- C.S. Peirce made a very clear and sharp distinction between formal or mathematical logic and logic as semiotic.
Short summary: When Peirce uses the word ‘logic’ by itself, it’s important to check the context to see whether he’s talking about formal logic or logic as semiotic.
The first post of this series was prompted by a post 4 years ago on the Gödel’s Lost Letter and P=NP blog which jumped from the frying pan of problems in programming to the fire of problems in philosophy. Then last week two more posts, linked above, made the leap to two of the most flagrant problems in politics, namely, (1) the passage from effective and efficient algorithms to ethical algorithms and (2) the perils of navigating turbulent seas in a ship of state guided by elective representation, where the people pick their pilots from among themselves to represent their collective will and whatever wits they can muster.
Bearing all that in mind, I would like to keep exploring the ancient issues of aesthetics, ethics, and logic from our contemporary algorithmic perspective. There the descriptive and normative orientations to knowledge parallel the systems-theoretic dimensions of information and control. And there we find normative sciences appearing under the banner of “design sciences”. In that frame the art of crafting a ship of state becomes a question of optimal design for a human society.
When it comes to logic, then, a generic conception will do for now, leaving Peirce’s definition of logic as formal semiotic and fine points of the difference between mathematical logic and mathematics of logic to another day.
- Descriptive Science
- Normative Science
- Theory and Therapy of Representations
- Prospects for Inquiry Driven Systems • Logic, Ethics, Aesthetics
- Scott, David K., and Awbrey, Susan M. (1993), “Transforming Scholarship”, Change : The Magazine of Higher Learning, 25(4), 38–43. Online (1) (2) (3).