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Logic reasons and reasoning George Matthews CC 2016 Licensed under the Creative Commons attribution license.

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theoretical reasons

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theoretical reasons reasons to believe

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theoretical reasons reasons to believe ! My senses may tell me that the sun moves across the sky.

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theoretical reasons reasons to believe ! My senses may tell me that the sun moves across the sky. ! But what is really going on here – what should I believe?

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theoretical reasons reasons to believe ! My senses may tell me that the sun moves across the sky. ! But what is really going on here – what should I believe? ! Whatever is based on the best available evidence.

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practical reasons

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practical reasons reasons to act

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practical reasons reasons to act ! My impulses tell me to scream at that jerk.

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practical reasons reasons to act ! My impulses tell me to scream at that jerk. ! But is that really the best thing to do – what should I do?

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practical reasons reasons to act ! My impulses tell me to scream at that jerk. ! But is that really the best thing to do – what should I do? ! Whatever course of action is supported by the best reasons.

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the structure of an argument

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the structure of an argument an argument in standard form Whatever is illegal is immoral. Murder is illegal. Thus murder is immoral. premises conclusion

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the structure of an argument an argument in standard form Whatever is illegal is immoral. Murder is illegal. Thus murder is immoral. premises conclusion ! Premises are the given information we start with – our reasons in support of the conclusion.

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the structure of an argument an argument in standard form Whatever is illegal is immoral. Murder is illegal. Thus murder is immoral. premises conclusion ! Premises are the given information we start with – our reasons in support of the conclusion. ! The conclusion is what we are trying to establish.

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Indicator words

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Indicator words premises

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Indicator words premises ! Since . . .

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Indicator words premises ! Since . . . ! Because of . . .

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Indicator words premises ! Since . . . ! Because of . . . ! Assume for the sake of argument that . . .

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Indicator words premises ! Since . . . ! Because of . . . ! Assume for the sake of argument that . . . ! We all know that . . .

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Indicator words premises ! Since . . . ! Because of . . . ! Assume for the sake of argument that . . . ! We all know that . . . conclusions

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Indicator words premises ! Since . . . ! Because of . . . ! Assume for the sake of argument that . . . ! We all know that . . . conclusions ! Therefore . . .

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Indicator words premises ! Since . . . ! Because of . . . ! Assume for the sake of argument that . . . ! We all know that . . . conclusions ! Therefore . . . ! Thus . . .

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Indicator words premises ! Since . . . ! Because of . . . ! Assume for the sake of argument that . . . ! We all know that . . . conclusions ! Therefore . . . ! Thus . . . ! So we can see that . . .

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Indicator words premises ! Since . . . ! Because of . . . ! Assume for the sake of argument that . . . ! We all know that . . . conclusions ! Therefore . . . ! Thus . . . ! So we can see that . . . ! It follows that . . .

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Identify Premises and Conclusion

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Identify Premises and Conclusion We know for a fact that my client was not at the scene of the crime. Furthermore, the chief prosecution witness is a known perjurer. Thus my client is not guilty.

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Identify Premises and Conclusion We know for a fact that my client was not at the scene of the crime. Furthermore, the chief prosecution witness is a known perjurer. Thus my client is not guilty. in standard form My client was not at the scene of the crime. The chief prosecution witness is a known perjurer. My client is not guilty.

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Identify Premises and Conclusion

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Identify Premises and Conclusion Christopher Columbus was a criminal. This is because whoever steals land or gold, enslaves people or kills innocent people is a criminal and he did all of the these things.

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Identify Premises and Conclusion Christopher Columbus was a criminal. This is because whoever steals land or gold, enslaves people or kills innocent people is a criminal and he did all of the these things. in standard form Whoever steals land or gold, enslaves people or kills innocent people is a criminal. Christopher Columbus did all of the these things. Christopher Columbus was a criminal.

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What makes a good argument?

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What makes a good argument?

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What makes a good argument? ! The best, most persuasive arguments are both valid and sound.

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What makes a good argument? ! The best, most persuasive arguments are both valid and sound. definition: In a valid argument, if the premises are true, the conclusion must be true.

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What makes a good argument? ! The best, most persuasive arguments are both valid and sound. definition: In a valid argument, if the premises are true, the conclusion must be true. definition: A sound argument is a valid argument with premises that are really true.

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Valid or invalid?

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Valid or invalid? All human beings are mortal. Socrates is a human being. Whoever is going to die worries about dying occasionally. Socrates worries about dying occasionally.

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Valid or invalid? All human beings are mortal. Socrates is a human being. Whoever is going to die worries about dying occasionally. Socrates worries about dying occasionally. If the premises are true must the conclusion also be true?

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Valid or invalid? All human beings are mortal. Socrates is a human being. Whoever is going to die worries about dying occasionally. Socrates worries about dying occasionally. If the premises are true must the conclusion also be true? YES, this argument is VALID.

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Valid or invalid?

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Valid or invalid? All human beings are animals. Plato is an animal. Plato is a human being.

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Valid or invalid? All human beings are animals. Plato is an animal. Plato is a human being. If the premises are true must the conclusion also be true?

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Valid or invalid? All human beings are animals. Plato is an animal. Plato is a human being. If the premises are true must the conclusion also be true? NO, this argument is INVALID.

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Valid or invalid?

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Valid or invalid? If abortion is wrong it should be illegal. Abortion is wrong. Abortion should be illegal.

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Valid or invalid? If abortion is wrong it should be illegal. Abortion is wrong. Abortion should be illegal. Can the premises both be true and the conclusion be false?

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Valid or invalid? If abortion is wrong it should be illegal. Abortion is wrong. Abortion should be illegal. Can the premises both be true and the conclusion be false? No. The only way for the conclusion to be false is if at least one of the premises were false, so this argument is VALID.

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Valid or invalid? If abortion is wrong it should be illegal. Abortion is wrong. Abortion should be illegal. Can the premises both be true and the conclusion be false? No. The only way for the conclusion to be false is if at least one of the premises were false, so this argument is VALID. But is it sound?

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counterexamples

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counterexamples definition: A counterexample is a description of a possible situation, case, or scenario in which the premises of an argument are true and the conclusion is false.

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counterexamples definition: A counterexample is a description of a possible situation, case, or scenario in which the premises of an argument are true and the conclusion is false. ! Counterexamples prove than an argument is invalid.

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counterexamples definition: A counterexample is a description of a possible situation, case, or scenario in which the premises of an argument are true and the conclusion is false. ! Counterexamples prove than an argument is invalid. ! Any case will do, as long it it describes a situation in which all premises are true and the conclusion false.

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counterexamples definition: A counterexample is a description of a possible situation, case, or scenario in which the premises of an argument are true and the conclusion is false. ! Counterexamples prove than an argument is invalid. ! Any case will do, as long it it describes a situation in which all premises are true and the conclusion false. ! If an argument is valid, there are no counterexamples – every case with a false conclusion will have at least one false premise.

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counterexamples

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counterexamples Fred is older than Betty. Barney is older than Betty. Thus Barney is older than Fred.

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counterexamples Fred is older than Betty. Barney is older than Betty. Thus Barney is older than Fred. counterexample

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counterexamples Fred is older than Betty. T Barney is older than Betty. Thus Barney is older than Fred. counterexample ! Fred is 48

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counterexamples Fred is older than Betty. T Barney is older than Betty. T Thus Barney is older than Fred. counterexample ! Fred is 48 ! Betty is 35

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counterexamples Fred is older than Betty. T Barney is older than Betty. T Thus Barney is older than Fred. F counterexample ! Fred is 48 ! Betty is 35 ! Barney is 45

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counterexamples

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counterexamples If you are in Paris, you are in France. Claudette is in France. Thus Claudette is in Paris.

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counterexamples If you are in Paris, you are in France. Claudette is in France. Thus Claudette is in Paris. counterexample

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counterexamples If you are in Paris, you are in France. T Claudette is in France. T Thus Claudette is in Paris. counterexample ! There is only one Paris and it is in France (we are ignoring Paris, Texas here).

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counterexamples If you are in Paris, you are in France. T Claudette is in France. T Thus Claudette is in Paris. F counterexample ! There is only one Paris and it is in France (we are ignoring Paris, Texas here). ! Claudette is currently in Marseilles, France.

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Sound or unsound?

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Sound or unsound? Poor people do not have much money. It costs a lot of money to buy first class airline tickets. So poor people do not fly first class except in unusual circumstances.

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Sound or unsound? Poor people do not have much money. It costs a lot of money to buy first class airline tickets. So poor people do not fly first class except in unusual circumstances. This argument is VALID.

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Sound or unsound? Poor people do not have much money. It costs a lot of money to buy first class airline tickets. So poor people do not fly first class except in unusual circumstances. This argument is VALID. The first premise is true by definition, the second is true in fact.

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Sound or unsound? Poor people do not have much money. It costs a lot of money to buy first class airline tickets. So poor people do not fly first class except in unusual circumstances. This argument is VALID. The first premise is true by definition, the second is true in fact. Thus this argument is SOUND, the conclusion is really true.

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Sound or unsound?

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Sound or unsound? Poor people do not have much money. If you do not have something, you must not want it. So poor people are poor of their own free will, because they want to be poor.

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Sound or unsound? Poor people do not have much money. If you do not have something, you must not want it. So poor people are poor of their own free will, because they want to be poor. Are both premises of this argument true?

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Sound or unsound? Poor people do not have much money. If you do not have something, you must not want it. So poor people are poor of their own free will, because they want to be poor. Are both premises of this argument true? The first premise is true by definition.

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Sound or unsound? Poor people do not have much money. If you do not have something, you must not want it. So poor people are poor of their own free will, because they want to be poor. Are both premises of this argument true? The first premise is true by definition. The second premise is false – so this argument is UNSOUND, even though it is VALID.

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Sound or unsound?

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Sound or unsound? If abortion is wrong it should be illegal. Abortion is wrong. Abortion should be illegal.

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Sound or unsound? If abortion is wrong it should be illegal. Abortion is wrong. Abortion should be illegal. This is a VALID argument, but are the premises really true?

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Sound or unsound? If abortion is wrong it should be illegal. Abortion is wrong. Abortion should be illegal. This is a VALID argument, but are the premises really true? The second premise might be true but needs more support.

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Sound or unsound? If abortion is wrong it should be illegal. Abortion is wrong. Abortion should be illegal. This is a VALID argument, but are the premises really true? The second premise might be true but needs more support. The first premise is false – not all that is wrong should be illegal, can you think of an example?

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Sound or unsound? If abortion is wrong it should be illegal. Abortion is wrong. Abortion should be illegal. This is a VALID argument, but are the premises really true? The second premise might be true but needs more support. The first premise is false – not all that is wrong should be illegal, can you think of an example? This argument is UNSOUND.

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Summary: analyzing arguments

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Summary: analyzing arguments identify argument

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Summary: analyzing arguments identify argument Is it valid?

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Summary: analyzing arguments identify argument Is it valid? INVALID discard

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Summary: analyzing arguments identify argument Is it valid? INVALID discard VALID

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Summary: analyzing arguments identify argument Is it valid? INVALID discard VALID Are premises true?

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Summary: analyzing arguments identify argument Is it valid? INVALID discard VALID Are premises true? no: UNSOUND discard

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Summary: analyzing arguments identify argument Is it valid? INVALID discard VALID Are premises true? no: UNSOUND discard yes: SOUND accept