Logic Must Take Care of Itself
Logic Must Take Care of Itself


This paper argues that there is a tension in Wittgenstein’s early conception of logic between the view that logic and language take care of themselves and the view inherited from Russell and Frege that logical analysis is ‘the caretaker’ of language.

My suggestion is that much of Wittgenstein’s criticism of Frege and Russell rests upon an alternative conception of logic and language animated by his preoccupation with the nature of the proposition and its sense. This conception is anticipated in his early insight that ‘logic must take care of itself’ and comes ever more into focus as he writes the Notebooks. I also argue, however, that at that time Wittgenstein’s thoughts about the self-sufficiency of logic were not radical enough to escape from the Russellian idea of analysis. I thus suggest that the main motivation for Wittgenstein’s ‘theory of logical portrayal’ might be triggered by what I shall call ‘Russell’s need’: the need “to justify the process of analysis”.

Table of contents

    1. A fundamental tension1 in Wittgenstein’s early conception of logic, which he became aware of at the time he started with Notebooks 1914-19162, surfaces in the question stated in the second entry: “How is it reconcilable with the task of philosophy, that logic should take care of itself?” (NB, 2). ‘The task of philosophy’, I take it, refers to the idea of complete analysis that is central to both Frege’s and Russell’s projects.

    The following brief reconstruction will outline several basic assumptions that underlie the concept of logically perfect language and logical analysis within Frege’s and Russell’s frameworks. Firstly, this conception entails a sharp divide between thoughts and expressions of thoughts in language – thoughts are what logic is interested in, not its expressions in everyday language, which is a matter for psychology. Consequently, we have a separation between logical form – which logic is exclusively interested in – and grammatical form3 – which has no importance for the ‘science of logic’ except as the source of impurity and confusion (“Instead of following grammar blindly, the logician ought rather to see his task as that of freeing us from the fetters of language” Frege 1997 [1897] 244). Logic deals with propositions – that is, with proper expressions of thoughts – not with sentences of ordinary language. Symbolism or logically perfect language (modelled on the example of maths) should be able, in contrast with the sentences of ordinary language, to present clearly the logical form of our thought (“A language of that sort would be completely analytic, and will show at glance the logical structure of the facts asserted or denied” Russell 1956 [1918], 197-98). Every (assertoric) sentence of our language should be translatable into symbolism – that means that a sentence is subjected to analysis. The idea behind symbolism is “one word and no more for every simple object” as Russell put it, or in Frege’s words: “every expression constructed as a proper name… in fact designate an object”. A combination of these simple words or names (in a proposition) is assumed to refer to a fact, or a complex made of simple objects (“In a logically perfect language the words in a proposition would correspond one by one with the components of the corresponding fact” Russell 1956 [1918], 197). Analysis is completed when we dissect the proposition so that simple objects that constitute a fact are shown to be clearly represented by simple names that stand for them. This also means that the logical form of a proposition is rendered perspicuous, and that the task of philosophy, as far as the proposition in question is concerned, is fulfilled.

    Note that this is a rather oversimplified version of the story. We have to bear in mind that many fine differences become visible if we focus more closely on the relation between Russell’s and Frege’s conceptions of logical analysis. One conception is given in the Tractatus as well. Here I merely sketch how the goal of ‘complete analysis’ relates to the task of philosophy and the shared basic assumptions of such a goal.

    2. Now we need to flesh out a rationale behind the “extremely profound and important insight” that “logic must take care of itself” (NB, 2). The significant portion of Wittgenstein’s early philosophy is condensed in the first few entries of the Notebooks. The account presented in this section is largely based on these opening passages and on several earlier remarks from Dictations to Moore (1914)4.

    Firstly, we are invited to consider the idea of something like the self-sufficiency of (logical) syntax – we must be able to set the rules of syntax by looking at the symbols alone. That is, every mention of the meaning of a sign is an empty move, as it were; it is absolutely unneeded as nothing is being said which was not already seen (“If syntactical rules for functions can be set up at all, then the whole theory of things, properties, etc., is superfluous” (NB, 2). This pertains especially to the theory of types: any such theory is superfluous, tautological and senseless – for it tries to do something that is always already done in a more trivial way in our language (“Even if there were propositions of [the] form "M is a thing" they would be superfluous (tautologous) because what this tries to say is something which is already seen when you see "M"” (DM, 110). What is given by ordinary sentences is enough for us to have a pretty good idea of what makes sense, i.e., that which we understand (“It is obvious that, e.g., with a subject-predicate proposition, if it has any sense at all, you see the form, so soon as you understand the proposition, in spite of not knowing whether it is true or false” (DM, 110). The same moral is expressed in the thought that whatever is possible is also legitimate (“A possible sign must also be capable of signifying” (NB, 2), viz. logic that governs the formation of any possible sign in our language makes it legitimate, puts it in traffic. I.e. “Every possible sentence is well-formed” (NB, 2).

    Secondly, we are faced with a question of nonsense: it is not as if the signs were responsible for the breakdown of sense – the responsibility is completely on our part (“Let us remember the explanation why "Socrates is Plato" is nonsense. That is, because we have not made an arbitrary specification, NOT because a sign is, shall we say, illegitimate in itself!” (NB, 2). We are free to utter whatever gibberish we like, only that does not entail that whatever it is that brings sense to our utterances will automatically lose its significance. Even though Wittgenstein does not spell out at this point what those conditions of sense might be, it is certain, given the quotations above, that every possible linguistic construction is designed legitimately i.e. to make the sense possible.

    A month after Wittgenstein wrote the above remarks, he envisaged conditions of sense in terms of the (extended) picture metaphor as the agreement between our thoughts, our language, and how our world is. But that discussion falls out of the scope of this paper. The crux of our examination herein is to point out an important contrast: in Frege/Russell’s case, it is ordinary language that is on trial, “for very many of the mistakes that occur in reasoning have their source in the logical imperfection of language” (Frege 1997 [1897] 244), whereas, for Wittgenstein, it is we who have not given any meaning to certain of its [sentence’s] parts. Even when we believe we have done so” (NB, 2).

    The first move towards making the picture metaphor applicable across the board has thereby been made: all sentences are to be treated equally in their capacity to display logical features; they are all able to express sense. Unanalysed sentences are not to be treated as logical failures. If there is something for analysis to determine, it is not sentences’ logical integrity, for they possess such integrity inherently (“Remember that even an unanalysed subject-predicate proposition is a clear statement of something quite definite” (NB 4). If a difference between the analysed and unanalysed form of a sentence is to be made, it should not depend on its capacity to express sense but perhaps on something additional.

    3. We can now go back to Wittgenstein’s question: “How is it reconcilable with the task of philosophy, that logic should take care of itself?”

    Here the idea that logic is already at work in any possible sentence clashes with the task of philosophy conceived in terms of complete analysis. Wittgenstein becomes acutely aware of this tension when he asks himself “Does such a complete analysis exist? And if not: then what is the task of philosophy?!!?” (NB, 2) That is, if everything that we need of logic is always already there in our language, is “shown by the existence of subject-predicate SENTENCES”, then why should we need analysis at all? The question is all the more pressing, for analysis is conceived as the task of philosophy, as our real need (“Then: if everything that needs to be shewn is shewn by the existence of subject-predicate SENTENCES etc., the task of philosophy is different from what I originally supposed” (NB, 3).

    With this astonishingly important question, Wittgenstein for the first time touched the heart of the matter – Frege’s and Russell’s expectations about what philosophy should accomplish, i.e., the ultimate clarity of logical form via the complete analysis of propositions, wherein analysis is taken as a necessary route towards such clarity, just did not fit the idea that “logic must take care of itself” whose main features I outlined above.

    It is hard to overstate the significance of this acknowledgement. Being stated in the form of a question it also suggests that the deepest difficulties related with what he took as a given from his teachers, in contrast with where his own investigations had brought him by this point, are yet to be met. If everything is already in ‘perfect order’ in our language, as his new picture of logic implies, then in what sense do we really need analysis? Is analysis a necessary precondition of clarity about the logic of our language such that in the absence of analysis we would not be able to know what we think, or what does and does not make sense?

    Wittgenstein was obviously not ready to reach any final verdict at this point, so likewise I could offer merely preliminary suggestions regarding his removal from Frege and Russell. Again, the thing to keep in mind is that the Tractatus does contain an account of ‘complete analysis’ and accordingly we should be wary of being overly or prematurely dismissive with regard to a possible role for analysis in achieving a certain level of perspicuity of the linguistic expressions. Equally, given that Wittgenstein’s ‘fundamental insight’ also appears in the Tractatus, it seems plausible to at least wonder if the reasons for having such a need for logical analysis are somewhat different than in Frege/Russell’s case as the following passage, for instance, suggests:

    Can't we say: It all depends, not on our dealing with unanalysable subject-predicate sentences, but on the fact that our subject-predicate sentences behave in the same way as such sentences in every respect, i.e. that the logic of our subject-predicate sentences is the same as the logic of those. The point for us is simply to complete logic, and our objection-in-chief against unanalysed subject-predicate sentences was that we cannot construct their syntax so long as we do not know their analysis. But must not the logic of an apparent subject-predicate sentence be the same as the logic of an actual one? If a definition giving the proposition the subject-predicate form is possible at all...? (NB, 4)

    4. As a result, I suggest that one way to gain a better perspective on the role of the ‘picture metaphor’ in Wittgenstein’s early work is to focus on his urge to reconcile what struck him as two conflicting lines of thought. On the one hand, he was partially committed to the idea that the task of philosophy, as Frege and Russell held, ought to address imperfections of ordinary language by a means of analysis (“a considerable part of what one would have to do to justify the sort of philosophy I wish to advocate would consist in justifying the process of analysis” Russell 1956 [1918], 178), and, on the contrary, he was seriously engaged with the idea that logic always takes care of itself and that ordinary language sentences are perfectly fine as they are.

    Hence, the ‘need’ that the picture metaphor attempted to fulfil could hardly have arisen from the conception that “logic must take care of itself”, as this view entails that, in principle, logic does not have needs that a logician is invited to discover and satisfy. It was actually one of ‘Russell’s needs’ i.e. the need to answer the question when the analysis should be considered complete that sought the fulfilment (or as Wittgenstein put it “when those signs [signs that behave like signs of the subject-predicate form] are completely analysed?” (NB, 2) In order to account for the problem of ‘completeness’ in the above mentioned sense, the analysis’ advocate needs the ‘world’ as an ontological excuse. I.e. he needs to assume ‘simple objects’ in the world which would, when reached, give him a ‘wink’ that the analysis is completed and, therefore, the logical form of a sentence rendered clear (logical atoms as “the last residue in the analysis” Russell, 1956 [1918], 178). Secondly, he needs to bridge the world and propositions so that the simple names arrived at in the process of analysis correspond to simple objects.

    Note, however, that the need is not to seek answers from the world, but to tune the metaphysics of the world/reality in such a way to serve the ‘analyst’ with the desired targets (“The demand for simple things is the demand for definiteness of sense” NB, 62).

    The metaphor of picturing was introduced as an account of the agreement between our sentences/thoughts and pieces of the world that allegedly dictate their analysis.

    The trouble is, I fear, that at least initially Wittgenstein adhered to ‘Russell’s need’ somewhat dogmatically, and thus the metaphor of picturing, which was to offer the fulfilment, turned out to be dangerously oversimplified. By the time of the Tractatus, however, Wittgenstein’s thoughts might have already gone in another direction, as the famous proposition 6.54 suggests – only this must stay a topic for some different occasion.


    1. Frege, Gottlob 1997 [1897] ‘Logic’, in: M. Beaney (ed.) The Frege Reader, Oxford: Blackwell, 227-250
    2. Russell, Bertrand 1956 [1918] ‘The Philosophy of Logical Atomism’, in: Logic and Knowledge, London: Allen and Unwin, 177-281
    3. Wittgenstein, Ludwig 1998 Notebooks 1914-1916, Oxford: Blackwell Publishers
    4. Wittgenstein, Ludwig 1998 [1914] Notes Dictated to G. E. Moore in Norway in: Notebooks 1914-1916 Appendix II, Oxford: Blackwell Publishers
    See the abstract
    Hereafter NB
    This general view is also highlighted in 4.0031 of the Tractatus
    Hereafter DM
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