Tag Archives: Sign Relations

Reflective Interpretive Frameworks • Incident 2

Re: Terence Tao • Modular Arithmetic Challenge Can a neural network learn to do modular multiplication efficiently? Incidental Reflection 1 There are alternative models of neural networks which do not depend on threshold neurons and endlessly fiddling with weights. Incidental … Continue reading

Posted in Arithmetization, C.S. Peirce, Gödel Numbers, Higher Order Sign Relations, Inquiry Driven Systems, Inquiry Into Inquiry, Logic, Mathematics, Quotation, Recursion, Reflection, Reflective Interpretive Frameworks, Semiotics, Sign Relations, Triadic Relations, Use and Mention, Visualization | Tagged , , , , , , , , , , , , , , , , | Leave a comment

Information = Comprehension × Extension • Comment 7

Let’s stay with Peirce’s example of inductive inference a little longer and try to clear up the more troublesome confusions tending to arise. Figure 2 shows the implication ordering of logical terms in the form of a lattice diagram. Figure … Continue reading

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Inquiry, Intension, Logic, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , | 1 Comment

Information = Comprehension × Extension • Comment 6

Returning to Peirce’s example of inductive inference in Comment 2, let’s try to get a clearer picture of why he connects it with disjunctive terms and indicial signs. At this point in time I can’t say I’m entirely satisfied with … Continue reading

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Inquiry, Intension, Logic, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , | 1 Comment

Information = Comprehension × Extension • Comment 5

Let’s stay with Peirce’s example of abductive inference a little longer and try to clear up the more troublesome confusions tending to arise. Figure 1 shows the implication ordering of logical terms in the form of a lattice diagram. Figure … Continue reading

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Inquiry, Intension, Logic, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , | 1 Comment

Information = Comprehension × Extension • Comment 4

Reflecting further on Comment 3, many things still puzzle me about Peirce’s account at this point.  The question marks I added to the Figures of that post indicate the node labels I have remaining doubts about.  For example, in Figure 3, … Continue reading

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Inquiry, Intension, Logic, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , | 1 Comment

Information = Comprehension × Extension • Comment 3

Peirce identifies inference with a process he describes as symbolization.  Let us consider what that might imply. I am going, next, to show that inference is symbolization and that the puzzle of the validity of scientific inference lies merely in … Continue reading

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Inquiry, Intension, Logic, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , | 3 Comments

Information = Comprehension × Extension • Comment 2

Let’s examine Peirce’s second example of a disjunctive term — neat, swine, sheep, deer — within the style of lattice framework we used before. Hence if we find out that neat are herbivorous, swine are herbivorous, sheep are herbivorous, and … Continue reading

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Inquiry, Intension, Logic, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , | 3 Comments

Information = Comprehension × Extension • Comment 1

Selection 1 ends with Peirce drawing the following conclusion about the links between information, comprehension, inference, and symbolization. Thus information measures the superfluous comprehension.  And, hence, whenever we make a symbol to express any thing or any attribute we cannot … Continue reading

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Inquiry, Intension, Logic, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , | 1 Comment

Information = Comprehension × Extension • Selection 6

Selection 1 opens with Peirce proposing, “The information of a term is the measure of its superfluous comprehension”, and it closes with his offering the following promise. I am going, next, to show that inference is symbolization and that the … Continue reading

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Inquiry, Intension, Logic, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , | 1 Comment

Information = Comprehension × Extension • Selection 5

Peirce now turns to his example of a conjunctive term, which he uses to show the connection between iconic reference and abductive inference. A similar line of thought may be gone through in reference to hypothesis.  In this case we … Continue reading

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Inquiry, Intension, Logic, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , | 3 Comments