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2.9 Bipolarity and Sense in the Tractatus Journal for the History of Bipolarity and Sense in the Tractatus Analytical Philosophy Peter Hanks Volume 2, Number 9 Although the terms ‘poles’, ‘bipolar’, and ‘bipolarity’ do not ap- pear in the Tractatus, it is widely held that Wittgenstein maintained Editor in Chief his commitment to bipolarity in the Tractatus. As it is usually un- Sandra Lapointe, McMaster University derstood, the principle of bipolarity is that every proposition must be capable of being true and capable of being false, which rules Editorial Board out propositions that are necessarily true or necessarily false. Here Juliet Floyd, Boston University I argue that Wittgenstein was committed to bipolarity in the Trac- Greg Frost-Arnold, Hobart and William Smith Colleges tatus, but getting a clear view of this commitment requires a dif- Henry Jackman, York University ferent understanding of bipolarity. Properly understood, bipolar- Chris Pincock, Ohio State University ity is the view that every proposition represents two possible Mark Textor, King’s College London states of affairs, one positive and the other negative. Of course, in Richard Zach, University of Calgary the case of elementary propositions, the sense of a proposition is only the positive state of affairs. There is thus an asymmetry be- Production Editor tween what a proposition represents, its true-false poles, and what Ryan Hickerson, University of Western Oregon it says, its sense. In this paper I show how Wittgenstein accounted for this asymmetry in Notes on Logic and I consider two ways he Editorial Assistant might have accounted for it in the Tractatus. Daniel Harris, Hunter College Design Daniel Harris, Hunter College ©2014 Peter Hanks Bipolarity and Sense in the Tractatus to see how Wittgenstein reconciles the bipolarity of propositions with the fact that they have sense. Properly understood, a proposi- Peter Hanks tion is bipolar insofar as it presents or represents two possible states of affairs, one positive the other negative.1 But the sense of the proposition is only one of these two states of affairs. The ele- 1. Introduction mentary proposition ‘aRb’ represents the possible positive state of affairs in which a bears R to b, and the possible negative state of The idea that propositions are bipolar figures prominently in Witt- affairs in which a does not bear R to b, but it only asserts the exis- genstein’s pre-Tractatus works. In Notes on Logic he puts the idea as tence of the positive state of affairs. There is thus an asymmetry follows: between what a proposition represents, its poles, and what it says, Every proposition is essentially true-false: to understand it, we must its sense. The problem I want to raise in this paper is a matter of know both what must be the case if it is true, and what must be the understanding how Wittgenstein accounts for this asymmetry in case if it is false. Thus a proposition has two poles, corresponding to the Tractatus. the case of its truth and the case of its falsehood. (Wittgenstein 1913, 98-99) 2. What is bipolarity? The Moore notes and the Notebooks also contain frequent refer- Bipolarity is widely understood to be the requirement that propo- ences to the poles of a proposition. The latest occurs on June 2, sitions must be capable of being true and capable of being false. 1915, where Wittgenstein remarks that “my theory does not really For example, according to Hacker: bring it out that the proposition must have two poles,” (Wittgen- stein 1979, 53). Although Wittgenstein’s preoccupation that ordinary language is in Surprisingly, there is no explicit discussion of bipolarity in the good logical order committed him to the requirement of bivalence and the applicability of the Law of Excluded Middle, he adopted, in Tractatus and nowhere does he use the terms ‘poles’, ‘bipolar’ or the course of his atomism, the much more radical position of Bipolar- ‘bipolarity’. This raises a question about whether he remained ity for elementary propositions. This of course satisfies bivalency, but committed to bipolarity in the Tractatus. The consensus among it goes much further, for it commits him to the unique position of de- commentators is that he was so committed. I will argue that this is nying that there are any necessary elementary propositions. Any correct, but the matter is not as straightforward as it is usually proposition that has a sense must not just be capable of being true or taken to be. As we will see, the consensus is based on an impover- false, it must be capable of being true and also capable of being false. ished understanding of what bipolarity amounts to, and once this (Hacker 1981, 96) misunderstanding is cleared up a problem arises. The problem is that, in the context of the picture theory of meaning, it is difficult Similarly, Glock: Journal for the History of Analytical Philosophy, vol. 2 no. 9 [1] The only genuine propositions are pictures of possible states of affairs. it by saying that a proposition has both a “positive sense” and a These are bipolar — capable of being true but also capable of being “negative sense”: false — and hence cannot be necessarily true. (Glock 1996, 199) The picture-theory of the proposition is that the proposition in the And Morris: positive sense says: ‘This is how things are’ and in the negative sense says: ‘This is how things aren’t’ — the ‘this’ in both cases being the It is sometimes suggested that Wittgenstein’s reasoning in the Tracta- same. (Anscombe 1959, 67) tus turns fundamentally on a principle known as the Principle of Bi- polarity. According to this principle, in its most general form, every Similarly, Black explains bipolarity as the idea that a proposition meaningful sentence must be capable both of being true, and of being specifies both verifying and falsifying conditions: false. It is not enough merely that every sentence must be either true or false: that is the principle known as the Principle of Bivalence. The W. liked to think of this ‘bi-polarity’ by imagining the proposition to Principle of Bipolarity demands, not merely that each proposition draw a boundary in ‘logical space’, with the verifying conditions on must fall into one of the two categories, but that both categories must one side and the falsifying conditions on the other. The need for a be, as it were, live options for every proposition. (Morris 2008, 133)2 proposition to specify both falsifying and verifying conditions then appears as the truism that a boundary must have two sides to it. Bipolarity, on this construal, is a stronger commitment than biva- (Black 1964, 106-7) lence. Not only must every proposition be either true or false, but every true proposition must also be capable of being false and These are both ways of capturing the thought that the representa- every false proposition capable of being true. This rules out tional content of a proposition includes two possible facts or con- propositions that are necessarily true or necessarily false. ditions or states of affairs, one positive and the other negative. Be- I have no wish to challenge the claim that Wittgenstein was fore we see how this thought figures in the picture theory of mean- committed to what Hacker, Glock, and Morris call bipolarity in the ing it will be useful to see how Wittgenstein explains bipolarity in Tractatus (see 2.225, 4.461-4.4661). Rather, I deny that they have Notes on Logic. The problem of the asymmetry of bipolarity and correctly captured the concept of bipolarity.3 The capacities for sense will emerge along the way. both truth and falsity are consequences of a deeper fact about propositions, and it is this deeper fact that should be identified 3. Bipolarity and sense in Notes on Logic with bipolarity. The deeper fact concerns the representational con- Wittgenstein dictated Notes on Logic in the fall of 1913, roughly a tents of propositions. A proposition has two poles in the sense that year before he discovered the picture theory of meaning. Some it represents both a possible positive state of affairs and a possible central aspects of the picture theory are prefigured in Notes on negative state of affairs. We find this idea in Anscombe, who puts Logic, in particular, the idea that elementary propositions are facts in which names are bound together by predicates.4 However, it is Journal for the History of Analytical Philosophy, vol. 2 no. 9 [2] important to see that the theory of sense in Notes on Logic is differ- and those that do not, and the names ‘a’ and ‘b’ (in that order) de- ent in its essentials from the picture theory of the Tractatus. termine the pair <a,b>. Taken together, this division and this pair Wittgenstein’s theory of sense in Notes on Logic is built upon present us with two possible states of affairs, one in which a bears the idea that “the form of a proposition is like a straight line, R to b and another in which a does not bear R to b. This is the ex- which divides all points of a plane into right and left,” (Wittgen- planation of bipolarity in Notes on Logic. stein 1913, 102). By “form of a proposition” Wittgenstein meant a To complete the account of sense Wittgenstein needs to explain linguistic predicate with argument places, e.g. ‘xRy’.5 He makes how the proposition ‘aRb’ takes the final step of saying that the this clear in the following remark, where he offers a “definition of pair <a,b> falls on the R side of the division instead of the non-R sense”: side.
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