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29 Cards in this Set
- Front
- Back
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What are the four names that are used to label Modern Logic?
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Non-syllogistic logic
Propositional Logic Logic of Connectives Truth-Functional Logic |
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Why is Modern Logic sometimes called Propositional logic?
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modern logic is sometimes called proositional logic because the component from which everything is built is the proposition in modern logic
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what is the component from which everything is built in Aristotelian logic?
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the terms
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Why is modern logic sometimes referred to as the Logic of Connectives?
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Modern logic is sometimes referred to as the Logic of Connectives because it deals with how the propositions connect and how simple propositions become compound.
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Why is modern logic sometimes referred to as truth-functional logic?
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modern logic is sometimes called truth-functional logic because Truth-function is a compound statement whose overall truth is determined solely and completely by the analysis of its parts. It is also a sense of complete thinking.
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who were the three key peop[le at the turn of the twentieth century who were the main developers of modern logic?
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Frege
Russell Wittgenstein |
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Why is modern logic sometimes called non-syllogistic?
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because the syllogism was not complex enough for the modern society. They abandoned it because they needed diversity.
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What are the four ways in which propositions can connect?
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propositions can connect through disjunction, conjunction, implication, and equivalence.
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What is the operator that goes along with the four connectives?
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negation
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What is disjunction?
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q or r
this or that alternative relations |
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What is conjunction?
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conjunction is this and that q and r, is is conjoining and bringing together
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what is implication?
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implication is: if q, then r. if this, then that. It includes hypothetical phrases.
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What is equivalence?
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equivalence is q is the same as r. q is equivalent to r
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What is negation?
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Not p, it is false that p
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What does the operator (negation) do?
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the operator gets applied to the four connections.
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what do p, q, r, etc. indicate
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each one refers to a simple statement.
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What are examples of ambiguities in the connectives and operator?
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ambiguities arise in language, so it leads to the need for symbols. For example, in a disjunction (this or that), the word "or" can sometimes mean "both" and sometimes mean "either one but not both" There is an exclusive "or": one or the other/ and there is an inclusive "or": Both or All.
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What is the symbol for a disjunction?
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a disjunction is labelled using a wedge, which just looks basically like a v.
p v q means p or q (loosely) |
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What is the symbol for a conjunction?
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A conjunction means q and r. It is represented by a dot. So, q (dot) r means q and r
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what is the symbol for an implication?
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the symbol for an implication is a horseshoe. It is a sideways "U" with the opening pointed toward the left. So, q (horseshoe) r means if q, then r.
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what is the symbol indicating an equivalence?
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an equivalence means q is the same as r
it is indicated by a triple bar. Therefore, q (triple bar) r means q is the same as r or q is equivalent to r. |
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what is the symbol that indicates a negation?
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A tilde indicates a negation, which means not p or it is false that p. it would look like this: ~p.
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What are the three things that truth tables provide?
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truth tables give us the precise meaning of the connectives, an understanding of the kinds of propositions that make up arguments, and help us to determine the validity of arguments.
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how is the horseshoe different from the other three connectives>?
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the horseshoe is different because it has an unequal balance of the sides. For example, you cannot switch the two "clauses" if you know what I mean :)
For example, the sun is shining and the games went on as scheduled is a conjunction. To provide an implication, it would be: The sun is shining, so the game is still on. To switch the conjunction around would be to say, the game is still on and the sun is shining. You cannot turn the implication around and get the same meaning. For example, you cannot rightfully say "The game will go on as scheduled, so the sun is shining.. If you passed the test, then you studied. |
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What is the common eleent that allows the determination of the true combinations of true and falseness of the implication?
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The knowledge of the fact that they are all false in the same circumstance: when the premise(s) is true and the conclusion is false
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What is a tautology?
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a tautology is a statement that is always true.
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what is a contradiction?
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a contradiction is a statement that is always false.
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what is a contingent?
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a contingent is a statement that is sometimes true and sometimes false.
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What is the relationship between a tautology and a contradiction?
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the relationship is ~ tilde
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