Real Semantics

It has become a commonplace that Bolzano, Frege and Husserl, by banishing thoughts from the mind, created the preconditions for the development of logic in the modern sense. By defending a view of thoughts or propositions as ideal or abstract entities, they made possible a conception of propositions as entities capable of being manipulated in different ways in formal theories. Just as Cantor had shown mathematicians of an earlier generation how to manipulate sets or classes conceived in abstraction from their members and from the manner of their generation, so logicians were able to become accustomed, by degrees, to manipulating propositional objects in abstraction from their contents and from their psychological roots in acts of judgment.

Now, however, we can see that the achievements of Bolzano, Frege and Husserl were part and parcel of a larger historical process, in which Lotze and Bergmann, but also Brentano, Stumpf, Marty, Meinong and above all Twardowski and his students in Poland, played a crucial role. We can see also that, as was clear to the author of the Tractatus, the squeezing apart of the two notions of proposition and Sachverhalt was no less important an achievement in the overcoming of psychologism than was the separation of judgment both from complex concepts on the one hand and from ideal propositions on the other.

It is noteworthy in this light that Tarski’s 1935 essay on the concept of truth, the single most important work arising out of the Lemberg-Warsaw school founded by Twardowski and his students, rests precisely on a discovery of how it is possible to manipulate formally not only sentences or propositions but also certain special sorts of object-structures in the world to which these sentences or propositions correspond. Tarski attempts, we might say, to capture mathematically the highest common factor running through the family of correspondence-theoretic views of truth, a factor which can be expressed in the form of a thesis to the effect that

a true sentence is one which says that things are so and so, and things are so and so.

This thesis derives in the end from Aristotle. But it is taken by Tarski from his teacher Kotarbiski, who had derived it in turn from Twardowski’s work on the Sachverhalt and on the so-called ‘absolute’ theory of truth.(45)

Logical or ‘model-theoretic’ semantics since 1935 has departed considerably from those aspects of Tarski’s work which reflected his original concern to find formal means of manipulating ways things stand in parallel to sentences or propositions. Model theorists have sought instead to exploit the mathematical resources which Tarski and others put at their disposal, and this has meant that their work has been confined to the construction and manipulation of abstract set-theoretic structures that have little or no relation to the actual world of what happens and is the case. Logic itself has hereby to a regrettable extent come to be freed of its relation to truth as classically conceived. More recent work, above all on the part of the situation semanticists, seems however to be pointing once more in the direction of a semantics that would be compatible with a Sachverhalt ontology of a more realistic sort, and to this extent there may perhaps be life yet in a conception of logic along Reinachian lines. Both Reinach and the situation semanticists suggest that we should shake ourselves free from the one-sided textbook conception of logic as a science of propositions conceived in abstraction from their realisations in the minds of thinking subjects and from their objectual correlates in the world. Logic should be seen, rather, not as a science of other-worldly ‘bearers of truth’, but as a discipline engaging whatever it is that can stand in truth-relations. And when matters are conceived in this light, then the temptation to embrace a special realm of propositions is much more easily resisted.

Barry Smith, Logic and the Sachverhalt

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