On the Tractarian Concept of 'senseless (sinnlos)'

2024-1 Wittgenstein

 

#1) Senseless (sinnlos)

‘Senseless,’ or in the original German, ‘sinnlos,’ is one of the three main categories used in the Tractatus to classify propositions (Sätze). The Tractarian concept of ‘sinnlos’ is particularly crucial for understanding the nature of logical propositions (die logischen Sätze).

According to Tractarian accounts of language, every proposition belongs to one of the following three categories: ‘sinnvoll,’ ‘sinnlos,’ and ‘unsinnig.’ When clarifying the distinction between ‘sinnvoll’ and ‘sinnlos,’ it is worth noting that the German suffixes ‘-voll’ and ‘-los’ correspond to the English suffixes ‘-ful’ and ‘-less,’ respectively. On the one hand, a proposition with a sense (i.e., ein sinnvoller Satz) is a picture of reality and thereby must be either true or false (but not both) (4.01, 4.06). Propositions of natural science, for instance, belong to this category (4.11). On the other hand, a senseless proposition lacks a sense and cannot be a picture of reality, despite being part of the symbolism (4.461-4.462). Logical propositions, i.e., tautologies and contradictions, are categorized as being senseless (4.46).

 While both a proposition with a sense and a senseless proposition are part of the symbolism of our language and have their truth-values, nonsensical (unsinnig) pseudo-propositions are made by the infringement of the rules of logical syntax, being neither true nor false (3.325, 4,003). The German word ‘Unsinn’ corresponds to the English word ‘Nonsense’ in that both can be used to refer to gibberish. Ethical, aesthetical, and religious propositions are described as nonsense, notwithstanding that they seem to hold special significance in the Tractarian worldview (I will address this issue later with more details).

Then, why does Wittgenstein consider logical propositions as being senseless, and yet unlike nonsense, still belonging to the symbolism of our language? To understand his thoughts, we must first distinguish logical propositions from logical properties. According to the Tractatus, the fact that the propositions of logic are tautologies shows the logical properties of language and the world (6.12). Plus, Wittgenstein often calls the latter simply “logic,” as follows: “The logic of the world, which is shown in tautologies by the propositions of logic, is shown in equations by mathematics” (6.22). In a nutshell, the function of the former is related to showing the latter. This is done by combining meaningful propositions into the proposition of logic that says nothing, called a zero-method (6.121). In the proposition of logic, the original propositions (conjuncts or disjuncts) would have lost their sense (This is the reason why all the logical propositions are senseless). But at the same time, their logical properties are demonstrated by the fact that the proposition of logic is a tautology. For example, the fact that ‘∼(p.∼p)’ is a tautology shows that ‘p’ and ‘∼p’ contradict each other; the tautology ‘(p⊃q).(p):⊃:(q)’ shows that ‘q’ follows from ‘p’ and ‘p⊃q’; the tautology ‘(x).fx :⊃: fa’ shows that ‘fa’ follows from ‘(x).fx.’ (6.1201).

It is also worth noting that tautologies and contradictions are still truth-functional, i.e., truth-functions of elementary propositions (die Elementarsätze) (5 ff). As Glock notes, “The truth-value of a molecular proposition depends on those of the ELEMENTARY PROPOSITIONS of which it is a truth-function. Among the truth-functional combinations of propositions there are two limiting cases [i.e., tautologies and contradictions]” (Glock 1996: 355). In this regard, tautologies and contradictions, like ‘0’ is part of the symbolism of arithmetic, belong to the symbolism of our language (4.4611).