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Philosophy 115 Lecture 1 What is Critical Reasoning? By David Kelsey
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Getting Started <ul><li>Before we begin the lecture let’s discuss the course syllabus. </li></ul><ul><li>Things to consider: </li></ul><ul><ul><li>Contact information </li></ul></ul><ul><ul><li>Course requirements </li></ul></ul><ul><ul><li>Academic dishonesty </li></ul></ul><ul><ul><li>The lecture schedule </li></ul></ul>
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Course Objectives <ul><li>Thinking Rationally : We will learn how to think correctly or rationally or logically. </li></ul><ul><ul><li>For someone to think rationally just means that she, from her set of beliefs, makes inferences that are justified given the laws of logic. </li></ul></ul><ul><li>Challenging others : And in learning how to think rationally we will also learn how to challenge others when they aren’t thinking rationally. </li></ul><ul><ul><li>And so we will learn how to challenge the inferences that other people make. </li></ul></ul><ul><ul><ul><li>Iraq example : the inference your friend makes in arguing that the war in Iraq is justified, or the inference made on the Television or the Newspaper advertisement. </li></ul></ul></ul><ul><ul><li>The laws of logic : And we will learn the laws of logic so that we know just which inferences are justified. </li></ul></ul>
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The Laws of Logic <ul><li>The laws of logic: dictate just which inferences we can make. </li></ul><ul><ul><li>They are rules for making good inferences. </li></ul></ul><ul><ul><li>Modus Ponens : the law Modus Ponens says that if P is true and if it is true that if P is true then Q is true it follows that Q is true as well. </li></ul></ul><ul><ul><li>Modus Tollens : says that if Q is false and if it is true that if P is true then Q is true it follows that P is false . </li></ul></ul><ul><ul><li>Sentence letters: Note here that ‘P’ and ‘Q’ are sentence letters. We use Capitalized letters like ‘P’ and ‘Q’ to stand for sentences. </li></ul></ul><ul><ul><ul><li>Thus, we might, instead of writing out the sentence ‘All ravens are black’ write ‘P’. </li></ul></ul></ul><ul><ul><ul><li>In this case ‘P’ stands for ‘All ravens are black’. </li></ul></ul></ul><ul><ul><ul><li>Looking back at Modus Ponens: </li></ul></ul></ul><ul><ul><ul><ul><li>Let P stand for the sentence ‘It rains’ and Q stand for the sentence ‘I will get wet’. </li></ul></ul></ul></ul><ul><ul><ul><ul><li>In this case Modus Ponens tells us that if it really is raining and if it is true that if it is raining then I will get wet I can infer that I will get wet. </li></ul></ul></ul></ul>
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Inferences <ul><li>An inference: a statement that follows from one or more other statements. </li></ul><ul><ul><li>To say that one statement follows from one or more other statements is to say that one can infer the first from the second. </li></ul></ul><ul><ul><li>In this case the first statement is the inference made. </li></ul></ul><ul><li>The Verb : Notice that by inferring one statement from another one is performing the action of inferring. </li></ul><ul><ul><li>Thus, the word ‘infer’ is a verb. </li></ul></ul><ul><li>The noun: On the other hand, when one infers a statement P from another Q, P is the inference made. </li></ul><ul><ul><li>In this case, the word ‘inference’ is a noun. </li></ul></ul>
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Inferences #2 <ul><li>Deductively Inferred: If one is able to infer a statement P from another Q under the condition that given Q is true so must be P she has deductively inferred P from Q. </li></ul><ul><li>In this case P is a deductive inference . </li></ul><ul><ul><li>A deductive inference is a statement, P, the truth of which is guaranteed by another statement Q. </li></ul></ul><ul><li>Inductively Inferred: In some cases, one is able to infer P from Q under the condition that given Q is true P is only likely to be true. </li></ul><ul><ul><li>In this case one has inductively inferred P from Q. </li></ul></ul><ul><ul><li>And in this case P is an inductive inference . </li></ul></ul><ul><li>An inductive inference: a statement P the likelihood of which is guaranteed by another statement Q. </li></ul>
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Inferences #3 <ul><li>Making an inference: One can make an inference to a statement P from another Q, when Q supports the truth of P. </li></ul><ul><ul><li>For Q to support the truth of P just means that if Q is true this at least weighs in favor of P being true. </li></ul></ul><ul><li>Deductive support: In some cases, Q’s supporting P will mean that if Q is true then P must be true as well. </li></ul><ul><ul><li>Let us call this kind of support ‘Deductive Support’. </li></ul></ul><ul><li>Inductive support: In other cases, Q’s supporting P will mean that if Q is true then P is likely to be true. </li></ul><ul><ul><li>We will call this kind of support ‘Inductive Support’. </li></ul></ul><ul><li>Strength: For cases of Inductive Support. </li></ul><ul><li>Strong Inferences : the more likely P is to be true given Q is true, the stronger the inference made to P is. </li></ul><ul><li>Weak Inferences : And the less likely P is to be true given Q is true, the weaker the inference made to P is. </li></ul><ul><ul><li>5 ravens: say we have seen 5 ravens all of which are black and from this we infer that all ravens are black. </li></ul></ul><ul><ul><li>1 million ravens : Now say we have seen a million ravens all of which are black and from this we infer that all ravens are black. </li></ul></ul><ul><ul><li>The first inference made is much weaker than the second because the support for the first inference is much weaker. </li></ul></ul>
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Statements <ul><li>Inferences & Statements : We learned earlier that an inference is a statement that follows from one or more other statements. </li></ul><ul><ul><li>A statement is a proposition. </li></ul></ul><ul><li>Sentences and Propositions : for any sentence, the meaning of that sentence is some proposition. </li></ul><ul><ul><li>For any word, that word has a meaning. </li></ul></ul><ul><ul><ul><li>For instance, the meaning of the word ‘cat’ is something like 4 legged, mammal that meows. </li></ul></ul></ul><ul><ul><li>Just as words have meanings, sentences have meanings . </li></ul></ul><ul><ul><ul><li>The meaning of a sentence is a proposition. </li></ul></ul></ul><ul><ul><ul><li>The cat is on the mat example : the meaning of the sentence ‘ the cat is on the mat.’ is that the cat is on the mat. </li></ul></ul></ul><ul><ul><ul><li>Walking on the beach example: the meaning of the sentence ‘I walked on the beach today and my girlfriend walked with me’ is that I walked on the beach today and that my girlfriend walked on the beach with me . </li></ul></ul></ul>
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Propositions <ul><li>The form of a proposition : A proposition always comes in the form ‘it is the case that…’. </li></ul><ul><ul><li>What goes in the … is usually just the sentence itself. </li></ul></ul><ul><ul><ul><li>For example, the proposition asserted by the sentence ‘The cat is on the mat’ is just it is the case that the cat is on the mat. </li></ul></ul></ul><ul><ul><li>True and False : Notice too that because the form of a proposition begins with the phrase ‘it is the case that’ a proposition is something that is either true or false. </li></ul></ul><ul><ul><li>The cat is on the mat again : the proposition it is the case that the cat is on the mat is either true or false because either the cat is on the mat or it isn’t. </li></ul></ul>
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Propositions & Sentences <ul><li>A sentence does two different things: it both expresses a proposition and asserts a proposition. </li></ul><ul><li>The expressed proposition : First, a sentence expresses a proposition. </li></ul><ul><ul><li>This expressed proposition is the meaning of the sentence. </li></ul></ul><ul><ul><li>More specifically, the proposition expressed by a sentence is the literal meaning of the words of that sentence. </li></ul></ul><ul><ul><ul><li>The literal meaning of a sentence : the meaning of the words of that sentence alone. Literal meaning excludes any effect that, for example, sarcasm can have on the meaning of a sentence. </li></ul></ul></ul><ul><ul><ul><ul><li>The literal meaning of the sentence ‘you always take out the trash’ is that you always take out the trash. </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Sarcasm: Of course, I might say this in a sarcastic tone and in this case the literal meaning of the sentence is not the actual meaning of the sentence. </li></ul></ul></ul></ul>
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Expressing a proposition <ul><li>For a sentence to express a proposition : </li></ul><ul><ul><li>is for that sentence to toss the proposition up in the air, so to speak. </li></ul></ul><ul><ul><li>It is to put the proposition up for usage. </li></ul></ul><ul><li>Knowing what proposition a sentence expresses is often quite easy. </li></ul><ul><ul><li>If the sentence contains no connectives such as ‘&’, ‘or’, ‘but’ or ‘if…then’ then we just attach the phrase ‘it is the case that’ to the front of the sentence. </li></ul></ul><ul><ul><ul><li>For example, the proposition expressed by the sentence ‘I went to the store’ is just: it is the case that I went to the store . </li></ul></ul></ul><ul><ul><li>Knowing what proposition a sentence expresses if it contains connectives can be a bit trickier. </li></ul></ul><ul><ul><ul><li>Let us just say for now that finding this proposition is a similar process to the one above. </li></ul></ul></ul>
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The asserted Proposition <ul><li>Making use of a proposition: A sentence also makes use of the proposition (the one it expresses) some how. </li></ul><ul><ul><li>Just how a sentence makes use of the proposition it expresses determines it’s actual or intended meaning. </li></ul></ul><ul><li>The actual or intended meaning of a sentence: what the speaker or writer of the sentence means when she writes or says it. </li></ul><ul><ul><li>This is the same meaning, hopefully, as what the reader or listener of the sentence understands it to mean. </li></ul></ul>
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Asserting a proposition #2 <ul><li>Assertion : The actual or intended meaning of a sentence is what is asserted by the words of the sentence. </li></ul><ul><ul><li>Thus, the proposition asserted by a sentence is its actual or intended meaning. </li></ul></ul><ul><li>Declaration : For a sentence to assert a proposition is simply for the sentence to declare of the proposition that it is the case. </li></ul><ul><ul><li>Take a declarative sentence, for instance ‘the cat is on the mat and the cat is orange’. </li></ul></ul><ul><ul><ul><li>This sentence expresses the proposition that the cat is on the mat & that the cat is orange . </li></ul></ul></ul><ul><ul><ul><li>The sentence also asserts that it is the case that the cat is on the mat and the cat is orange. </li></ul></ul></ul><ul><ul><ul><li>Thus, the actual meaning of the sentence is that the cat is on the mat and that it is orange. </li></ul></ul></ul>
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Sarcasm <ul><li>Other kinds of sentences : Besides declarative sentences, there are other kinds of sentences and so other ways in which sentences make use of the propositions they express. </li></ul><ul><li>Sarcasm : </li></ul><ul><ul><li>The messy roomate : One might say, referring to your very messy roommate: “She always takes out the trash”. </li></ul></ul><ul><ul><li>This sentence expresses: the proposition that the roommate always takes out the trash. </li></ul></ul><ul><ul><li>But the sentence asserts: that it is not the case that she always takes out the trash. </li></ul></ul><ul><ul><ul><li>Thus, the actual meaning of the sentence is that it isn’t the case that she always takes out the trash. </li></ul></ul></ul>
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The laws of logic <ul><li>The laws of logic: are rules for making a correct inference P given a certain set of propositions Q 1-n . </li></ul><ul><ul><li>For example, we might believe both the proposition that Socrates is a man and the proposition that all men are mortal . </li></ul></ul><ul><ul><li>The laws of logic tell us that from these propositions we can infer the other proposition that Socrates is mortal . </li></ul></ul><ul><li>Arguments: And when we have one proposition (such as that Socrates is mortal) inferred from one or more other propositions (such as that Socrates is a man & that all men are mortal) we have an argument. </li></ul><ul><ul><li>An argument is any instance in which an asserted proposition is supported by one or more others. </li></ul></ul><ul><ul><li>We might also say that we have an argument when we have one asserted proposition supported by reasons for the truth of that proposition. </li></ul></ul>
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Arguments <ul><li>Argument: can also be defined as a position supported by reasons for its truth. </li></ul><ul><ul><li>To take a position: is to make or declare a claim, which is just to assert a proposition. </li></ul></ul><ul><ul><ul><li>To take a position entails taking a side or stand on an issue. </li></ul></ul></ul><ul><ul><ul><li>It is to choose between two sides of an issue and then assert of one of those sides, your position, that it is true. </li></ul></ul></ul><ul><ul><li>An issue: is what is raised when one considers whether or not a proposition is true. </li></ul></ul><ul><ul><ul><li>Thus, for any issue one can claim that it is true or that it is false. These are the two sides of an issue . </li></ul></ul></ul>
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Issues <ul><li>Issues: What is raised when a proposition is in doubt or in question. </li></ul><ul><ul><li>Questions: we might go as far as to say that an issue just is a question. </li></ul></ul><ul><ul><li>Intelligent life: we might, for instance, consider the issue of whether there is intelligent life in the universe outside of Earth and we might take the position that yes there is such intelligent life in the universe. </li></ul></ul><ul><ul><li>Safety belt law : Or we might ask whether the safety belt law is just and we might take the position that it isn’t. </li></ul></ul><ul><ul><li>Mac vs. Pc: Or we might ask whether Macintosh computers are better than PCs and we might hold the position that Mac’s are better. </li></ul></ul>
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Arguments & Positions <ul><li>Arguments & Positions: so when we take a position on an issue and support it with reasons we have given an argument. </li></ul><ul><ul><li>Intelligent life: we give an argument if we hold that there is intelligent life in the universe outside Earth and we support this position with the reason that, say, evolution plus the DRAKE equation show that there is such intelligent life. </li></ul></ul><ul><ul><li>Safety Belt law: Or we might claim that the safety belt law is unjust because of a person’s right to control what happens in and to her body. </li></ul></ul><ul><ul><li>Mac vs. Pc: Or we might claim that Mac’s are better than PC’s and give as a reason for our claim that Mac’s are much more user friendly than PC’s. </li></ul></ul>
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Conclusions & Premises <ul><li>An argument: is an attempt to support an asserted proposition by providing a reason or reasons for accepting it. </li></ul><ul><ul><li>The conclusion of an argument is the proposition that is being supported. </li></ul></ul><ul><ul><li>The premises of an argument are the supporting propositions. </li></ul></ul><ul><ul><li>So If we argue that because Socrates is a man and all men are mortal that Socrates is mortal: </li></ul></ul><ul><ul><ul><li>the premises of the argument are 1) that Socrates is a man and 2) that all men are mortal </li></ul></ul></ul><ul><ul><ul><li>the conclusion is 3) that Socrates is mortal. </li></ul></ul></ul><ul><ul><li>And if we argue that if it rains I will get wet and that it does in fact rain so I will get wet: </li></ul></ul><ul><ul><ul><li>The premises of the argument are 1) that if it rains I will get wet and 2) it rains </li></ul></ul></ul><ul><ul><ul><li>The conclusion is 3) that I will get wet. </li></ul></ul></ul>
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What an argument isn’t <ul><li>What an argument isn’t : Let us be a bit clearer about what an argument is by stating what it isn’t. </li></ul><ul><ul><li>Not a Fight: By argument, we do not mean the kind of fight you have with your girlfriend. A disagreement is different from an argument. </li></ul></ul><ul><ul><li>Not Persuasion : By argument we do not mean an attempt at persuasion. </li></ul></ul><ul><ul><ul><li>Consider an ad for toothpaste: </li></ul></ul></ul><ul><ul><ul><ul><li>Although this ad is attempting to persuade you to buy the toothpaste it needn’t be an argument. </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Instead, the ad might make use of some rhetorical technique in its attempt at persuasion. </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Rhetorical techniques make use of the emotive power of words to persuade. </li></ul></ul></ul></ul>
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Persuasion <ul><li>Persuasion vs. Argument : You must be careful not to confuse persuasion for an argument. </li></ul><ul><ul><li>An argument proves a point . </li></ul></ul><ul><ul><ul><li>It offers support for some claim, its conclusion. </li></ul></ul></ul><ul><ul><li>Persuasion needn’t offer any support for a point. </li></ul></ul><ul><ul><ul><li>Not Logic: It merely attempts to get you to believe a point. </li></ul></ul></ul><ul><ul><ul><ul><li>This attempt needn’t be one through logic though. </li></ul></ul></ul></ul><ul><ul><ul><li>Persuasion through rhetoric : Persuasion can come through the psychological or rhetorical power of words. </li></ul></ul></ul><ul><ul><ul><ul><li>Words can be used to disgust us, enrage us, scare us, flatter us, make us jealous, confuse us or mislead us. </li></ul></ul></ul></ul><ul><ul><ul><li>Rhetoric: is “a broad category of linguistic techniques people use when their primary objective is to influence beliefs and attitudes and behavior” (M&P, 118.) </li></ul></ul></ul><ul><ul><ul><ul><li>For example, my using the rhetorical technique of claiming a democrat is a left wing liberal isn’t an argument for that claim. </li></ul></ul></ul></ul>
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Arguments vs. Explanations <ul><li>Arguments vs. Explanations : Neither, by argument, do we mean an attempt to explain. </li></ul><ul><ul><li>Explanation of X: If one gives an explanation about some thing X, one gives some details about X with the hope of coming to better understand X. </li></ul></ul><ul><ul><ul><li>An explanation might specify how something works or what caused something to occur. </li></ul></ul></ul><ul><ul><ul><li>Fixing a flat tire: to explain how to fix a flat tire is entirely different from arguing that your method of fixing the flat is an efficient one. </li></ul></ul></ul>
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Recognizing Arguments <ul><li>Conclusion Indicators: when we read or listen to an argument we can find its conclusion by looking or listening for particular words called conclusion indicators. </li></ul><ul><ul><li>Examples of Conclusion Indicators: therefore, hence, thus, so, it follows that, consequently & accordingly. </li></ul></ul><ul><ul><li>Examples in arguments : </li></ul></ul><ul><ul><ul><li>Murderers deserve to die. Thus, capital punishment is permissible. </li></ul></ul></ul><ul><ul><ul><li>Given Saddam Hussein’s crimes against his people, it follows that the U.S. invasion of Iraq was justified. </li></ul></ul></ul><ul><li>Premise Indicators : when we read or listen to an argument we can find its premises by looking or listening for particular words called premise indicators. </li></ul><ul><ul><li>Examples of Premise Indicators : because, since, given, for & this is implied by. </li></ul></ul><ul><ul><li>Examples in argument: </li></ul></ul><ul><ul><ul><li>Since seatbelts save lives, the seatbelt law is justified. </li></ul></ul></ul><ul><ul><ul><li>Mac’s are better than PC’s because they are more user-friendly. </li></ul></ul></ul>
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An introduction to formalizing an argument <ul><li>Challenging an argument : when we read or listen to an argument we must learn not to just accept the argument. </li></ul><ul><ul><li>We must question and challenge the argument. </li></ul></ul><ul><ul><li>In challenging the argument you must first formalize it. </li></ul></ul><ul><li>Formalizing an argument: </li></ul><ul><ul><li>Let us define, for now, the formalization of an argument in a very broad sense. </li></ul></ul><ul><ul><li>The formalization of an argument is the reconstruction of that argument in its most simplified form. </li></ul></ul><ul><ul><li>Read: In simplifying the form of an argument one must first read the text the argument is written in. </li></ul></ul><ul><ul><li>Write: One must write down each premise of the argument and then its conclusion. </li></ul></ul><ul><ul><ul><li>We must write down both explicit and implicit premises. </li></ul></ul></ul>
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Explicit Premises <ul><li>Explicit premises: are premises that are asserted by the words of the text. </li></ul><ul><ul><li>These premises are made explicit by the text. </li></ul></ul><ul><ul><li>Simplification : Note that although these premises needn’t be inferred from the text, they sometimes are simplified in the formalization of the argument. </li></ul></ul><ul><ul><ul><li>Thus, in our formalizations we don’t always write down explicit premises exactly as they look in the text. </li></ul></ul></ul>
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Implicit Premises <ul><li>Implicit or unstated premises: are entailed by the words of the text. </li></ul><ul><ul><li>For one claim Q to be entailed by another P it must be the case that if P is true so is Q. </li></ul></ul><ul><ul><li>We can symbolize this by writing: </li></ul></ul><ul><ul><ul><li>P Q </li></ul></ul></ul><ul><li>Implicit premises again: To put it another way, an implicit premise is a premise that isn’t explicitly stated in the text. </li></ul><ul><ul><li>Inferred: Instead, the premise is inferred from what is written in the text. </li></ul></ul><ul><ul><li>As stated on page 243: you must ask of the argument: “Is there a reasonable assumption I could make that would make this argument valid?” </li></ul></ul><ul><ul><li>Bloodhound example: </li></ul></ul><ul><ul><ul><li>Moore’s dog is a bloodhound, so it has a keen sense of smell </li></ul></ul></ul><ul><ul><ul><li>This argument includes the implicit premise that all bloodhounds have a keen sense of smell . </li></ul></ul></ul>
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Factual claims <ul><li>Arguments and Claims : </li></ul><ul><ul><li>So an argument consists of a number of propositions some of which are premises and one of which is the conclusion. </li></ul></ul><ul><ul><li>Asserting a Proposition : When one asserts a proposition she makes a claim. </li></ul></ul><ul><ul><li>There are different kinds of claims though. </li></ul></ul><ul><li>Factual Claims are claims that are either true or false. </li></ul><ul><ul><li>Methods: there are established methods for determining the truth or falsity of factual claims. </li></ul></ul><ul><ul><li>Criteria : there are generally accepted criteria or standards upon which the claim can be judged. </li></ul></ul><ul><ul><li>Disagreement: f two folks disagree about the claim there is a means of settling the issue. </li></ul></ul><ul><ul><li>Water is H2O : the claim ‘water is H2O’ is a factual claim. </li></ul></ul><ul><ul><ul><li>It is either true or false. </li></ul></ul></ul><ul><ul><ul><li>It happens to be true and we know this because of what science has told us about the molecular structure of water. </li></ul></ul></ul>
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Non-factual claims <ul><li>Non-factual claims : </li></ul><ul><ul><li>Methods: there are no established methods for determining the truth or falsity of a non-factual claim. </li></ul></ul><ul><ul><li>Disagreement: If two folks disagree about a non-factual claim there is no means of settling the dispute. </li></ul></ul><ul><ul><li>Some examples : </li></ul></ul><ul><ul><ul><li>That monster truck rally was beautiful. </li></ul></ul></ul><ul><ul><ul><li>Wearing sandals with socks is cool. </li></ul></ul></ul><ul><ul><ul><li>That Jeff Foxworthy is funny. </li></ul></ul></ul>
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Value Claims <ul><li>Value claims: are non-factual claims that assert that some moral property such as Rightness (or goodness or wrongness,) is instantiated in some object or action or event. </li></ul><ul><ul><li>A property is a way that something can be. </li></ul></ul><ul><ul><ul><li>For instance, the property of being grey is a way that a table can be. </li></ul></ul></ul><ul><ul><ul><li>And if being grey is a way that the table is, then the property of being grey is instantiated in the table. </li></ul></ul></ul><ul><ul><li>A moral property is any way that something can be morally. </li></ul></ul><ul><ul><ul><li>Examples: Goodness, rightness, wrongness and evil-ness. </li></ul></ul></ul><ul><ul><ul><ul><li>Thus, ‘Donating 1000$ to the Red Cross is the right thing to do’ is a value claim. </li></ul></ul></ul></ul><ul><li>Why worry about factual & Non-factual claims : So why talk about these kinds of claims at all? </li></ul><ul><ul><li>Never Ought from Is: If the conclusion of an argument is a non-factual claim then at least one of its premises must be a non-factual claim. </li></ul></ul><ul><ul><ul><li>Thus, we cannot go from purely factual claims in the premises of an argument to a non-factual claim in its conclusion. </li></ul></ul></ul>
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Subjectivism and Relativism <ul><li>Subjectivism : the view that just as two people can be correct in their contrary opinions about a non-factual claim, two people can be correct in their contrary opinions about a factual claim. </li></ul><ul><ul><li>But this view is False. </li></ul></ul><ul><ul><li>Consider ‘ Water is H2O’ . </li></ul></ul><ul><ul><ul><li>If I believe this false and you believe it true only one us is correct: you. </li></ul></ul></ul><ul><ul><li>Or ‘I am 5 feet 10 inches tall’ . </li></ul></ul><ul><ul><ul><li>This is either true or false, case closed! </li></ul></ul></ul><ul><li>Relativism is the view that two different cultures can be correct in their contrary opinions about a factual issue. </li></ul><ul><ul><li>This view is wrong for the same reasons subjectivism is. </li></ul></ul><ul><li>True & False: And if either of these views is correct then propositions can be both true and false. </li></ul><ul><ul><li>But then the premises and conclusions of arguments can be both true and false. </li></ul></ul><ul><ul><li>Wrong inferences: if this is the case then our system of logic will incorrectly prescribe the wrong inferences. </li></ul></ul><ul><li>Thus, for the purposes of this class, both Subjectivism and Relativism are taken to be false. </li></ul>
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