Category Archives: Diagrams

Survey of Precursors Of Category Theory • 2

A few years ago I began a sketch on the “Precursors of Category Theory”, aiming to trace the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice.  A Survey of … Continue reading

Posted in Abstraction, Ackermann, Analogy, Aristotle, C.S. Peirce, Carnap, Category Theory, Diagrams, Foundations of Mathematics, Functional Logic, Hilbert, History of Mathematics, Hypostatic Abstraction, Kant, Logic, Mathematics, Peirce, Propositions As Types Analogy, Relation Theory, Saunders Mac Lane, Semiotics, Type Theory, Universals | Tagged , , , , , , , , , , , , , , , , , , , , , , | 3 Comments

Types of Reasoning in C.S. Peirce and Aristotle • 2

Re: Peirce List Discussion • Ben Udell • Gary Richmond Present business has kept me from following much of the recent discussion on Peirce’s three types of reasoning, but we have been down this road before and so old tunes … Continue reading

Posted in Abduction, Analogy, Argument, Aristotle, C.S. Peirce, Constraint, Deduction, Determination, Diagrammatic Reasoning, Diagrams, Differential Logic, Functional Logic, Hypothesis, Indication, Induction, Inference, Information, Inquiry, Logic, Logic of Science, Mathematics, Peirce, Peirce List, Philosophy, Probable Reasoning, Propositional Calculus, Propositions, Reasoning, Retroduction, Semiotic Information, Semiotics, Sign Relations, Syllogism | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Types of Reasoning in C.S. Peirce and Aristotle • 1

Re: Peirce List Discussion In one of his earliest treatments of the three types of reasoning, from his Harvard Lectures “On the Logic of Science” (1865), Peirce gives an example that illustrates how one and the same proposition might be … Continue reading

Posted in Abduction, Analogy, Argument, Aristotle, C.S. Peirce, Constraint, Deduction, Determination, Diagrammatic Reasoning, Diagrams, Differential Logic, Functional Logic, Hypothesis, Indication, Induction, Inference, Information, Inquiry, Logic, Logic of Science, Mathematics, Peirce, Peirce List, Philosophy, Probable Reasoning, Propositional Calculus, Propositions, Reasoning, Retroduction, Semiotic Information, Semiotics, Sign Relations, Syllogism | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Systems Of Interpretation • 9

Figure 2. An Elementary Sign Relation Re: Peirce List Discussion • Jerry Chandler It is above all important to understand that Peirce’s concept of a sign relation is defined at a higher order of abstraction than any notion of causal … Continue reading

Posted in Artificial Intelligence, Communication, Community of Interpretation, Diagrammatic Reasoning, Diagrams, Interpretation, Interpretive Frameworks, Knowledge, Knowledge Representation, Logic, Logic of Relatives, Logical Graphs, Objective Frameworks, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , | Leave a comment

Systems Of Interpretation • 8

Figure 3. Aspects of a Sign Relation Re: Peirce List Discussion • Kirsti Määttänen One of the chief advantages of Peirce’s systems of logical graphs, entitative and existential, is the way they escape the bounds of 1-dimensional syntax and thus make … Continue reading

Posted in Artificial Intelligence, Communication, Community of Interpretation, Diagrammatic Reasoning, Diagrams, Interpretation, Interpretive Frameworks, Knowledge, Knowledge Representation, Logic, Logic of Relatives, Logical Graphs, Objective Frameworks, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , | Leave a comment

Systems Of Interpretation • 7

Figure 2. An Elementary Sign Relation Re: Peirce List Discussion • Gary Fuhrman Peirce’s existential graphs are a general calculus for expressing the same subject matter as his logic of relative terms and thus they serve to represent the structures … Continue reading

Posted in Artificial Intelligence, Communication, Community of Interpretation, Diagrammatic Reasoning, Diagrams, Interpretation, Interpretive Frameworks, Knowledge, Knowledge Representation, Logic, Logic of Relatives, Logical Graphs, Objective Frameworks, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , | Leave a comment

Systems Of Interpretation • 6

Figure 2. An Elementary Sign Relation Re: Peirce List Discussion • Jon Awbrey • John Collier I strongly agree, Jon.  Reading meaning into artefacts of the representation is not typically transparent.  I would say that the whole symbol represents the … Continue reading

Posted in Artificial Intelligence, Communication, Community of Interpretation, Diagrammatic Reasoning, Diagrams, Interpretation, Interpretive Frameworks, Knowledge, Knowledge Representation, Logic, Logic of Relatives, Logical Graphs, Objective Frameworks, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , | Leave a comment

Systems Of Interpretation • 5

Figure 2. An Elementary Sign Relation Re: Peirce List Discussion • Jerry Chandler An elementary sign relation is an ordered triple   It is called elementary because it is one element of a sign relation where is a set of … Continue reading

Posted in Artificial Intelligence, Communication, Community of Interpretation, Diagrammatic Reasoning, Diagrams, Interpretation, Interpretive Frameworks, Knowledge, Knowledge Representation, Logic, Logic of Relatives, Logical Graphs, Objective Frameworks, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , | 2 Comments

Systems Of Interpretation • 4

Re: Peirce List Discussion • Mike Bergman • Valentine Daniel For its pertinence to the present discussion, here again is what Peirce wrote about the mathematical way of using individual or particular cases to make general hypotheses or suppositions: Mathematical … Continue reading

Posted in Artificial Intelligence, C.S. Peirce, Communication, Community of Interpretation, Diagrammatic Reasoning, Diagrams, Interpretation, Interpretive Frameworks, Knowledge, Knowledge Representation, Logic, Logic of Relatives, Logical Graphs, Objective Frameworks, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , | Leave a comment

Systems Of Interpretation • 3

Figure 2. An Elementary Sign Relation Re: Peirce List Discussion • Mike Bergman • Valentine Daniel That “triskelion” stick-figure for an elementary sign relation or individual triple (o, s, i) is about the simplest possible.  There are some problems with … Continue reading

Posted in Artificial Intelligence, Communication, Community of Interpretation, Diagrammatic Reasoning, Diagrams, Interpretation, Interpretive Frameworks, Knowledge, Knowledge Representation, Logic, Logic of Relatives, Logical Graphs, Objective Frameworks, Peirce, Peirce List, Relation Theory, Semiotics, Sign Relations, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , | Leave a comment