Lecture Notes 2
... That is, each step but the premises has to be justified by a proof rule As we introduce more pieces of FOL, we will introduce more proof rules We’ll start now with proof rules involving identity ...
... That is, each step but the premises has to be justified by a proof rule As we introduce more pieces of FOL, we will introduce more proof rules We’ll start now with proof rules involving identity ...
Truth and Meaning
... position to see that it is probably false, but I do not expect many to agree with me about this. Since the publication of “Meaning and Truth,” truth-conditional semantics has been pretty much all the semantics there is. In the current climate, therefore, it is something of a challenge to get philoso ...
... position to see that it is probably false, but I do not expect many to agree with me about this. Since the publication of “Meaning and Truth,” truth-conditional semantics has been pretty much all the semantics there is. In the current climate, therefore, it is something of a challenge to get philoso ...
Lecture 23 Notes
... The logical truth expressed in the LEM, that for any proposition P either it or its negation, ∼ P , is true can now be explained in terms of constructive evidence that does not refer to truth. Virtual evidence and the constructive impossibility of negative evidence are sufficient semantic grounds fo ...
... The logical truth expressed in the LEM, that for any proposition P either it or its negation, ∼ P , is true can now be explained in terms of constructive evidence that does not refer to truth. Virtual evidence and the constructive impossibility of negative evidence are sufficient semantic grounds fo ...
Reason and Argument Lecture 2: Arguments and Validity
... There may be any number of premisses (0 – infinity) but only ONE conclusion. In an argument it is meant to be the case that the premisses support the conclusion (Lepore says “the conclusion purportedly follows from the premisses”) ...
... There may be any number of premisses (0 – infinity) but only ONE conclusion. In an argument it is meant to be the case that the premisses support the conclusion (Lepore says “the conclusion purportedly follows from the premisses”) ...
Interpolation for McCain
... interpret it in a rather more general sense, and that, so interpreted, it can be seen as a continuation of a well-established tradition. The idea of questions and answers is quite appropriate here. According to Hintikka [1976; 1972], and Harrah [1975] a question can be regarded as denoting its set ...
... interpret it in a rather more general sense, and that, so interpreted, it can be seen as a continuation of a well-established tradition. The idea of questions and answers is quite appropriate here. According to Hintikka [1976; 1972], and Harrah [1975] a question can be regarded as denoting its set ...
PAUL SNOWDON VIRTUAL ISSUE NO. 1 Strawson`s Truth
... think it is true to say that Strawson does not himself really engage head on with this aspect of Austin’s paper, although he picks up some issues connected to it. Now, whatever one’s reactions to these central proposals of Austin’s fairly short paper, it is hard to escape the feeling that the paper ...
... think it is true to say that Strawson does not himself really engage head on with this aspect of Austin’s paper, although he picks up some issues connected to it. Now, whatever one’s reactions to these central proposals of Austin’s fairly short paper, it is hard to escape the feeling that the paper ...
The Compactness Theorem for first-order logic
... When doing calculus, differential equations, mathematical physics, etc. we often pretend that we have infinitesimally small real numbers (we call them things like dx, δ, or ∆y, etc). If you’ve taken a course in mathematical analysis, you’ve probably seen how we can often formalize these types of int ...
... When doing calculus, differential equations, mathematical physics, etc. we often pretend that we have infinitesimally small real numbers (we call them things like dx, δ, or ∆y, etc). If you’ve taken a course in mathematical analysis, you’ve probably seen how we can often formalize these types of int ...
Natural deduction
... • Before going on, let’s consider another example: p → r ⇒ p ∧ q → r – you might wonder, is this really valid? – if so, then this can be checked! try doing a truth-table. Or you can intuitively explain it to yourself like this. “Suppose that the conclusion is false. Then p ∧ q must be true while r i ...
... • Before going on, let’s consider another example: p → r ⇒ p ∧ q → r – you might wonder, is this really valid? – if so, then this can be checked! try doing a truth-table. Or you can intuitively explain it to yourself like this. “Suppose that the conclusion is false. Then p ∧ q must be true while r i ...
CS3234 Logic and Formal Systems
... 6 A Consider an arbitrary propositional formula φ in which say n propositional atoms occur. Let us call these atoms p1 , . . . , pn . In order to construct a corresponding formula in predicate logic, we use the set of predicate symbols P = {IsTrue}, where IsTrue is a unary predicate, and the set ...
... 6 A Consider an arbitrary propositional formula φ in which say n propositional atoms occur. Let us call these atoms p1 , . . . , pn . In order to construct a corresponding formula in predicate logic, we use the set of predicate symbols P = {IsTrue}, where IsTrue is a unary predicate, and the set ...
Chapter 0. Introduction to the Mathematical Method
... Mathematical language has to be uniform (everybody must use it in the same way) and univocal (i.e., without any kind of ambiguity). We start from some initial statements called axioms, postulates and definitions. These elements are not questioned, they are not true or false, they simply are, and the ...
... Mathematical language has to be uniform (everybody must use it in the same way) and univocal (i.e., without any kind of ambiguity). We start from some initial statements called axioms, postulates and definitions. These elements are not questioned, they are not true or false, they simply are, and the ...
Implication - Abstractmath.org
... Pascal does not have variables or expressions of type proposition. It does have Boolean variables, which have TRUE and FALSE as their only possible values. An expression such as ` X
... Pascal does not have variables or expressions of type proposition. It does have Boolean variables, which have TRUE and FALSE as their only possible values. An expression such as ` X