Abstract
Peirce, among his vast logical works, also invented a less known logical framework called by him Existential Graphs. It offers a diagrammatic method to represent logical expressions and logical deductions, so that logical deductions are formulated as transformations of diagrams. In this paper, after a short introduction to Existential Graphs (EGs hereafter), I will propose an interpretation of the framework of EGs in a way that it offers a method for meaning explanation of logical connectives. According to this interpretation, I will try to show, that the meaning explanation displayed by EG is different both from truth-functional and inferentialist approaches. I will focus on the philosophical merits of this framework, more precisely I am going to suggest that the features of EGs satisfy certain essential criteria of a theory of logic as put forward by transcendental investigations. Indeed EGs provide us with a powerful tool to carry out logical analyses not only in a formal way but also as belonging to what Husserl calls the “phenomenology of reason”.
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Notes
- 1.
As Husserl emphasizes: (Husserl 1969, p. 264).
- 2.
As emphasized by Peirce, e. g. in “The first rule of logic” (Peirce 1998, p. 44).
- 3.
Kant says :
It would therefore concern the origin of our cognitions of objects in so far as that cannot be ascribed to the objects; while general logic, on the contrary, has nothing to do with this origin of cognition, but rather ... deals only with the form of the understanding, which can be given to the representations wherever they may have originated (Kant 1998, A56, B81).
- 4.
Notice that in his classification, Peirce uses the term objective logic (Peirce 1976, p. 30), but it is different from our definition of the term here. It goes without saying that our conception is also different from the employment of this term by Hegel.
- 5.
- 6.
It is worth mentioning that (Mohanty 1976, p. 131 f) sees a similarity between this Husserlian distinction which we are going to discuss and the distinction between three branches of logic that Peirce makes in his classification of sciences.
- 7.
For further discussions about the distinction between consequence-level and truth-level see the corresponding part in Shafiei (2019).
- 8.
This is a wonderful property of a logical framework, as far as the exact investigations pertained to transcendental logic are concerned. Among the various frameworks developed in the last century, besides EG, Dialogical logic introduced by Paul Lorenzen and Kuno Lorenz also possesses such a property, as I discussed in Shafiei (2019). About the basic accordance of the dialogal logic with the logical features offered by the transcendental investigations, I have discussed in Shafiei (2018).
- 9.
Roberts describes the shape of the pseudograph as “a cut entirely filled in, or blackened” (Roberts 1973, p. 36), which is indeed an unsuitable chose of the words.
- 10.
Peirce CP. 4.430.
- 11.
In “Habits of Reasoning: On the Grammar and Critics of Logical Habits” (Pietarinen and Bellucci 2016) authors say:
According to Peirce, any proof of a leading principle can only consist in showing that the leading principle to be proved is already admitted to be true in another form in the argument that is supposed to prove it. The only proof of a principle is the proof of its un-eliminability.
This observation is also provides further evidence for the affinity of Peirce’s approach with the transcendental method.
- 12.
As I already mentioned, the only other framework which fulfills the mentioned phenomenological requirement is the dialogical logic, in which the rules for logical connectives should be symmetric, which means that they should not depend on the role of the utterer.
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Shafiei, M. (2019). Peirce’s Existential Graphs as a Contribution to Transcendental Logic. In: Shafiei, M., Pietarinen, AV. (eds) Peirce and Husserl: Mutual Insights on Logic, Mathematics and Cognition. Logic, Epistemology, and the Unity of Science, vol 46. Springer, Cham. https://doi.org/10.1007/978-3-030-25800-9_6
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