An argument is rationally unpersuasive if there is no good reason to accept a premise, even though the argument is deductively valid and sound. An argument is defeated if a person reasonably believes the premises, but, nevertheless, reasonably rejects the conclusion. An argument is rationally persuasive for a person if the argument is either deductively valid or inductively forceful (1), the person reasonably believes the premises (2) and the argument is not defeated for that person (3). There are several points considering rational persuasiveness:It is not possible for the conclusion of a deductively valid argument to be defeated by a person’s total evidence. It is only possible for inductively forceful arguments.An argument does not have to be sound in order to be rationally persuasive.Rational persuasiveness is a matter of degreeRationally persuasive does not merely mean persuasive or convincing. A rationally persuasive argument may fail to persuade anyone. Judgements about the rational persuasiveness very frequently depends on estimates of the legitimacy oft eh authority behind certain propositions. A rationally persuasive argument does not mean that the premises of this argument will and have to be used in further conclusions. There are three ways in which someone can be mistaken about the rational persuasiveness of an argument:People can mistakes concerning whether or not an argument is valid or inductively forcefulPeople can think they have a good reason to accept a premise when they don’t or the other way around.People can be mistaken about whether or not an argument is defeated for themLOGICAL ASSESMENTIf an argument is not valid, the question should always be asked whether the argument is inductively forceful. When assessing conditionals, we should always assume the antecedent is true in order to see whether the consequent is true and the argument is thus deductively valid. Conditional proof refers to determining...


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      Scientific & Statistical Reasoning – Summary interim exam 1 (UNIVERSITY OF AMSTERDAM)

      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 1

      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 1

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      The reason answers the ‘why’ question to a statement. Asking for a reason is asking for justification. An argument is a set of propositions of which one is a conclusion and the remainder are premises, intended as support for the conclusion. A proposition is the factual content expressed in an argument.

      RECOGNISING ARGUMENTS
      Not all attempts to persuade are attempts to persuade by arguments. Attempts to persuade by means of rhetorical devices are also possible. Rhetoric is any verbal or written attempt to persuade someone that does not attempt to give good reasons but attempts to motivate solely through the power of the words used. It relies on the persuasive power of some words (e.g. instil fear using words without good reason). In analysing attempts to persuade, three tasks have to be performed:

      1. Identify
        It is important to identify the issue being discussed and whether an argument is being presented.
      2. Reconstructing
        The next step is reconstructing the argument so as to express it clearly. This includes putting arguments in the standard form.
      3. Evaluating
        The last step is evaluating the argument.

      Putting forward an argument is used to either advance an opinion (1) or recommend an action (2). Arguments are attempts to provide reasons that some claim is true. An argument requires more than one claim. If only one claim is used in an attempt to persuade, it is an unsupported claim. The second claim should give support to the first claim. The primary claim which we try to persuade people of is the conclusion. The supporting claims are premises. Indexicals are words of which the meaning changes relative to its context of use or relative to the person to whom it refers.

      STANDARD FORM
      The standard form of an argument is:

      1. A is B
      2. B is C
        -------------
      3. A is C

      There are five steps to reconstruct an argument:

      1. Identify the conclusion
      2. Identify the premises
      3. Number the premises and write them in order
      4. Draw in the inference bar
      5. Write out the conclusion, placing ‘C’ in front of it

      IDENTIFYING CONCLUSIONS AND PREMISES
      The context refers to the circumstances in which the passage or speech appeared or took place. Attempts to persuade often include hidden premises, premises that are not being spoken out loud. Any proposition of any topic can be a conclusion. A single text may contain several arguments for several connected conclusions. Indicator words are not parts of the proposition that the argument comprises. They introduce or frame the conclusion and premises. Implicit conclusions are conclusions that are not explicitly being expressed.

      Information that puts emphasis on words, is used for rhetoric or has any function besides being a premise or conclusion is extraneous material and should be discarded when identifying the argument.

      ARGUMENTS AND EXPLANATIONS
      An explanation is used to assert a

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      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 2

      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 2

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      There are several problems with linguistic phenomena that makes an argument difficult to understand. The set of things a word is about is called the extension.

      Ambiguity occurs if a sentence can be interpreted in more than one way and should be avoided when trying to persuade using an argument. There are two types of ambiguity:

      1. Lexical ambiguity
        This can occur if certain words have more than one meaning. This means that a word can be lexical ambiguous if it has more extensions. Lexical ambiguous words are not ambiguous in every context. There are words that can be ambiguous in speech but not in written text, as it is written differently, but sounds the same.
      2. Syntactic ambiguity
        This can occur if the arrangement of words in a sentence is such that it can be understood in multiple ways. Syntactic ambiguity is more difficult to understand using the context.

      Vagueness occurs if the meaning of a word is indefinite or unclear (e.g. rights). Vagueness can also refer to words of which the meaning is clear, but there is no precise demarcation between that word and another (e.g. orange and yellow).

      The primary connotation of a word are the necessary and sufficient conditions for something to count as part of that term’s extension (e.g. ram: male, sheep). The secondary connotation of a word are characteristics of the word but are not necessary for something to count as part of that term’s extension (e.g. ram: woolly, horns). Words that are vague often have an unclear primary connotation and a rich secondary connotation.

      Metaphors function by only using the secondary connotation of a word. Rhetorical questions are questions that indirectly assert a proposition. Irony refers to making a statement that, taken literally, conveys the opposite of the message people are trying to convey (e.g. ‘very tasteful’).

      Implicitly relative sentences make a comparison with some group of things but that comparison is not explicitly mentioned. Quantifiers are words and phrases that tell us how many/much there are/is or how often something happens (e.g. all). There are three potential problems of using quantifiers:

      1. Quantifiers are not always used with sufficient proposition.
      2. Quantifier-words and phrases can be vague (e.g. some).
      3. Quantifiers are sometimes omitted from an uttering.

      Counterexamples are cases that are used to challenge the truth of a generalising claim. Soft generalizations are used to make a statement of how things typically or normally are. Hard generalizations are used to make a statement of how things always are.

      ASPECTS OF MEANING
      A sentence’s meaning has different aspects:

      1. Rhetorical force
        This is the rhetorical aspect of a sentence’s meaning and it is not part of the propositional content that it expresses.
      2. Implicature
        This is a non-stated meaning but which one can reasonably take to be intended given the context. Implicature requires context.
      3. Definitions
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      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 3

      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 3

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      Argument reconstruction clarifies what the arguer actually said and to supplement the arguer, as some statements are implicit. The reconstruction of an argument can be presented as a bad argument or as a good argument, depending on the goal (e.g. political debate). A bad argument does not mean that the proposition is false. The principle of charity states that people should also choose the best reconstruction of an argument to discover reasons for accepting or rejecting particular prepositions, advancing the cause of knowledge.

      TRUTH
      The truth-value of a proposition is the truth of the proposition. The two truth-values are true and false.

      DEDUCTIVE VALIDITY
      A conclusion is valid if the conclusion would be true, given that the premises are also true. The truth of premises is, in principle, not relevant for the validity of an argument. Validity should be judged by disregarding the truth-values of the premises.

      PRESCRIPTIVE CLAIMS VS DESCRIPTIVE CLAIMS
      Statements that state facts are descriptive claims and statements which express desires, norms or moral rules are prescriptive claims.

      CONDITIONAL PROPOSITIONS
      Conditional propositions use the ‘if-then’ format. A double negative in logic is equal to a positive and it is called contraposition (e.g: if not A, then not B = if B then A). The word ‘or’ can be used in the inclusive sense or in the exclusive sense. In the inclusive sense, it means that ‘A or B’ that either A is true or B is true or they are both true. That statement is only false if both A and B are false. In the exclusive sense ‘A or B’ means that either A is true or B is true but not both. The word ‘either’ is often used here too.

      The words ‘if only’ create a conditional proportion that sets a necessary condition for it to apply, but it does not implicate that it is true the other way around. For example, ‘A only if B’ implies that A only occurs if B occurs, but B can occur without A occurring. A does not necessarily have to occur if B occurs, but if B does not occur A will never occur. The ‘if and only if’ statement creates a necessary condition. It means that either both happens or neither happens. For example: ‘A if and only if B’ means that A will never occur without B and that when B occurs A also occurs. In this case, B is the sole condition for A. If and only if means the same as either both A and B or neither. Unless (‘A unless B’) implies that A if not B. It does not mean that A will occur if B does not occur, but it does mean that A will not occur if B does not occur.

      THE ANTECEDENT AND CONSEQUENT OF A CONDITIONAL
      Formal logic can be denoted in another way.

      A →B

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      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 4

      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 4

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      Precise generalisations make it more difficult to divert from the topic. The quantifier ‘some’ does not mean ‘most’ or ‘all’ when making generalizations, although when stating ‘some A are B’ it is possible that all A are B.

      An argument is inductively forceful if the conclusion does not necessarily follow from the premises but is still ‘probably true’. It is very likely to be true and unlikely to be false. To say that an argument is inductively forceful means that the probability of A relative to the set is greater than one-half but less than one.

      The proportion indicate the part of A in the total (e.g. 7/8). Frequency refers to the number of times something occurs. The degree of rational expectation refers to the degree to which a person is entitled to believe a proposition given the evidence provided. Frequency and proportion could be used to calculate probability. Probability is a matter of degree and so is an argument being inductively forceful. The degree of indicative force of an argument is independent of the truth-values of the premises.

      INDUCTIVE SOUNDNESS
      An argument is inductively sound if the argument is inductively forceful and its premises are true. Another word for inductive soundness is cogency. An inductive inference refers to extrapolating from a sample of a total population of things either to something outside the sample or to a generalisation about the population as a whole. An inference is an inductive inference if it is not deductively valid, its premises include a generalisation about a sample of a given population and its conclusion extrapolates the generalisation to all or part of the total population from the sample. It frequently involves extrapolation from the past to the future. The inductive force of an argument is equal to the conditional probability of the conclusion relative to the premises.

      In order to make a proper inductive inference, the sample needs to be representative of the population. An argument can be forceful and sound but the conclusion may still not be accepted. The argument is then overridden by other information one has and the argument is defeated.

      CONVERSION OF INDUCTION TO DEDUCTION
      An inductive argument can be converted into a deductive one by making explicit the basis for the inductive principle:

      For example:

      • P1: All of the observed sample of jackdaws are monogamous
        P2: If all of the observed sample of jackdaws are monogamous, then all jackdaws are monogamous
        -----------------------
        C: All jackdaws are monogamous

      P2 is the added premise to make it a deductive argument. If P2 is not added it is a forceful inductive argument. People tend to make the base rate fallacy.

      A PROGRAMME FOR ASSESSMENT
      There is a programme for assessment of arguments:

      1. Is the argument deductively valid?
      2. If not, proceed to 2
      3. If yes, are all the premises true?
      4. If yes, the argument is deductively sound. STOP
      5. If not, the argument is valid but unsound. STOP
      6. Is the argument inductively
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      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 5

      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 5

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      A lot of things people write plays no argumentative role. It can serve the function of emphasis, rhetoric or something else. This extraneous material should not be included in the reconstructing of an argument. The word ‘since’ transforms a conditional statement into a statement that asserts both the conditional and the antecedent of that conditional. The first step in reconstructing an argument is to make a list of the argument’s premises and conclusion that leaves out extraneous material.

      DEFUSING THE RHETORIC
      Metaphors, slang and expressive epithets should be eliminated while reconstructing an argument. Expressive epithets are terms used to refer to some person, group or other entity, without actually using the name.

      LOGICAL STREAMLINING
      When reconstructing arguments, the logical relationships should be displayed in the simplest, clearest and most familiar ways possible. There are two rules of thumb when logical streamlining:

      1.        Where appropriate, rewrite sentences as either conditional or disjunctive sentences in simple forms.
      2.       Rewrite generalisations in simple forms using a clear quantifier.

      IMPLICIT AND EXPLICIT
      In arguments, some essential propositions are left implicit. Reconstruction of arguments should make all propositions explicit. The first step is always identifying the conclusion. The next step is identifying the argument’s premises. The third step is making any implicit statements explicit.

      CONNECTING PREMISES
      A connecting premise is a premise that has to be made explicit in order to make the argument valid. The connection premise can be not true or not lead to the argument being valid.

      COVERING GENERALISATIONS
      Asserting conditionals often happens on the basis of some covering generalisation. The conditional often relies on a generalization.

      RELEVANCE
      Whether a certain premise is true or false is not always equally relevant.

      AMBIGUITY AND VAGUENESS
      In reconstructing arguments, ambiguity and vagueness have to be eliminated. If we are unable to choose one interpretation of an ambiguous term when reconstructing an argument, they should all be presented. While reconstructing an argument, vagueness should be eliminated where possible as this clarifies the argument and allows us to focus on the matter, without being distracted by a vague and possibly controversial term.

      PRACTICAL REASONING
      Practical reasoning or means-end reasoning refers to reasoning that includes a practical conclusion. It includes desirable or undesirable outcomes. For practical reasoning, the cost and the benefit of the outcome must be considered.

      BALANCING COSTS, BENEFITS AND PROBABILITIES
      If an argument is represented as inductive, the cost, benefit and probability have to be discussed and weighted. The expected value can be used to systematically give an overview of the costs, benefits and probabilities of things happening. To calculate the expected value, the cost or benefit of the action is multiplied with its probability. The expected value should be maximised.

      EXPLANATIONS AS CONCLUSIONS
      Abduction is also called inference to the best explanation. There is a distinct pattern when explanations are used as conclusion:

      P1) Agreed fact
      P2) Agreed fact was caused by either A, B or C
      P3)

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      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 6

      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 6

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      An argument is rationally unpersuasive if there is no good reason to accept a premise, even though the argument is deductively valid and sound. An argument is defeated if a person reasonably believes the premises, but, nevertheless, reasonably rejects the conclusion. An argument is rationally persuasive for a person if the argument is either deductively valid or inductively forceful (1), the person reasonably believes the premises (2) and the argument is not defeated for that person (3).

      There are several points considering rational persuasiveness:

      1. It is not possible for the conclusion of a deductively valid argument to be defeated by a person’s total evidence. It is only possible for inductively forceful arguments.
      2. An argument does not have to be sound in order to be rationally persuasive.
      3. Rational persuasiveness is a matter of degree
      4. Rationally persuasive does not merely mean persuasive or convincing. A rationally persuasive argument may fail to persuade anyone.
      5. Judgements about the rational persuasiveness very frequently depends on estimates of the legitimacy oft eh authority behind certain propositions.
      6. A rationally persuasive argument does not mean that the premises of this argument will and have to be used in further conclusions.

      There are three ways in which someone can be mistaken about the rational persuasiveness of an argument:

      1. People can mistakes concerning whether or not an argument is valid or inductively forceful
      2. People can think they have a good reason to accept a premise when they don’t or the other way around.
      3. People can be mistaken about whether or not an argument is defeated for them

      LOGICAL ASSESMENT
      If an argument is not valid, the question should always be asked whether the argument is inductively forceful. When assessing conditionals, we should always assume the antecedent is true in order to see whether the consequent is true and the argument is thus deductively valid.

      Conditional proof refers to determining whether ‘if A then B’ follows from some premises. In order to do so, we should ask ourselves whether B follows from those premises together with A.

      One way of assessing the validity of an argument is to suppose the premises are true but the conclusion is false. If this is impossible, then the argument must be valid.

      REFUTATION BY COUNTEREXAMPLE
      A counterexample, especially using the same reasoning as the original argument, can illustrate why an argument is invalid or not inductively forceful.

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      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 7

      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 7

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      Fallacies are arguments which make use of a mistake in reasoning. They do count as arguments, but are faulty arguments. There is an inappropriate connection between premises an conclusion. Formal fallacies are fallacies where there is an inappropriate logical connection. Substantive (informal) fallacies involve reliance or unjustified assumptions or inferences. Substantive fallacies are different from unsound arguments in the sense that the false premise is of general nature and has nothing to do specifically with the subject.

      There are several formal fallacies:

      1. Affirming the consequent
        This is affirming the consequent and using this to reason that the antecedent must be true because of this.
        --------------
        If A, then B
        B
        --------------
        A
      2. Denying the antecedent
        This is denying the antecedent and using this to reason that the consequent must be false because of this.
        -----------------
        If A, then B
        Not A
        -----------------
        Not B
      3. Deriving ought from is
        A prescriptive conclusion cannot be validly derived from purely descriptive premises.
      4. Base rate fallacy
        This is neglecting the base rate to make a conclusion.

      There are several informal fallacies:

      1. Majority belief
        This is concluding that the proposition is true on the basis that the majority beliefs that the proposition is true.
      2. Common practice
        This is concluding that the proposition is true on the basis that ‘everyone does it’.
      3. Gambler’s fallacy
        This is concluding that the probability of winning something is increased because of previous events (e.g. roulette ball falls on red twice in a row, so it must be black now).
      4. Ad hominem
        This is responding to a claim by making an attack upon the person or by rejecting a claim because of dislike for the person making the claim.
      5. Ad hominem circumstantial
        This is believing an argument is discounted because the person making the argument would allegedly benefit from people believing the argument (e.g. academic want more students because they will have more jobs).
      6. Tu quoque (you too)
        This is making unwarranted connections between a person’s alleged lack of credibility and the strength of their argument. It assumes that whenever a person’s behaviour is inconsistent with their advice, we should not take it seriously or it is false.
      7. Appeal to authority
        This is an unjustified appeal to authority.
      8. The perfectionist fallacy
        This is placing excessive demands on an idea or a proposal and reject the idea or proposal solely because it will not completely solve a problem.
      9. Conflation of morality with legality
        This is assuming that anything that is legal must be moral or that anything that is illegal must be immoral. It is summarised in: ‘there’s no law against it, so it’s acceptable’.
      10. Weak analogy
        This is assuming that if one thing is similar to another in one
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      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Book summary

      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 1

      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 1

      Image

      The reason answers the ‘why’ question to a statement. Asking for a reason is asking for justification. An argument is a set of propositions of which one is a conclusion and the remainder are premises, intended as support for the conclusion. A proposition is the factual content expressed in an argument.

      RECOGNISING ARGUMENTS
      Not all attempts to persuade are attempts to persuade by arguments. Attempts to persuade by means of rhetorical devices are also possible. Rhetoric is any verbal or written attempt to persuade someone that does not attempt to give good reasons but attempts to motivate solely through the power of the words used. It relies on the persuasive power of some words (e.g. instil fear using words without good reason). In analysing attempts to persuade, three tasks have to be performed:

      1. Identify
        It is important to identify the issue being discussed and whether an argument is being presented.
      2. Reconstructing
        The next step is reconstructing the argument so as to express it clearly. This includes putting arguments in the standard form.
      3. Evaluating
        The last step is evaluating the argument.

      Putting forward an argument is used to either advance an opinion (1) or recommend an action (2). Arguments are attempts to provide reasons that some claim is true. An argument requires more than one claim. If only one claim is used in an attempt to persuade, it is an unsupported claim. The second claim should give support to the first claim. The primary claim which we try to persuade people of is the conclusion. The supporting claims are premises. Indexicals are words of which the meaning changes relative to its context of use or relative to the person to whom it refers.

      STANDARD FORM
      The standard form of an argument is:

      1. A is B
      2. B is C
        -------------
      3. A is C

      There are five steps to reconstruct an argument:

      1. Identify the conclusion
      2. Identify the premises
      3. Number the premises and write them in order
      4. Draw in the inference bar
      5. Write out the conclusion, placing ‘C’ in front of it

      IDENTIFYING CONCLUSIONS AND PREMISES
      The context refers to the circumstances in which the passage or speech appeared or took place. Attempts to persuade often include hidden premises, premises that are not being spoken out loud. Any proposition of any topic can be a conclusion. A single text may contain several arguments for several connected conclusions. Indicator words are not parts of the proposition that the argument comprises. They introduce or frame the conclusion and premises. Implicit conclusions are conclusions that are not explicitly being expressed.

      Information that puts emphasis on words, is used for rhetoric or has any function besides being a premise or conclusion is extraneous material and should be discarded when identifying the argument.

      ARGUMENTS AND EXPLANATIONS
      An explanation is used to assert a

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      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 2

      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 2

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      There are several problems with linguistic phenomena that makes an argument difficult to understand. The set of things a word is about is called the extension.

      Ambiguity occurs if a sentence can be interpreted in more than one way and should be avoided when trying to persuade using an argument. There are two types of ambiguity:

      1. Lexical ambiguity
        This can occur if certain words have more than one meaning. This means that a word can be lexical ambiguous if it has more extensions. Lexical ambiguous words are not ambiguous in every context. There are words that can be ambiguous in speech but not in written text, as it is written differently, but sounds the same.
      2. Syntactic ambiguity
        This can occur if the arrangement of words in a sentence is such that it can be understood in multiple ways. Syntactic ambiguity is more difficult to understand using the context.

      Vagueness occurs if the meaning of a word is indefinite or unclear (e.g. rights). Vagueness can also refer to words of which the meaning is clear, but there is no precise demarcation between that word and another (e.g. orange and yellow).

      The primary connotation of a word are the necessary and sufficient conditions for something to count as part of that term’s extension (e.g. ram: male, sheep). The secondary connotation of a word are characteristics of the word but are not necessary for something to count as part of that term’s extension (e.g. ram: woolly, horns). Words that are vague often have an unclear primary connotation and a rich secondary connotation.

      Metaphors function by only using the secondary connotation of a word. Rhetorical questions are questions that indirectly assert a proposition. Irony refers to making a statement that, taken literally, conveys the opposite of the message people are trying to convey (e.g. ‘very tasteful’).

      Implicitly relative sentences make a comparison with some group of things but that comparison is not explicitly mentioned. Quantifiers are words and phrases that tell us how many/much there are/is or how often something happens (e.g. all). There are three potential problems of using quantifiers:

      1. Quantifiers are not always used with sufficient proposition.
      2. Quantifier-words and phrases can be vague (e.g. some).
      3. Quantifiers are sometimes omitted from an uttering.

      Counterexamples are cases that are used to challenge the truth of a generalising claim. Soft generalizations are used to make a statement of how things typically or normally are. Hard generalizations are used to make a statement of how things always are.

      ASPECTS OF MEANING
      A sentence’s meaning has different aspects:

      1. Rhetorical force
        This is the rhetorical aspect of a sentence’s meaning and it is not part of the propositional content that it expresses.
      2. Implicature
        This is a non-stated meaning but which one can reasonably take to be intended given the context. Implicature requires context.
      3. Definitions
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      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 3

      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 3

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      Argument reconstruction clarifies what the arguer actually said and to supplement the arguer, as some statements are implicit. The reconstruction of an argument can be presented as a bad argument or as a good argument, depending on the goal (e.g. political debate). A bad argument does not mean that the proposition is false. The principle of charity states that people should also choose the best reconstruction of an argument to discover reasons for accepting or rejecting particular prepositions, advancing the cause of knowledge.

      TRUTH
      The truth-value of a proposition is the truth of the proposition. The two truth-values are true and false.

      DEDUCTIVE VALIDITY
      A conclusion is valid if the conclusion would be true, given that the premises are also true. The truth of premises is, in principle, not relevant for the validity of an argument. Validity should be judged by disregarding the truth-values of the premises.

      PRESCRIPTIVE CLAIMS VS DESCRIPTIVE CLAIMS
      Statements that state facts are descriptive claims and statements which express desires, norms or moral rules are prescriptive claims.

      CONDITIONAL PROPOSITIONS
      Conditional propositions use the ‘if-then’ format. A double negative in logic is equal to a positive and it is called contraposition (e.g: if not A, then not B = if B then A). The word ‘or’ can be used in the inclusive sense or in the exclusive sense. In the inclusive sense, it means that ‘A or B’ that either A is true or B is true or they are both true. That statement is only false if both A and B are false. In the exclusive sense ‘A or B’ means that either A is true or B is true but not both. The word ‘either’ is often used here too.

      The words ‘if only’ create a conditional proportion that sets a necessary condition for it to apply, but it does not implicate that it is true the other way around. For example, ‘A only if B’ implies that A only occurs if B occurs, but B can occur without A occurring. A does not necessarily have to occur if B occurs, but if B does not occur A will never occur. The ‘if and only if’ statement creates a necessary condition. It means that either both happens or neither happens. For example: ‘A if and only if B’ means that A will never occur without B and that when B occurs A also occurs. In this case, B is the sole condition for A. If and only if means the same as either both A and B or neither. Unless (‘A unless B’) implies that A if not B. It does not mean that A will occur if B does not occur, but it does mean that A will not occur if B does not occur.

      THE ANTECEDENT AND CONSEQUENT OF A CONDITIONAL
      Formal logic can be denoted in another way.

      A →B

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      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 4

      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 4

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      Precise generalisations make it more difficult to divert from the topic. The quantifier ‘some’ does not mean ‘most’ or ‘all’ when making generalizations, although when stating ‘some A are B’ it is possible that all A are B.

      An argument is inductively forceful if the conclusion does not necessarily follow from the premises but is still ‘probably true’. It is very likely to be true and unlikely to be false. To say that an argument is inductively forceful means that the probability of A relative to the set is greater than one-half but less than one.

      The proportion indicate the part of A in the total (e.g. 7/8). Frequency refers to the number of times something occurs. The degree of rational expectation refers to the degree to which a person is entitled to believe a proposition given the evidence provided. Frequency and proportion could be used to calculate probability. Probability is a matter of degree and so is an argument being inductively forceful. The degree of indicative force of an argument is independent of the truth-values of the premises.

      INDUCTIVE SOUNDNESS
      An argument is inductively sound if the argument is inductively forceful and its premises are true. Another word for inductive soundness is cogency. An inductive inference refers to extrapolating from a sample of a total population of things either to something outside the sample or to a generalisation about the population as a whole. An inference is an inductive inference if it is not deductively valid, its premises include a generalisation about a sample of a given population and its conclusion extrapolates the generalisation to all or part of the total population from the sample. It frequently involves extrapolation from the past to the future. The inductive force of an argument is equal to the conditional probability of the conclusion relative to the premises.

      In order to make a proper inductive inference, the sample needs to be representative of the population. An argument can be forceful and sound but the conclusion may still not be accepted. The argument is then overridden by other information one has and the argument is defeated.

      CONVERSION OF INDUCTION TO DEDUCTION
      An inductive argument can be converted into a deductive one by making explicit the basis for the inductive principle:

      For example:

      • P1: All of the observed sample of jackdaws are monogamous
        P2: If all of the observed sample of jackdaws are monogamous, then all jackdaws are monogamous
        -----------------------
        C: All jackdaws are monogamous

      P2 is the added premise to make it a deductive argument. If P2 is not added it is a forceful inductive argument. People tend to make the base rate fallacy.

      A PROGRAMME FOR ASSESSMENT
      There is a programme for assessment of arguments:

      1. Is the argument deductively valid?
      2. If not, proceed to 2
      3. If yes, are all the premises true?
      4. If yes, the argument is deductively sound. STOP
      5. If not, the argument is valid but unsound. STOP
      6. Is the argument inductively
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      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 5

      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 5

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      A lot of things people write plays no argumentative role. It can serve the function of emphasis, rhetoric or something else. This extraneous material should not be included in the reconstructing of an argument. The word ‘since’ transforms a conditional statement into a statement that asserts both the conditional and the antecedent of that conditional. The first step in reconstructing an argument is to make a list of the argument’s premises and conclusion that leaves out extraneous material.

      DEFUSING THE RHETORIC
      Metaphors, slang and expressive epithets should be eliminated while reconstructing an argument. Expressive epithets are terms used to refer to some person, group or other entity, without actually using the name.

      LOGICAL STREAMLINING
      When reconstructing arguments, the logical relationships should be displayed in the simplest, clearest and most familiar ways possible. There are two rules of thumb when logical streamlining:

      1.        Where appropriate, rewrite sentences as either conditional or disjunctive sentences in simple forms.
      2.       Rewrite generalisations in simple forms using a clear quantifier.

      IMPLICIT AND EXPLICIT
      In arguments, some essential propositions are left implicit. Reconstruction of arguments should make all propositions explicit. The first step is always identifying the conclusion. The next step is identifying the argument’s premises. The third step is making any implicit statements explicit.

      CONNECTING PREMISES
      A connecting premise is a premise that has to be made explicit in order to make the argument valid. The connection premise can be not true or not lead to the argument being valid.

      COVERING GENERALISATIONS
      Asserting conditionals often happens on the basis of some covering generalisation. The conditional often relies on a generalization.

      RELEVANCE
      Whether a certain premise is true or false is not always equally relevant.

      AMBIGUITY AND VAGUENESS
      In reconstructing arguments, ambiguity and vagueness have to be eliminated. If we are unable to choose one interpretation of an ambiguous term when reconstructing an argument, they should all be presented. While reconstructing an argument, vagueness should be eliminated where possible as this clarifies the argument and allows us to focus on the matter, without being distracted by a vague and possibly controversial term.

      PRACTICAL REASONING
      Practical reasoning or means-end reasoning refers to reasoning that includes a practical conclusion. It includes desirable or undesirable outcomes. For practical reasoning, the cost and the benefit of the outcome must be considered.

      BALANCING COSTS, BENEFITS AND PROBABILITIES
      If an argument is represented as inductive, the cost, benefit and probability have to be discussed and weighted. The expected value can be used to systematically give an overview of the costs, benefits and probabilities of things happening. To calculate the expected value, the cost or benefit of the action is multiplied with its probability. The expected value should be maximised.

      EXPLANATIONS AS CONCLUSIONS
      Abduction is also called inference to the best explanation. There is a distinct pattern when explanations are used as conclusion:

      P1) Agreed fact
      P2) Agreed fact was caused by either A, B or C
      P3)

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      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 6

      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 6

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      An argument is rationally unpersuasive if there is no good reason to accept a premise, even though the argument is deductively valid and sound. An argument is defeated if a person reasonably believes the premises, but, nevertheless, reasonably rejects the conclusion. An argument is rationally persuasive for a person if the argument is either deductively valid or inductively forceful (1), the person reasonably believes the premises (2) and the argument is not defeated for that person (3).

      There are several points considering rational persuasiveness:

      1. It is not possible for the conclusion of a deductively valid argument to be defeated by a person’s total evidence. It is only possible for inductively forceful arguments.
      2. An argument does not have to be sound in order to be rationally persuasive.
      3. Rational persuasiveness is a matter of degree
      4. Rationally persuasive does not merely mean persuasive or convincing. A rationally persuasive argument may fail to persuade anyone.
      5. Judgements about the rational persuasiveness very frequently depends on estimates of the legitimacy oft eh authority behind certain propositions.
      6. A rationally persuasive argument does not mean that the premises of this argument will and have to be used in further conclusions.

      There are three ways in which someone can be mistaken about the rational persuasiveness of an argument:

      1. People can mistakes concerning whether or not an argument is valid or inductively forceful
      2. People can think they have a good reason to accept a premise when they don’t or the other way around.
      3. People can be mistaken about whether or not an argument is defeated for them

      LOGICAL ASSESMENT
      If an argument is not valid, the question should always be asked whether the argument is inductively forceful. When assessing conditionals, we should always assume the antecedent is true in order to see whether the consequent is true and the argument is thus deductively valid.

      Conditional proof refers to determining whether ‘if A then B’ follows from some premises. In order to do so, we should ask ourselves whether B follows from those premises together with A.

      One way of assessing the validity of an argument is to suppose the premises are true but the conclusion is false. If this is impossible, then the argument must be valid.

      REFUTATION BY COUNTEREXAMPLE
      A counterexample, especially using the same reasoning as the original argument, can illustrate why an argument is invalid or not inductively forceful.

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      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 7

      Critical thinking a concise guide by Tracy Bowell & Gary Kemp, fourth edition – Summary chapter 7

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      Fallacies are arguments which make use of a mistake in reasoning. They do count as arguments, but are faulty arguments. There is an inappropriate connection between premises an conclusion. Formal fallacies are fallacies where there is an inappropriate logical connection. Substantive (informal) fallacies involve reliance or unjustified assumptions or inferences. Substantive fallacies are different from unsound arguments in the sense that the false premise is of general nature and has nothing to do specifically with the subject.

      There are several formal fallacies:

      1. Affirming the consequent
        This is affirming the consequent and using this to reason that the antecedent must be true because of this.
        --------------
        If A, then B
        B
        --------------
        A
      2. Denying the antecedent
        This is denying the antecedent and using this to reason that the consequent must be false because of this.
        -----------------
        If A, then B
        Not A
        -----------------
        Not B
      3. Deriving ought from is
        A prescriptive conclusion cannot be validly derived from purely descriptive premises.
      4. Base rate fallacy
        This is neglecting the base rate to make a conclusion.

      There are several informal fallacies:

      1. Majority belief
        This is concluding that the proposition is true on the basis that the majority beliefs that the proposition is true.
      2. Common practice
        This is concluding that the proposition is true on the basis that ‘everyone does it’.
      3. Gambler’s fallacy
        This is concluding that the probability of winning something is increased because of previous events (e.g. roulette ball falls on red twice in a row, so it must be black now).
      4. Ad hominem
        This is responding to a claim by making an attack upon the person or by rejecting a claim because of dislike for the person making the claim.
      5. Ad hominem circumstantial
        This is believing an argument is discounted because the person making the argument would allegedly benefit from people believing the argument (e.g. academic want more students because they will have more jobs).
      6. Tu quoque (you too)
        This is making unwarranted connections between a person’s alleged lack of credibility and the strength of their argument. It assumes that whenever a person’s behaviour is inconsistent with their advice, we should not take it seriously or it is false.
      7. Appeal to authority
        This is an unjustified appeal to authority.
      8. The perfectionist fallacy
        This is placing excessive demands on an idea or a proposal and reject the idea or proposal solely because it will not completely solve a problem.
      9. Conflation of morality with legality
        This is assuming that anything that is legal must be moral or that anything that is illegal must be immoral. It is summarised in: ‘there’s no law against it, so it’s acceptable’.
      10. Weak analogy
        This is assuming that if one thing is similar to another in one
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