remark in MS 116 is later, since both the remark and the surrounding discusssion is quite similar to that of MS 119, but much more polished and to the point.

[4]The «Urfassung» of the Philosophical Investigations  (MS 142) was finished it in the the spring of 1937. It was dictated and typed , and  comprises what we know as §§ 1-188 of the published version. In 1937-1938 Wittgenstein continued this project, working manly on remarks concerning the philosophy of mathematics. In august 1938 he dictated a preface to a typescript that comprised what we know as the «Frühfassung» of the Philosophical Investigations  (TS 220 + TS 221) and wrote to Cambridge University Press inquiring about their interest in publishing a bilingual edition of it (that he wanted to call Philosophische Bemerkungen). What is interesting here is that the second part of this typescript deals extensively with themes from the philosophy of mathematics, and was not included in the later version that was finally printed after Wittgenstein's death (see Schulte [2001]: 20-21).

[5] At the time Wittgenstein wrote down the aesthetic analogy his version of the Philosophical Investigations was quite different from the book as we know it: much shorter and containing a substantive part dedicated to themes in the philosophy of mathematics (cfr. note 3 above).

[6]In the same manner as we should distinguish between an aesthetic investigation and an investigation in aesthetics (see note 1 above).

[7] I’m here referring to MSS 117, 118 and 119 (from the autumn of 1937), and MS 121 (from 1938-39), which are partly published in Wittgenstein [1939].

[8]  For instance Wittgenstein’s way of dealing with the question of the nature of «open problems» in mathematics can be seen as an example of this. See Säätelä (2011).

DOI: http://dx.doi.org/10.13128/Aisthesis-12836

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