How to make tautologies clear?


Angelina S. Bobrova


The paper shows how the first part of Peirce’s Existential Graphs theory answers Wittgenstein's question: “how must a system of signs be constituted in order to make every tautology recognizable as such in one and the same way?” Existential Graphs theory or Graphs theory is a diagrammatical system. Its basic unit is a graph or diagram that reminds Euler’s diagrams. The first part of the theory, which is alpha, corresponds, approximately, to classical propositional logic. The theory provides graphic or iconic syntax. So, it is clear why Wittgenstein's problem is also solved in an iconic way. Graphs let observe tautologies. No transformations are required to identify a formula type. The possibility to observe tautologies is due to not only the diagrammatical syntax peculiarities but also its minimalism. The cut (it is the boundary of a diagram) is the only sign of the alpha-graphs. It plays both technical and logical functions. The theory is even more concise than approaches with NAND or NOR operators. In light of the talk about tautologies, the paper concerns the problem of cut evolution. The cut is treated as negation, but it is a generated implication. Thus, implication but not negation and conjunction or disjunction is a primitive and most analytic sign. At first glance, it might look strange as the implication is the most complex logical connective. However, the implication tracks the idea of logical consequence and reflects its main properties, such as antisymmetry and transitivity.




Philosophy and Logic


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