-
Handling variables
The third in a series of posts laying out the process, step by step, of building an interpreter in Ruby for working with propositional logic. In this post, we expand the interpreter to work with variable expressions in classical propositional logic, like
Continue reading …~p & q. Since we are dealing with variable expressions and not fixed expressions (like~T & F), we need to be able to output full truth tables, and not simply resolve the final boolean output. -
An interlude with minitest/autorun
An interlude in a series of posts laying out the process, step by step, of building an interpreter in Ruby for working with propositional logic. In this small post, we take our hand-rolled "tests" and move the code into an executable test script with
Continue reading …minitest/autorun. -
Proper Propositional Logic
The second in a series of posts laying out the process, step by step, of building an interpreter in Ruby for working with propositional logic. In this second post, we expand the interpreter to handle the full range of valid expressions in classical propositional logic.
Continue reading … -
Starting Simple
The first in a series of posts laying out the process, step by step, of building an interpreter in Ruby for working with propositional logic. In this first post, we build an interpreter for working with simple logical expressions and dig into the specifics of the parts of an interpreter as well as the basics of propositional logic.
Continue reading … -
On Antinomies and Paradoxes
Should the central tenets of Christian theology be best understood as antinomies, or paradoxes, or both?
Continue reading … -
Degrees of Separation
When talking about God, I’m not so certain that we have a great understanding of what we can and cannot say properly, or what we can and cannot understand properly.
Continue reading … -
Encoding the Logic of Sets: More on Sets as Procedures
How can procedures be used to encode the logic of both infinite and finite sets?
Continue reading … -
Initial Thoughts on Infinite Sets and Procedures
Is modern mathematics built on a logical fallacy? How ought we to understand infinite sets? What's a procedure? I'm starting to explore these topics as I think through the mathematics and logic of infinity.
Continue reading … -
1 = 0.9999...
In mathematics it is proven that
Continue reading …1 = 0.9999.... How is this so? But more importantly, in understanding how and why this is true, what can we glean about the nature of paradoxes? Let's explore. -
Conjunctive Binarism
What is truth? I'm not sure, but I'm starting to think its
Continue reading …~(P & ¬P). This post introduces what those symbols mean and how they represent my growing idea of Conjunctive Binarism, which is my theory of what truth is.