Let us assume that logic cleaves the world at its corners. Then everything can be divided into the logically privileged, that which makes up the corners, and the not logically privileged, that which makes up everything else. Where then does the concept of logical privilege fall? If logical privilege is logically privileged, then it describes it as something that is at the corners, and not the content. But then it must describe not have described […]
Category: logic
Punny Logic
Update 12 Feb: This post had been expanded upon and, after submission, accepted for publication in Analysis published by Oxford University Press. View the final version here. [draft] It is hard to explain puns to kleptomaniacs because they take things literally. On the surface, this statement is a statement of logic, with a premise and conclusion. Given the premise: Kleptomaniacs take things literally. We may deduce the conclusion: It is hard to explain puns to […]
Shaking the Tree
Life often results in situations such that no strategy suggests any further moves. We just don’t know what to do next. In a game of perfect information, where each player knows all the previous moves, this can signal stalemate. Take chess: given both sides know everything that has transpired and have no reason to believe that the opponent will make a mistake, there can come a time when both sides will realize that there are […]
Cynic Argumentation
Many arguments are called ‘cynical,’ but is there anything that is common to them? Is there a general form of cynical argument? One type of cynical argument is a kind of reductio ad absurdem, a proof by contradiction, to discredit a premise. The first step is to take the premise and associate it with some worldview. Assume P. (premise) P holds under worldviews W. (Cynical Generalization) Then, the cynic discredits those worldviews. Worldviews W are […]
An Introduction to the Game Theoretic Semantics view of Scientific Theory
What is a scientific theory? In an abstract sense, a scientific theory is a group of statements about the world. For instance the Special Theory of Relativity has, “The speed of light in a vacuum is invariant,” as a core statement, among others, about the world. This statement is scientific because, in part, it is meant to hold in a ‘law-like’ fashion: it holds across time, space and observer. The Popperian view is that we […]
EIFL (Domainless Logic)
I saw this post by Mark Lance over at New APPS and he brought up one of the issues that I have recently been concerned with: What is a logical domain? He said: So our ignorance of our domain has implications for which sentences are true. And if a sentence is true under one interpretation and false under another, it has different meanings under them. And if we don’t know which of these interpretations we […]
The Paradox of Unreasonability
“You’re being unreasonable!” One or more of you may have had this directed at you. But what does the speaker mean by it? Presumably the speaker believes that the listener is not acting according to some given standard. However, if the speaker had an argument to that effect, the speaker should’ve presented it. Hence, all the above statement means is that the speaker has run out of arguments and has resorted to name-calling: being unreasonable […]
Яandom Logic
If we try to represent tossing a coin or a die, or picking a card out of a deck at random, in logic, how should we do it? Tossing a coin might look like: Toss(coin) → (Heads or Tails) Tossing a die might be: Toss(die) → (1 or 2 or 3 or 4 or 5 or 6) Picking a card: Pick(52 card deck) → (1♣ or 2♣ or … or k♥) This begs asking, do […]
IF Logic and Cogito Ergo Sum
(∃x∃x) → ∃x Descartes Law If something has informational dependence upon itself, then that thing exists. For example, thinking that you are thinking is informationally self dependent and therefore a thinking thing (you) exists.
New Quantifier Angle-I, and Agent Logic
I was thinking that upside down A and backwards E were feeling lonely. Yes, ∀ and ∃ love each other very much, but they could really use a new friend. Introducing Angle I: Now, Angle I, , is just like her friends ∀ and ∃. She can be used in a formula such as ∀x∃yz(Pxyz). But how should we understand what is going on with the failure of the quantified tertium non datur? With that […]