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Chapter 2 part 2

by: Tamina Sabnani

Chapter 2 part 2 Philosophy 09

Tamina Sabnani
Philosophy 09: Intro to Logic
Kyle Robertson

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Here are the notes for the second reading we had for Chapter 2!
Philosophy 09: Intro to Logic
Kyle Robertson
Class Notes
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This 3 page Class Notes was uploaded by Tamina Sabnani on Tuesday October 6, 2015. The Class Notes belongs to Philosophy 09 at University of California - Santa Cruz taught by Kyle Robertson in Fall 2015. Since its upload, it has received 29 views. For similar materials see Philosophy 09: Intro to Logic in PHIL-Philosophy at University of California - Santa Cruz.


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Date Created: 10/06/15
Chapter 2 Part 2 NonTruthFunctional Connectives If a connective sentence is truthfunctional that means there will never have a situation where the sentence is true in one case and false in another and yet the truthvalue of the component sentences is same in both cases Example of NonTruthFunctiona sentence Connective before I had straight A s before I went to school 0 Although the individual atomic sentences I had straight A s and I went to school are true the sentence as a whole is not because before implies that the grades were BEFORE I started school which isn t true p and q are any two sentences just as x and y are any two numbers Statement Variable Has no truthvalue Can be substituted by an actual truth variable statement Ex p and q Lowercase letters represent sentence variables whereas uppercase letters represent actual sentences T T F F This table clearly shows that if there is even one false part of the sentence the whole statement is false The conjunction is only true if both conjuncts are true T F F F 39n I39n I Negation A sentence whose main connective is not no or a similar term Negation can be used to represent the opposite of what was just said Example of Negation This statement is not true T Negation TruthTable T F n This is pretty selfexplanatory whatever is not something is the opposite truth wise Parentheses and brackets are both used in sentence logic in order to separate the sentence s connectives similarly to how one would in a math equation They are interchangeable too The scope of a connective is the component sentences on which the connective operates The more complex sentences need parentheses and brackets Example of Scope A B v C the scope is the entire sentence A B v C WellFormed Formula a sentence where it is clear which operator is the main operator for the sentence and which operators have which component sentences within their scope Wffs usually have parentheses Example of non wff A v B 2 C is NOT a wff because it doesn t make it clear which is the main connec ve A v B 2 C or A v B 2 C IS wff because it s clear which is the main connec ve Main Connectives The main connective is the one you focus on when looking at the sentences Examples of Main Connectives 1 B 2 C 3 2 AvB no N 3 AvB DR 4 AvBEBZC 5 AvBEBC III 2 Use vs Mention Use to use a word to point something else out Ex California is a state in the United States of America Mention to use a word specifically for the purpose of that word Ex California has 10 letters Metalanguage vs Object Language Metalanguage The language we use to talk about another language Example we use English to talk about Sentential language Object language the language we are talking about by using another language Example we are talking about Sentential language using EngHsh Disjunction The use of either or The two sentences being connected by this either or are called disjuncts Exclusive or means that only one or the other options is true Inclusive or means that either one or both of the options are true Example of Exclusive I am going to live to be one hundred or I am not P 0 P q Example of Inclusive I am going to listen to music tonight or tomorrow TruthFunctions for disjunctions P Cl PVC T T T T F T F T T F F F INCLUSIVE or sentences are mostly represented using or a wedge EXCLUSIVE or sentences are mostly represented using T F v F T


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