Wst-r
Chapter 3
Logic: deductive validity
Argument reconstruction: the representation of arguments in standard form, so as to give us a clear and comprehensive view of them.
Argument assessment: the determination of whether or not arguments provide good reasons for accepting their conclusions.
An argument is a system of propositions.
Propositions: a set of premises advanced in support of a conclusion.
People succeed in expressing the propositions they have in mind in varying degrees of clarity. An argument may depend upon premises that the arguer does not state at all, but which he or she is implicitly assuming.
Since the purpose of argument-reconstruction is to determine exactly what argument has been given, part of the task is to clarify what the arguer actually said, and to supplement what the arguer actually said (to make explicit what was merely implicit in the arguer’s statements).
Argument-reconstruction is essentially a task of interpretation.
The principle of charity.
In such facts pertaining to the context in which the argument is given, together with the specific words used by the person, will constitute the total evidence you have for reconstructing the argument.
If, in the third case, you have to chose what representation of the argument is true, it depends on your purpose.
Otherwise you could conclude nothing.
The fact that someone has given a bad argument for some proposition is not, in itself, a reason to reject the proposition as false. → if you reject the argument, the proposition is unchanged. If you accept, you have a different proposition, it is true.
The principle of charity: we should always choose the best reconstruction of a given argument.
In that way, we discover reasons for accepting or rejecting particular propositions, advancing the cause of knowledge.
And because of respect for others. You want to understand others, also when they struggle with finding the right words.
The principle of charity has a certain threshold.
If our task is to reconstruct the argument actually intended by the person, then we must not go beyond what, based upon the evidence available for us, we may reasonably expect the arguer to have had in mind.
Once we go beyond what we may reasonably assume the arguer have had in mind, then we are no longer in the business of interpreting their argument. Instead, we have become the arguer.
If our concern is with how well a particular person has argued, we should not overstep this boundary.
If our concern is with the truth of the matter in question, then to overstep this boundary is perfectly all right.
It often happens that, in reconstructing an argument, we hit upon another, similar or related argument for the same conclusion which is better than the one we are reconstructing.
Logic gives us some very clear answers as to what does make arguments good or bad.
The fundamental concept of logic is the concept of truth.
Truth: (for this book) the way things are.
To say a proposition is true is to say it is the way things are.
If A and B are equivalent is that, necessarily, if A is true, then so is B. And if B is true, then so is A.
Discomfort with the word ‘true’ is sometimes due to a failure to distinguish truth from belief.
Beliefs depend on a person, not on the world.
Truth-value of a proposition: the truth of the proposition, if its true, or its falsity, if it is false.
There are two truth-values. True and false.
Deductive validity (or simply validity)
The concept of validity pertains to the connection between the premises and conclusion of an argument, not their actual truth-values considered individually.
It pertains to inferences. Extended arguments may contain more than one inference, and each one is subject to being valid or invalid.
A single proposition can be true or false, but not valid or invalid.
An argument can be valid or invalid, but not true or false.
To say that an argument is valid is to say: if the premises are (or were) true, the conclusion would also have to be true.
If the condition specified by the definition does not hold, then the argument is invalid.
The following cases of valid argument are possible
The only case in which an argument cannot be valid is the case when the premises are all (actually) true, but the conclusion is (actually) false.
How to judge validity
The way to determine whether or not an argument is valid is to ignore the actual truth-values of the premises and the actual truth-value of the conclusion.
Whether or not they are actually true, suppose or pretend that the premises were all true, then in that situation, could the conclusion conceivably be false? If it could not be false, then the argument is valid. If it could be false, then the argument is valid.
Descriptive claims: fact-stating claims.
Prescriptive claims: claims which state or express desires, norms or moral values.
To claim a proposition is true, is the same thing as agreeing with it.
The distinction between descriptive and prescriptive claims is not be made out in terms of truth.
Contraposition: saying ‘if not-Q then not-P’ is equivalent to saying ‘if P then Q’ in logic
Usually, when wo statements are joined by ‘either-or’, or just by ‘or’ to form a compound statement, the compound is equivalent to a statemetn using if-then, and vice versa. But to pass from the version using ‘or’ to the version using ‘if-then’, or vice versa, we have to insert the word ‘not’.
The word ‘or’ is used in either of two ways.
P only if Q.
‘P only if Q’ means the same as ‘If P then Q.’
‘If and only if P then Q’ means the same as ‘If P then Q’, and if ‘if Q then P’.
The trick for dealing with ‘unless’ is to think of it as meaning ‘if not’.
In general, a conditional is a compound proposition consisting of two parts, each of which is itself a proposition, where these two parts are joined by some connecting words.
What a conditional says is that the truth of one proposition ensures that of another.
In formal logic it is →
Antecedent: the one form which the arrow points.
Consequent: the one to which the arrow points.
Conditionals vs arguments
A conditional is said to be true or false, rather than valid or invalid.
A conditional is not itself an argument.
A conditional: one proposition that comprises two propositions as parts, joined by ‘if-then’ or a similar device.
An argument cannot consists of just one proposition.
A conditional does not assert either its antecedent or its consequent.
An argument asserts its premises and its conclusion.
But, many arguments have conditional conclusions.
Argument trees: devices that can be used for representing arguments in the form of a diagram.
They are helpful when we are reconstructing arguments, particularly complex ones, because they provide a means of showing the ways in which the different parts of an argument are related to each other.
The process of constructing an argument tree is especially useful before you have supplied missing premises and before you have settled upon a reconstruction of the argument in standard form.
Knowing that the argument is valid, is not enough to show you that the conclusion is true.
In order to determine that, you must determine the truth-values of the premises.
To say that an argument is deductively sound is to say: the argument is valid, and all its premises are (actually) true.
The conclusion of a deductively sound argument must be true.
An argument that is not deductively sound is deductively unsound.
Deductive soundness pertains to whole arguments.
If we know that the conclusion of an argument is false, then we know that the argument is deductively unsound.
If the argument is deductively unsound, it follows that either the argument has (at least) one false premise, or the argument is invalid.
If the argument is valid, but unsound, (at least) one of the premises must be false.
If you found that the argument is invalid, you can conclude nothing about the premises.
Modus ponens:
P1) If P then Q
P2) P
C) Q
Modus tollens:
P1) If P then Q
P2) Not-Q
C) Not-P
Disjunctive syllogism:
P1) P or Q
P2) Not-P
C) Q
Argument by cases:
P1) P or Q
P2) If P then R
P3) If Q then R
C) R
Chain (or hypothetical syllogism):
P1) If P then Q
P2) If Q then R
P3) If R then S
C) If P then S
Formal logic:
→ If then
V: inclusive
‘or’, ‘&’, ‘Ʌ’ : and
¬ (or ~): not
Letters (like P and Q) are placeholders for whole sentences or whole statements.
Quantificational logic.
Representing arguments in rigorous ways has certain advantages
Formal logic claims that logical relationships are made by abstracting from the particular subject matter we talk about and concentrating on the logical forms of arguments.
But logical forms are not completely without content or meaning.
Refutation by counterexample: an argument with the same logical form as the original content, thereby proving that the logical form of the original argument is invalid, and therefore that he original argument itself is invalid.
Introducing Arguments - summary of chapter 1 of Critical thinking: A concise guide by Bowell & Kemp (4th edition)
Critical thinking
Chapter 1
Introducing Arguments
To attempt to persuade by giving good reasons is to give an argument.
Not all attempts to persuade (using language) are attempts to persuade by argument.
some are attempts to persuade by means of rhetorical devices
Rhetoric: any verbal or written attempt to persuade someone to believe, desire or do something that does not attempt to give good reasons for the belief, desire or action, but attempts to motivate that belief, desire or action solely through the power of the words used.
An attempt to persuade by argument is an attempt to provide you with reasons for believing a claim, desiring something or doing something.
Arguments appeal to your critical faculties, your reason.
Rhetoric tends to rely on the persuasive power of certain words and verbal techniques to influence your beliefs, desires and actions by appeal to your desires, fears and other feelings.
threats and bribes are arguments (not rhetorics), for they give a reason to do something
Rhetorical techniques can be manipulative and coercive. Their use should generally be avoided by those who aspire to think critically and to persuade by reason.
When analysing attempts to persuade, we have to perform three tasks:
When we put forward an argument we are either advancing an opinion or recommending an action.
In either case we give a number of claims intended to support the claim or the recommendation.
These two types of argument can be collapsed into one.
All arguments can be understood as attempting to provide reasons for thinking that some claim is true (it states how things really are).
To say that a claim is true is to say that what is claimed is how things actually are.
A single claim does not constitute an argument.
An argument needs
Language and rhetoric - summary of chapter 2 of Critical thinking: A concise guide by Bowell & Kemp (4th edition)
Critical thinking
Chapter 2
Language and rhetoric
Once we’ve determined that a text or a speech contains an attempt to persuade by argument, the remainder of argument-reconstruction is largely a matter of interpreting the speech or text as accurately as possible.
Ambiguity
Ambiguity can be used, often deliberately, to obfuscate the content of an argument or rhetorically to obscure the persuaders true point.
A sentence is ambiguous in a given context when there is more than one possible way of interpreting it in that context.
There are two types of ambiguity:
Lexical ambiguity
Lexical ambiguity: a property of individual words and phrases that occurs when the word or phrase has more than one meaning.
Extension: the set or group of things to which an expression applies.
(for example, the extension of the word ‘cow’ are all the cows in the world).
An ambiguous word or phrase has two or more separate and different extensions.
Ambiguous words and phrases can bring their ambiguity into sentences, making those sentences capable of having more than one possible interpretation.
Words that are potentially lexically ambiguous are not necessarily ambiguous in every context.
When interpreting sentences that are lexically ambiguous, we have to focus on the context in which they are written or said and the consequent probability of each of the possible interpretations being the correct one.
Syntactic ambiguity
Syntactic ambiguity: when the arrangement of words in a sentence is such that the sentence could be understood in more than one way.
Vagueness
The meaning of a word or expression is vague if it is indefinite or if it is uncertain what is conveyed by the word in the context under consideration.
Sometimes, someone aware of the weakness of their own position will deliberately leave their meaning vague in order to camouflage that weakness and to evoke strong feelings of approval or disapproval in their readers or listeners.
Words can also have a clear meaning, but which have an indefinitely demarcated extension.
(like colors)
Primary and secondary connotation
The rich secondary connotation (bijbetekenis) of some words provides a further source of vagueness.
Primary connotation: a given thing falls within a word’s extension if, and only if, it fist a certain rule associated with the
.....read more Logic: deductive validity - summary of chapter 3 of Critical thinking: A concise guide by Bowell & Kemp (4th edition)
Wst-r
Chapter 3
Logic: deductive validity
Argument reconstruction: the representation of arguments in standard form, so as to give us a clear and comprehensive view of them.
Argument assessment: the determination of whether or not arguments provide good reasons for accepting their conclusions.
An argument is a system of propositions.
Propositions: a set of premises advanced in support of a conclusion.
People succeed in expressing the propositions they have in mind in varying degrees of clarity. An argument may depend upon premises that the arguer does not state at all, but which he or she is implicitly assuming.
Since the purpose of argument-reconstruction is to determine exactly what argument has been given, part of the task is to clarify what the arguer actually said, and to supplement what the arguer actually said (to make explicit what was merely implicit in the arguer’s statements).
Argument-reconstruction is essentially a task of interpretation.
The principle of charity.
In such facts pertaining to the context in which the argument is given, together with the specific words used by the person, will constitute the total evidence you have for reconstructing the argument.
If, in the third case, you have to chose what representation of the argument is true, it depends on your purpose.
The practice of argument-reconstruction - summary of chapter 5 of Critical thinking: A concise guide by Bowell & Kemp (4th edition)
Critical thinking
Chapter 5
The practice of argument-reconstruction
The first step in reconstructing an argument is to make a list of the argument’s premises and conclusion as concisely and clearly as possible.
Making such a list is only the first step towards a complete reconstruction.
Expressive epithet: terms used to refer to some person, group or other entity but that characterize the entity referred to for rhetorical purposes.
When reconstructing arguments we should strive to display the logical relationships in an argument in the simplest, clearest and most familiar ways possible.
This is not always possible, and doing it will sometimes distract us from other points we are trying to make.
Not only do actual statements of arguments typically include a lot of material that is inessential to the argument, they often exclude some of what is essential to the argument.
Our task is to make the argument fully explicit.
A proposition is implicit: the proposition is part of the argument intended by the arguer but it has not actually been stated by the arguer.
To make a proposition explicit: to state it.
Connecting premise: the premise which you have to make
.....read more Issues in argument assessment - summary of chapter 6 of Critical thinking: A concise guide by Bowell & Kemp (4th edition)
Critical thinking
Chapter 6
Issues in argument assessment
The role of an argument is to give us reasons for accepting its conclusion as true.
The aim is to give an argument by which the intended audience is ought to be persuaded.
We cannot always tell whether or not the argument is sound.
Sound arguments must have true premises.
Since we do not always know which propositions are true and which false, we cannot always tell whether an argument is sound or not.
To say that an inductively forceful argument is defeated for a person: the person reasonably believes the premises, but, nevertheless, reasonably rejects the conclusion.
(They have, for example, extra information).
An inductively forceful argument whose premises you have reason to accept is rationally persuasive only if your total evidence does not defeat the argument for you.
To say that an argument is rationally persuasive for a person:
Rationally unpersuasive argument: an argument that is deductively sound and valid, but gets you no closer to knowing the truth-value of the conclusion.
Rational persuasiveness is doubly relative.
Since people are in different states of information at different times, an argument may be rationally persuasive for one person, but not for another.
Seven points to bear in mind as regards rational persuasiveness:
1 It is not possible for the conclusion of a deductively valid argument to be defeated by a person’s total evidence. This is only possible for inductively forceful arguments.
2 Rational persuasiveness is not part of the definition that the argument be sound (either deductively or inductively).
Pseudo-reasoning - summary of chapter 7 of Critical thinking: A concise guide by Bowell & Kemp (4th edition)
Critical thinking
Chapter 7
Pseudo-reasoning
Fallacies count as arguments in the sense that they fit our definition of an argument. They consist of a set of propositions, some of which premises, one of which is a conclusion. But, one way or another, they are bad arguments.
A fallacy: a mistake in reasoning.
One commits a fallacy when the reasons advanced or accepted in support of a claim fail to justify its acceptance.
A fallacy can be committed either when one is deciding whether to accept a claim on the basis of a fallacious argument with which one has been presented or when one is presented the fallacious argument oneself.
A fallacious argument or inference: one in which there is an inappropriate connection between premises and conclusion.
Almost all fallacies fall under one of the following two types:
The majority of fallacies that we encounter in everyday texts and speech are substantive fallacies.
A fallacious argument can have true or false premises.
Simply having false premises does not make an argument fallacious.
Nor does having true premises guarantee that an argument is not fallacious.
A proposition accepted on the basis of a fallacious argument may turn out to be true as a matter of actual fact.
The best way to become acquainted with the different types of fallacies is to practise identifying and analysing them.
As they are attempts to persuade by argument, you need to reconstruct them in standard form and then use techniques of argument analyses and assessment to demonstrate the ways in which they are fallacious.
Many types of fallacious argument are effective as rhetorical ploys.
Formal fallacies
Formal fallacies: patterns of argument whose reasoning makes purely logical mistakes.
Each type of fallacy constitutes an invalid argument.
The fallacies will be recognized by the presence of the particular invalid pattern.
Affirming the consequent of a conditional
Affirming the consequent for short.
This occurs when we argue from the conditional premise that if P (the antecedent), then Q (the consequent) together with the premise that Q to the conclusion that P.
P1) If P then Q
P2) Q
---------------------
C) P
Example:
P1) Is someone is a philosopher, then
.....read more Everything you need for the course WSRt of the second year of Psychology at the Uva
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