Peirce aspired for the completeness of his logic cum the theory of signs in his 1903 Lowell Lectures and other late manuscripts. Semeiotic completeness states that everything that is a consequence in logical critic is derivable in speculative grammar. The present paper exposes the reasons why Peirce would fall short of establishing semeiotic completeness and thus why he would not continue seeking a perfect match between the theories of grammar and critic. Some alternative notions are then proposed.

Peirce wrote in late 1901 a text on formal logic using a special Dragon-Head and Dragon-Tail notation in order to express the relation of logical consequence and its properties. These texts have not been referred to in the literature before. We provide a complete reconstruction and transcription of these previously unpublished sets of manuscript sheets and analyse their main content. In the reconstructed text, Peirce is seen to outline both a general theory of deduction and a general theory of consequence (...) relation. The two are the cornerstones of modern logic and have played a crucial role in its development. From the wider perspective, Peirce is led to these theories by three important generalizations: propositions to all signs, truth to scriptibility, and derivation to transformability. We provide an exposition of such proposed semiotic foundation for logical constants and point out a couple of further innovations in this rare text, including the sheet of assertion, correction as a dual of deduction and the nature of conditionals as variably strict conditionals. (shrink)

We present a category-theoretical analysis, based on the concept of generic figures, of a diagrammatic system for propositional logic ). The straightforward construction of a presheaf category \ of cuts-only Existential Graphs provides a basis for the further construction of the category \ which introduces variables in a reconstructedly generic, or label-free, mode. Morphisms in these categories represent syntactical embeddings or, equivalently but dually, extensions. Through the example of Peirce’s system, it is shown how the generic figures approach facilitates the (...) formal investigation of relations between syntax and semantics in such diagrammatic systems. (shrink)

We present a category-theoretical analysis, based on the concept of generic figures, of a diagrammatic system for propositional logic ). The straightforward construction of a presheaf category \ of cuts-only Existential Graphs provides a basis for the further construction of the category \ which introduces variables in a reconstructedly generic, or label-free, mode. Morphisms in these categories represent syntactical embeddings or, equivalently but dually, extensions. Through the example of Peirce’s system, it is shown how the generic figures approach facilitates the (...) formal investigation of relations between syntax and semantics in such diagrammatic systems. (shrink)

The logic of assertive graphs is a modification of Peirce’s logic of existential graphs, which is intuitionistic and which takes assertions as its explicit object of study. In this paper we extend AGs into a classical graphical logic of assertions whose internal logic is classical. The characteristic feature is that both AGs and ClAG retain deep-inference rules of transformation. Unlike classical EGs, both AGs and ClAG can do so without explicitly introducing polarities of areas in their language. We then compare (...) advantages of these two graphical approaches to the logic of assertions with a reference to a number of topics in philosophy of logic and to their deep-inferential nature of proofs. (shrink)

Some have suggested that images can be arguments. Images can certainly bolster the acceptability of individual premises. We worry, though, that the static nature of images prevents them from ever playing a genuinely argumentative role. To show this, we call attention to a dilemma. The conclusion of a visual argument will either be explicit or implicit. If a visual argument includes its conclusion, then that conclusion must be demarcated from the premise or otherwise the argument will beg the question. If (...) a visual argument does not include its conclusion, then the premises on display must license that specific conclusion and not its opposite, in accordance with some demonstrable rationale. We show how major examples from the literature fail to escape this dilemma. Drawing inspiration from the graphical logic of C. S. Peirce, we suggest instead that images can be manipulated in a way that overcomes the dilemma. Diagrammatic reasoning can take one stepwise from an initial visual layout to a conclusion—thereby providing a principled rationale that bars opposite conclusions—and the visual inscription of this correct conclusion can come afterward in time—thereby distinguishing the conclusion from the premises. Even though this practical application of Peirce’s logical ideas to informal contexts requires that one make adjustments, we believe it points to a dynamic conception of visual argumentation that will prove more fertile in the long run. (shrink)

Mercier and Sperber (MS) have ventured to undermine an age-old assumption in logic, namely the presence of premise-conclusion structures, in favor of two novel claims: that reasoning is an evolutionary product of a reason-intuiting module in the mind, and that theories of logic teach next to nothing about the mechanisms of how inferences are drawn in that module. The present paper begs to differ: logic is indispensable in formulating conceptions of cognitive elements of reasoning, and MS is no less exempt (...) from taking notice of premise-conclusion structures than the commonplace theories of reasoning are. Our counterclaim is realized in terms of diagrammatic reasoning dating back to Charles Peirce’s pragmaticism. The upshot is that pragmatist logic restores the premise-conclusion structures in argumentation, supplants reason-intuition module with logical content, and validates good reasoning as an indispensable resource evident to all rational minds that claim ownership of reason and understanding. (shrink)