Affect Blog

Beyond the collective, experimental data of modern science upon which the philosophy of empiricism is based, what else can teach us about the world? What of analysis – and more specifically – its mode in the form of logic? Can logic teach us anything itself - or is it just a tool to be used to apply to data? The Cambridge eccentric Wittgenstein argued that logic can in two instances, and in two instances only, advance anything independent of the world: (1) When the structure of logical is tautological, that is to say the conclusion of any set of propositions cannot be other than true. Take the instance where we say “Either it is raining or it is not raining.” Now if the term p denotes “It is raining” then the logician may denote the above as p or not p. It stands as obvious that one of the two is true and so we have learnt nothing about the world, just about the obviousness of a formal truth. To develop the point we may also consider two separate propositions - take “the apples are ripe,” and “the orange juice is fresh” and imagine someone saying “Either the apples are ripe and the orange juice is fresh or the apples are not ripe or the orange juice is not fresh.” The very structure of that statement means that at least one of the possible given scenarios must be true. (2) Similar is the case of self contradictions, where all scenarios are equally false, the very converse of tautologies. By way of an example, let us revert to our assertion p= “It is raining.” Now it stands as obvious that “It is raining and it is not raining” is impossible as the two are mutually exclusive. Thus p and not p is structurally invalid. Statements such as this are false in all circumstances. Wittgenstein argued that both (1) and (2) were logic’s effective equivalent of the zero in mathematics – they set the ground.

Ground set, Wittgenstein as one of the key originators of Logical Positivism worked to promote language as essentially logical. True he conceded, logic was cloaked and disguised in the ambiguities and irregularities of language and emotion – but any expressed proposition could be essentially thought to be logical in content. Logic was the skeletal backbone of language. These ideas would be further developed by his close collaborator Bernard Russell in his skepticism of all metaphysical systems including most specifically theology. AJ Ayer went on to develop the idea that all propositions should be tested for corroboration with what truths we can gather from sense perception. If sense perception could not corroborate any assertion, the assertion was meaningless and should not be discussed. God could not be empirically proved, thus it was futile to discuss Him.

The startling ingenuity of the Logical Positivist system was to argue that all real sentences with any genuine meaning had a logical content. All language, skeletally, was trying to make assertions about the world – assertions which could either be true or false. Therefore if language could be reduced to its logical frame and all propositions which could be said, said (the number of propositions being n) – we would be in the position to know that there was exactly 2ⁿ possible scenarios in the entire cosmos – meaning that one out of 2ⁿ possibilities would be a completely accurate description of the universe.

Sounds simple. Not quite. For a problem remained in the form of existence. True if all that can be said for existing items is n propositions, there may be only 2ⁿ possibilities. Yet we could surely make almost infinite statements about things that don’t exist. If we were to start listing all the possible Unicorns, round squares etc and all the possible features they may or may not have we would make the number of propositions n infinite, giving us infinite possibilities. And so language really solves nothing at all………….