2.1-2.3: Reasoning in Geometry
... cats freak, then mice frisk. If sirens shriek, then dogs howl. If dogs howl, then cats freak. ...
... cats freak, then mice frisk. If sirens shriek, then dogs howl. If dogs howl, then cats freak. ...
8.3 Conditional Statements and Material Implication
... p, then q.” But it is not the same kind of implication as any of those mentioned earlier. It is called material implication by logicians. In giving it a special name, we admit that it is a special notion, not to be confused with other, more usual, types of implication. Not all conditional statements ...
... p, then q.” But it is not the same kind of implication as any of those mentioned earlier. It is called material implication by logicians. In giving it a special name, we admit that it is a special notion, not to be confused with other, more usual, types of implication. Not all conditional statements ...
Chapter 0 - Ravikumar - Sonoma State University
... • Assertions: Mathematical statement expresses some property of a set of defined objects. Assertions may or may not be true. ...
... • Assertions: Mathematical statement expresses some property of a set of defined objects. Assertions may or may not be true. ...
Proof Theory - Andrew.cmu.edu
... I will assume the reader is familiar with the language of first-order logic. Contemporary logic textbooks often present formal calculi for first-order logic with a long list of axioms and a few simple rules, but these are generally not very convenient for modeling deductive arguments or studying the ...
... I will assume the reader is familiar with the language of first-order logic. Contemporary logic textbooks often present formal calculi for first-order logic with a long list of axioms and a few simple rules, but these are generally not very convenient for modeling deductive arguments or studying the ...
Abstract for ‘Consequentialism’ 1 Inferentialism vs referentialism David Ripley
... While the label is new, views of this sort are not. Consequentialism, in this sense, is adopted by [Restall, 2009] and [Ripley, 2013]. Both of these papers claim that the views they put forward are inferentialist, but this is not in fact the case, if inferentialism is understood as above; neither pa ...
... While the label is new, views of this sort are not. Consequentialism, in this sense, is adopted by [Restall, 2009] and [Ripley, 2013]. Both of these papers claim that the views they put forward are inferentialist, but this is not in fact the case, if inferentialism is understood as above; neither pa ...
Moore`s Paradox and the Context Principle
... principle in circulation is that the meaning of a sentence (or any linguistic sign) is given by its context. Frege’s context principle is often taken to suggest a fact: that the smallest meaning-bearing element of language is ‘the proposition’ (or sentence, Satz). From this fact, it would follow tha ...
... principle in circulation is that the meaning of a sentence (or any linguistic sign) is given by its context. Frege’s context principle is often taken to suggest a fact: that the smallest meaning-bearing element of language is ‘the proposition’ (or sentence, Satz). From this fact, it would follow tha ...
Section 1.3 Predicates and Quantifiers Assume universe of
... coincides with our everyday usage of this term. However, the mathematical meaning of the existential quantifier does not. When we use the word “some” in everyday language we ordinarily mean two or more, in mathematics the word some means “at least one” which is true when there is exactly one. The Ne ...
... coincides with our everyday usage of this term. However, the mathematical meaning of the existential quantifier does not. When we use the word “some” in everyday language we ordinarily mean two or more, in mathematics the word some means “at least one” which is true when there is exactly one. The Ne ...
![overhead 8/singular sentences [ov]](http://s1.studyres.com/store/data/009258618_1-2a98e952bde8fd34c716ae0716ce6df4-300x300.png)
The Significance of "On Denoting"
... words if I had in fact met Jones. It is, after all, the same proposition that would be false in the one case and true in the other. Russell's answer to this sort of difficulty is to say that the proposition in question contains the denoting concept, a man. Similarly, we have also the denoting concep ...
... words if I had in fact met Jones. It is, after all, the same proposition that would be false in the one case and true in the other. Russell's answer to this sort of difficulty is to say that the proposition in question contains the denoting concept, a man. Similarly, we have also the denoting concep ...
Plural Quantifiers
... For just this reason, Quine [3] famously objected that second-order logic was just “set theory in sheep’s clothing.” His point was that if we’re going to be talking about sets, it’s more honest just to make that explicit. (For a useful critical examination of Quine’s charge, see [2].) But there are ...
... For just this reason, Quine [3] famously objected that second-order logic was just “set theory in sheep’s clothing.” His point was that if we’re going to be talking about sets, it’s more honest just to make that explicit. (For a useful critical examination of Quine’s charge, see [2].) But there are ...
A History of the Connectives
... in Mates 1961, 114). Kneale and Kneale take this as accurate (162–163) on grounds that all the basic Stoic inference patterns have two premises. The basic unit of Stoic logic is not the term, as in Aristotle, but the proposition (lecton). A sentence signifies a proposition, a “sayable” that is a bea ...
... in Mates 1961, 114). Kneale and Kneale take this as accurate (162–163) on grounds that all the basic Stoic inference patterns have two premises. The basic unit of Stoic logic is not the term, as in Aristotle, but the proposition (lecton). A sentence signifies a proposition, a “sayable” that is a bea ...
com.1 The Compactness Theorem
... c < k in ∆0 have k < K. If we expand Q to Q0 with cQ = 1/K we have that Q0 |= Γ ∪ ∆0 , and so Γ ∪ ∆ is finitely satisfiable (Exercise: prove this in detail). By compactness, Γ ∪ ∆ is satisfiable. Any model S of Γ ∪ ∆ contains an infinitesimal, namely cS . Problem com.2. In the standard model of arit ...
... c < k in ∆0 have k < K. If we expand Q to Q0 with cQ = 1/K we have that Q0 |= Γ ∪ ∆0 , and so Γ ∪ ∆ is finitely satisfiable (Exercise: prove this in detail). By compactness, Γ ∪ ∆ is satisfiable. Any model S of Γ ∪ ∆ contains an infinitesimal, namely cS . Problem com.2. In the standard model of arit ...
Propositional Logic
... Arguments are made by propositions. A proposition is a declarative sentence, an affirmation of certain facts. Examples: London is the capital of England. Humans are the only animals that use language. Hernán Cortés conquered México. ...
... Arguments are made by propositions. A proposition is a declarative sentence, an affirmation of certain facts. Examples: London is the capital of England. Humans are the only animals that use language. Hernán Cortés conquered México. ...
CLASSICAL LOGIC and FUZZY LOGIC
... collection of elements in X that are strictly true or strictly false. The veracity (truth) of an element in the proposition P can be assigned a binary truth value, called T (P), For binary (Boolean) classical logic, T (P) is assigned a value of 1 (truth) or 0 (false). If U is the universe of all pro ...
... collection of elements in X that are strictly true or strictly false. The veracity (truth) of an element in the proposition P can be assigned a binary truth value, called T (P), For binary (Boolean) classical logic, T (P) is assigned a value of 1 (truth) or 0 (false). If U is the universe of all pro ...
Scoring Rubric for Assignment 1
... argument or is vague and incomplete – components are missing or inaccurate or unclear. Theory is not relevant or only relevant for some aspects; theory is not clearly articulated and/or has incorrect or incomplete components. Relationship between theory and research is unclear or inaccurate, major e ...
... argument or is vague and incomplete – components are missing or inaccurate or unclear. Theory is not relevant or only relevant for some aspects; theory is not clearly articulated and/or has incorrect or incomplete components. Relationship between theory and research is unclear or inaccurate, major e ...