ABSTRACT
In a science it is not possible to prove every opinion which we set forth. For every proof rests upon certain presuppositions; if we prove these, it is upon the basis of still further presuppositions. But this process cannot go on forever. We cannot avoid this infinite regress by arguing in a circle, for then we simply explain the term in question by means of the same term, but in a disguised form. (However, some proofs of this kind are utterly undisguised. Molière parodies them in The Imaginary Invalid: ‘Mihi a docto doctore domandatur causam et rationem, quare opium facit dormire. A quoi respondeo: Quia est in eo virtus dormitiva,* cujus est natura sensus stupifire’.†)
Hence we must start with unproven principles, with immediate assumptions. This point is the basis for the attacks of the ancient sceptics: the first principles are arbitrary and therefore all proofs untenable. Even Pascal (1625-62) was troubled by it. He said it would be best if we could define every word and prove every proposition, and thought it unfortunate that we cannot. But his regret was quite unjustified. A simple comparison of the process of defining with the process of setting up a proof would have set him straight. When someone asks us the meaning of a word unfamiliar to him, we do not always have at our disposal a word that has the same meaning but is easier to understand, i.e. a definition, but sometimes we do not need one because we can get him to understand the meaning by showing him things which are designated by the name in question. Similarly, we lose nothing by basing proofs upon propositions which cannot be proven. Of course, they may not be just any arbitrary assumptions; if they were, everything based upon them would be groundless. They must be immediately guaranteed, i.e. they must be insights which exclude all possibility of error.
