#cspeirce

Differential Propositional Calculus • 10

Special Classes of Propositions (cont.)

Let’s pause at this point and get a better sense of how our special classes of propositions are structured and how they relate to propositions in general.  We can do this by recruiting our visual imaginations and drawing up a sufficient budget of venn diagrams for each family of propositions.  The case for 3 variables is exemplary enough for a start.

Linear Propositions

The linear propositions, may be written as sums:

One thing to keep in mind about these sums is that the values in are added “modulo 2”, that is, in such a way that

In a universe of discourse based on three boolean variables, the linear propositions take the shapes shown in Figure 8.

At the top is the venn diagram for the linear proposition of rank 3, which may be expressed by any one of the following three forms.

Next are the venn diagrams for the three linear propositions of rank 2, which may be expressed by the following three forms, respectively.

Next are the three linear propositions of rank 1, which are none other than the three basic propositions,

At the bottom is the linear proposition of rank 0, the everywhere false proposition or the constant function, which may be expressed by the form or by a simple

Resources

Logic Syllabus
Survey of Differential Logic

cc: Academia.edu • Cybernetics • Structural Modeling • Systems Science
cc: Conceptual Graphs • Laws of Form • Mathstodon • Research Gate

#Amphecks #Animata #BooleanAlgebra #BooleanFunctions #CSPeirce #CactusGraphs #CategoryTheory #Change #Cybernetics #DifferentialAnalyticTuringAutomata #DifferentialCalculus #DifferentialLogic #DiscreteDynamics #EquationalInference #FunctionalLogic #GraphTheory #Hologrammautomaton #IndicatorFunctions #InquiryDrivenSystems #Leibniz #Logic #LogicalGraphs #Mathematics #MinimalNegationOperators #PropositionalCalculus #Time #Topology #Visualization

Pragmatic Maxim • Introduction
• https://inquiryintoinquiry.com/2023/08/07/pragmatic-maxim-2/

The “pragmatic maxim”, also known as the “maxim of pragmatism” or the “maxim of pragmaticism”, is a maxim of logic formulated by Charles Sanders Peirce. Serving as a practical recommendation or regulative principle in the normative science of logic, its function is to guide the conduct of thought toward the achievement of its purpose, advising the addressee on an optimal way of “attaining clearness of apprehension”.

Charles Sanders Peirce
• https://mywikibiz.com/Charles_Sanders_Peirce

Normative Science
• https://mywikibiz.com/Normative_science

#Peirce #Logic #Inquiry #PragmaticMaxim #RequlativePrinciple
#CSPeirce #CharlesSandersPeirce #NormativeScience #Semiotics

Pragmatic Maxim • Et Sic Deinceps
• http://inquiryintoinquiry.com/2023/08/07/pragmatic-maxim-2/

The pragmatic maxim is a guideline for the practice of inquiry formulated by Charles Sanders Peirce. Serving as a practical recommendation or regulative principle in the normative science of logic, its function is to guide the conduct of thought toward the achievement of its purpose, advising the addressee on an optimal way of “attaining clearness of apprehension”.

#Peirce #Logic #Inquiry #PragmaticMaxim #RequlativePrinciple
#CSPeirce #CharlesSandersPeirce #NormativeScience #Semiotics

@Inquiry @Harishjosev

Yes, another version of #CSPeirce's triad is #WRAshby's distinction between #Machine (object, observed phenomenon), #System (a finite set of variables and their relationships selected by the #Observer), and the #Model created by the observer to describe or/and #Control the machine.

However, I was speaking about the different phenomena (machines) and their *controllability*.
Mere #Physical (static or dynamic) #Structures driven by known (discoverable, invariant) #NaturalLaws as opposed to emergent #DynamicalSystems that are under the influence of arbitrary, local #Rules as explained by #HHPattee.

In this new post for the Erraticus Blog, Jon Alan Schmidt was gracious enough to take some time challenging @ironick17 and me on our views of truth and the great chasm that exists between #CSPeirce and #williamjames. #pragmatism #philosophy

https://erraticus.co/2022/11/28/truth-as-pragmatisms-only-hope/

@algersanpin @philosophy "abduction", also know as "retroduction" .... or as the way our knowledge progresses from a prior "what we believe we know" through a scientific process and logic to a posterior "what we believe we know".

I'm curious if the author's take on #pragmatism is in the spirit of #CSPeirce #pragmaticism

@emilyherring

Maybe you should try writing in the way of #CSPeirce ?

De Tienne, André. "The Peirce papers: How to pick up manuscripts that fell to the floor." Text 10 (1997): 259-282.

#CategoryTheory meets #CSPeirce 's notion of Firstness, Secondness and Thirdness.

@emilyherring I would have answered C.S. Peirce #cspeirce