Beliefs and consistency

Critical thinking is the art of evaluating the judgements and decisions we make by examining the process the leads to them. It improves our rationality, and helps us evaluate arguments.

Arguments

Arguments aim to persuade, as opposed to explanations, which aim to clarify:

Argument: You shouldn't change currency at the border because the exhange rate is bad
Explanation: You lost money when you changed currency are the border because the exhange rate is bad

A good argument is not necessarily convincing, nor necessarily saying things that are true. A good argument must simply have acceptable premises and a conclusion that follows from them. Typically, the conclusion is less certain than the premises, whilst in explanations the converse is the case.

Arguments can have premises that aren't explict, called enthymematic premises, e.g.

"Of course I won't vote for Blair. Do you take me for a fool?"
Implictly presumes that only a fool would vote for Blair.

Consistency

A set of beliefs is consistent if they can all be believed at the same time. Consistency isn't a matter of them persisting through time, i.e. one can be fickle over time but consistent at any one point in time when all your beliefs could possibly be true. Consistent beliefs can even be false. For example, "Anyone with at least one brother or sister is not an only child and Bart is an only child. Bart has no bothers, but he does have two sisters" is an inconsistent belief, whilst "The earth is a planet with one satellite, which revolves around the sun. Planets are spherical. The earth is not flat" is consistent.

A belief is consistent if it could be true, and inconsistent if it is self-contradictory. Again, it needn't actually be true, but only possible. For example, "I invented a new sedative that makes people faster and more excited" is inconsistent, whilst "that tree is made of wood" is consistent.

Sentences express beliefs, but it is not always clear which belief(s) a sentence expresses. Thus it is important to be able to find what beliefs a sentence is expressing before we can establish whether or not it is consistent. Beyond finding enthymematic premises, we face other challanges.

Declarative sentences

A declarative sentence is one that in English can be put in the form "Is it true that X?". For example, one might ask, "Is it true that cats can swim?" In this case, "cats can swim" is a declarative sentence, and so unambiguously expresses a belief. Spotting declarative sentences is usually easy, but there are more difficult cases, e.g. "Blackmail is wicked" might be said to be declarative, but at the same time could equally be considered imperative.

But even once isolated, declarative sentences can be made difficult to analyse by several problems:

Lexical ambiguity occurs with homononyms, e.g. "she went to the bank". Without further information on the context it is difficult to analyse the semantics of this sentence.
- Equivocation is a special case of lexical ambiguity, in which two different meanings are used in the same sentence, e.g. "It is right to do X, and no-one has a right not to do X"

Structural ambiguity occurs when the words in a string of words can be meaningfully grouped together in two or more different ways, e.g. "fruit flies like a banana". Here there are two possible structural units, "fruit flies" or "fruit", i.e. the sentence could be describing what fruit flies like to eat, or how fruit travels through the air.
- Ambiguity of cross-reference is a special case of structural ambiguity in which a word or phrase in a string of words refers to something mentioned elsewhere, but it is not clear to which thing it thus refers, e.g. "He stood on his head"; on whose head did "he" stand... his own, or somebody else's head?

Vagueness occurs when a claim's meaning is indeterminate, unclear, e.g. "Ted is thin"; what do we mean by "thin"?

Indexicality occurs when sentences that contain indexical terms say different things in different contexts, e.g. "It is raining now" could be referring to this moment in time, or it could have been referring to 12pm on 01/05/2003, etc.

Propositions

"Pierre est chaud" and "Peter is hot" express the same proposition/belief, despite appearing semantically different. "It is cold today", on the other hand, can express different propositions depending on the context, despite being one single declarative sentence. In other words, a declarative sentence must be understood as distinct from a proposition, and so when analysing sentences, we must look for propositions rather than for declarative sentences, to avoid the problems described above.

Good and bad arguments

Bad arguments

A bad, or fallacious argument is a misleading one. It leads to a conclusion, often very persuasively, by illicit steps of argumentation. There are three types of fallacious argument:

1) Those that depend on dubious premises
2) Those weakened by irrelevance
3) Those that draw hasty conclusions

Dubious premises

Dubious premises needn't be obviously false, but are nonetheless unacceptable. They are often deployed in the hope that the audience will misunderstand or completely fail to understand the argument, or to benefit from them in a particular context, e.g. an advertisement might premise that its product is of a high quality.

A fallacy may often arise from equivocation, ambiguity or vagueness in the premises, making it impossible for the audience to accept them.

A fallacy might also occur when the argument begs the question, i.e. where the argument's conclusion supports the premises, or when the conclusion merely restates the premises. For example: "Older people should avoid psychotropic drugs because they should stay away from mind-altering drugs".

An argument might present a complex question, whereby a question, possibly question-begging, is presented as a premise, and so forces the audience to accept the loaded conclusion of that embedded question in answering the argument as a whole. Thus one can only refuse to acknowledge the argument. For example: "Have you stopped cheating?" assumes that you were cheating in the first place

Finally, an argument may contain premises that are either insufficiently informative for us to accept them as true, or that are simply nonsense.

Fallacies weakened by irrelevance

Arguments often bring in irrelevant information, intended to divert the audience's attention from the argument, and often particular dubious parts of an argument. Fallacies of irrelevance are also used to illegitimately strengthen or weaken arguments.

Ad hominem fallacies are perhaps the most common, where criticism is directed at the opinion holder rather than their argument. They can be abusive attacks (totally irrelevant) or circumstantial (to shed doubt upon a particular aspect of the argument).

Tu quoque fallacies involve accusing the opinion holder of hypocrisy or inconsistency. Whilst they may seem persuasive, they fail to address the opinion holder's argument itself. For example, one person says "You shouldn't take cocaine, it's bad for your health", and the other retorts "You can talk, you're an alcoholic".

Often people will deploy straw man fallacies, setting up uncharitable or inaccurate reconstructions of another's argument to make it easy to criticise it.

Often to strengthen straw man arguments, people will improperly manipulate emotion, providing guilt by association. Appeals to sympathy, vanity, rewards, threats and associations to other loaded subjects can distract from the argument in question. For example: "Positive discrimination is just another form of Naziism"

Association also works in other ways. Ad populum fallacies are deployed to convince the audience that the argument is popular and therefore correct. The opinion holder can also make an improper appeal to authority to lend weight to an argument, in particular to the authority of experts, tradition, and often to nature.

Hasty conclusions

Often an argument will employ enthymematic premises that are supressed deliberately or accidentally overlooked, and that are dubious. Thus the argument, as presented, is hasty in its conclusions. Such arguments will often employ various other kinds of fallacies as diversions to fool you into thinking that the supressed issue has in fact been addressed.

An argument may also appeal to ignorance to support a conclusion, by trying to suggest that because something hasn't been show to be true, it must be false. For example: "That theory doesn't prove God's existence, therefore God doesn't exist".

Finally, an argument may affirm to consequent. For example, in the following form of argument, it can only be accepted if both A and B are sound
1) If A, then B
2) B
A

Good arguments

There are two kinds of good argument - deductive and inductive. Good deductive arguments guarantee the truth of their conclusions, whilst good inductive arguments make their conclusions probable.

Evaluating inductive arguments

Inductive generalisations usually involve projecting general conclusions from particular observations, where by particular we understand a truth that describes a property of an individual entity. For example:

1) Hackers eat a lot of pizza
2) Tom is a hacker
Tom (probably)eats a lot of pizza

The strength of an argument by inductive generalisation can be affected by the size of the sample, the size of the population and how representative of the whole population the sample is; one might be more or less correct by using linear, modal or random sampling methods when determining the generalisation. So in the example, if premise (1) was established after studying the eating habits of ten hackers out of the hundreds of thousands that exist, you might doubt the conclusion. The content and context of the argument may also be important, for example the hackers who did eat a lot of pizza might have lived above a pizza restaurant.

Arguments by analogy draw on similarities between things to suggest that further similarities might exist. In other words, they rest on the assumption that if certain similarities X and Y exist between A and B, then it is reasonable to assume that A and B might also share similarity Z. Such arguments therefore take the form:

1) A and B share important characteristics X and Y
2) A also has important characteristic Z
B (probably) also has characteristic Z

The strength of an argument by analogy rests on the degree of similarity between the objects being considered, and the relevance of these known similarities to the inferred similarities. For example, suggesting that both potatoes and carrots grow in the ground, and that since potatoes are brown carrots must also be brown, is a bad argument by analogy since the colour is not relevant to the place of growth.

Arguments by inference to the best explanation are used when we attempt to formulate a hypothesis that best explains data that cannot be explained otherwise. We infer the correctness of a hypothesis according both to how good the explanation is, and how much better it is than any competing explanations.

Evaluating deductive arguments

Since valid deductive arguments can't ever be false, if we can determine absolutely the validity of deductive arguments, we ought to be able to extend our knowledge indefinitely without ever risking falsehood. Formal logic is the tool we can use to do this, by reducing the complicated syntax of natural language into a symbolic language of logic, which can be more easily and accurately appraised.

The first task of formal logic, then, is to come up with a more formal definition of an argument, which is as follows: a set of sentences that are its premises, and a sentence that is its conclusion. The premises may be empty, since it's possible to state a conclusion without any evidence to support it.

An argument is valid if both whenever its premises are true, its conclusion is also true, or in other words the conclusion logically follows from the premises and cannot be false if the premises are true. An argument is sound if it is valid and its premises are true.

The general form of an argument is very simple:
1) If A, B (if there is a relationship between A and B)
2) A
B

Validity needn't always be a matter of form, however. Consider the following:
1) A (e.g. 'John is a bachelor')
B (John is unmarried)

In that example, the validity is semantic, not syntactic. But it can be made syntactic, like so:
1) A, x (bachelors are unmarried men)
2) Y, A (John is a bachelor)
Y, x (B)