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Logic Unit 1.pdf

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University of Toronto St. George
Niko Scharer

UNIT 1 REASON AND ARGUMENT 1.1 WHAT IS MODERN SYMBOLIC LOGIC? Logic. The Study & Evaluation of Reasoning & Argument An argument probably seems logical if it look likes the conclusion must be true, based on what you are told is the case and what you already know to be true. This is because logical deductive arguments are truth-preserving: if the premises are true, then the conclusions must be true. Studying logic can help you recognize which arguments are good ones, and thus improve your ability to distinguish truths or probable claims from ones that are poorly supported by the evidence. Symbolic. Use Tidy Symbols instead of Messy Words! Using symbols instead of words lets you to focus on the logical form of the argument, so you can evaluate the reasoning of the argument without being distracted by other considerations, e.g. whether you agree with it, whether it‟s interesting or has true premises, etc. Symbolization also can clear up ambiguities in meaning. Sometimes sentences, phrases and words can be interpreted different ways. Symbolization can force you to be more precise and consider exactly what is meant. Modern. After such people as ...  Aristotle (384-322 BC). Aristotelian or syllogistic logic is the earliest system intended to classify and evaluate a wide range of arguments.  Chrysippus (c.280-c.205 BC) developed a system of propositional logic that anticipates modern logic.  Gottfried Wilhelm Leibniz (1646-1716), perhaps the father of symbolic logic, developed some of the first logical calculi.  Gottlob Frege (1848-1925) laid foundations for mathematical logic, further developed by Alfred North Whitehead (1861-1947) and Bertrand Russell (1872-1970) in their Principia Mathematica. Logic Unit 1: Introduction ©2011 Niko Scharer 1.2 WHAT IS AN ARGUMENT? In philosophy, logic, essays and many other contexts, arguments are bits of reasoning which present justifications for certain statements – a conclusion (a statement, opinion, thesis, etc.) supported by a justification or evidence. An argument is a discourse in which some statements (the premises) are presented in support of another statement (the conclusion). In a valid deductive argument, the logical structure of that discourse is such that if the premises are true, then the conclusion * must also be true. It is truth-preserving! Two parts of an Argument Premises or assumptions: reasons or justification for the conclusion. Conclusion: the statement, thesis or opinion being argued for. Premises and conclusions are sentences, statements or propositions that can be true or false – they have truth-value. Arguments are generally composed of statements and usually don‟t include questions, commands and other sentences without truth-value. „Premise‟ and „conclusion‟ are relative terms. The same sentence can serve as a premise in one argument and as the conclusion in another. STRUCTURE OF AN ARGUMENT This argument (center) is in standard form. The premises are stated above a horizontal line, and the conclusion is stated below. The argument is presented on the right in symbolic form. Premise If you will study then you will pass. S  P Premise You will study. S Conclusion Therefore, you will pass.  P *This and other illustrations are the property of Gerald Grow, Professor of Journalism, Florida A&M University, and are here by his permissiohttp://www.longleaf.net/ggrow/CartoonPhil.html Logic Unit 1: Introduction 2 ©2011 Niko Scharer 1.3 IDENTIFYING THE ARGUMENT What to look for ... Signs of Reasoning or Inference Indicators Some words or phrases at the beginning of sentences or clauses tell us that the sentence or clause is part of an argument. Some introduce premises (premise indicators) and others introduce conclusions (conclusion indicators). Premise Indicators: words or phrases showing that the sentence or clause is being given in support of a conclusion, as reason or justification. because as indicated by being that since in the first place inasmuch as as you can see from may be inferred from for seeing that can be deduced from as shown by for the reasons that whereas follows from assuming that on account of Conclusion Indicators: words or phrases showing that the sentence or clause is the conclusion for which reasons or justification will be given. therefore accordingly we can conclude that thus consequently we can deduce that so as a result proves that hence it follows that shows that then for this reason we see that indicates that in conclusion it can be inferred that this makes it clear that BE CAREFUL – THINK ABOUT HOW WORDS ARE BEING USED! Inference indicators are just words and words perform different functions in different contexts. In arguments, words like “because,” “for,” “thus,” and “then” are often inference indicators. But, in explanations, descriptions, or even in arguments, they perform many other functions. Consider the different ways that „since‟ can be used: I realize that I haven‟t seen my cousin since we were kids. Since I was sick, I have to turn my essay in late. Clearly Sam will win since he has the support of the party. In the third sentence „since‟ acts as a premise indicator, introducing a reason for accepting the conclusion (that Sam will win). In the other sentences, „since‟ is not a premise indicator. In the first, it introduces a clause that provides information; in the second sentence, it introduces an explanation. Logic Unit 1: Introduction 3 ©2011 Niko Scharer 1.4 PUTTING ARGUMENTS IN STANDARD FORM When you are analyzing a piece of writing think about what the piece as a whole is trying to do. If you think that there is an argument, start by picking out the main conclusion (the conclusion indicators may help with that). Then, try to use the premise indicators to pick out the premises from other bits of writing (elaborations, illustrations, explanations, filleThink it through! When you present it in standard form, only state the premises and conclusion (leave out inference indicators and other filler). State the premises first, putting them in logical order and starting each one on a new line. Then draw a line. After the line, state the conclusion. You may want to put a therefore sign () before the conclusion. Three Easy Steps! State the premises. Draw a line. Then state the conclusion. EXAMPLE Extract the argument and rewrite it in standard form: Either Professor Plum or the butler committed the murder. But, as everybody knows, no sane person would commit murder without some sort of a motive. So it has to be the Professor. After all, not only is the butler sane but he couldn‟t possibly have had a motive to kill him. This argument has a clearly indicated conclusion, introduced by „so‟. “…it has to be the Professor.” After that, it is just a matter of identifying the premises. The first and second sentences are both premises. The last sentence has a premise indicator, „after all,‟ introducing “not only is the butler sane.” And the last premise is that the butler did not have a motive to kill the victim. Either Professor Plum committed the murder or the butler committed the murder. No sane person commits murder without a motive. The butler is sane. The butler had no motive to commit the murder.   Professor Plum committed the murder. Logic Unit 1: Introduction 4 ©2011 Niko Scharer A few more to try: In each of the following, extract the argument and rewrite it in standard form: 1.4 E 1 Some students will undoubtedly pass this course. Hence it is clear that some students in this class will do the exercises, since nobody passes who doesn‟t do at least some of the exercises. 1.4 E 2 Anybody who smokes is irrational. Any rational person knows that smoking can kill you, and engaging in an activity that can kill you is suicide! No rational person commits suicide. 1.4 E 3 If I study, I won‟t have much free time in which to party. On the other hand, if I don‟t study, my parents will cut off my funds. Without parental funds I‟m not going to be going out much at all. So it looks like there won‟t be any partying for me. 1.4 E 4 At some point in the far distant past, the universe came into existence. But nothing can come from nothing; nothing can come into existence unless there is something to create it. Accordingly, there must be a God – a first creator, outside time. This follows from the fact that there must exist, outside the universe, some being that caused the universe to exist. Such a being must not have been created at all, unless there was some greater being that caused it that creator to exist, and hence this being would be the first creator. 1.4 E 5 Some people think that Ms. Peacock murdered Mr. Green, but that is wrong! It‟s evident that Ms. Peacock could not have murdered Mr. Green unless the murder occurred in the library. Yet, there were signs of struggle and drops of blood in the dining room, indicating that the murder occurred there and not in the library where the body was found. 1.4 E 6 I realized, as I lay in bed thinking, that we are not responsible for what we do. This is because either determinism or indeterminism must be true. If determinism is true, we cannot do other than we do. If so, we are but puppets on strings – our actions are not free. If indeterminism is true, then human actions are random, and hence not free. If our actions are not free, it must be conceded that we are not responsible for what we do. 1.4 E 7 From the way that people act, it would seem that some people desire power. It is true that all people desire what is good, and that nobody desires what is evil. So if people do desire power then it must be good. Yet, power leads to corruption and nobody can deny that corruption is evil. So power cannot be desired for it‟s own sake. Those who think they want power are mistaken, and rarely attain what they truly desire when they act to obtain power. Logic Unit 1: Introduction 5 ©2011 Niko Scharer 1.5 SENTENCES AND TRUTH-VALUE Many sentences (i.e. statements or propositions) are either true or false at some particular time and place. Such sentences have a truth-value. Not all sentences have truth-value. Questions, commands, exclamations, proposals and requests are neither true nor false, and have no truth-value. True sentences have truth-value T. False sentences have truth-value F. These sentences have truth-value T (they are true) Ottawa is the capital of Canada. The volume of fixed mass of gas is proportional to its temperature at a fixed pressure. The last living passenger pigeon was named Martha. These sentences have truth-value F (they are false) Toronto is the capital of Canada. The volume of a gas is inversely proportional to its temperature. A foreign oil company official wants to transfer millions of dollars into your bank account. These sentences have no truth-value: Take me to your leader! (An order or imperative sentence) What planet are you from? (A question or interrogatory sentence) Gee willikers! (An exclamation or exclamatory sentence) In the arguments that we will be looking at, each sentence of the argument must have a truth-value – it must be a statement. In real life, arguments often have imperatives for conclusions. If you don‟t do the homework you‟ll fail the course. You don‟t want to fail the course.  Therefore, do the homework! Logic Unit 1: Introduction 6 ©2011 Niko Scharer 1.6 IS IT A GOOD ARGUMENT? VALIDITY AND SOUNDNESS Different kinds of a
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