Reasoning and Logic

Reasoning and Logic Week 02

In today’s lecture… • recap of last week’s lecture • deductive and inductive reasoning • truth and truth-value • basic principles of logic • problem cases

Before we start… Students who missed the first lecture may go to the course website to download the course outline, lecture notes (PowerPoint) and other reading materials. The address is: filmandphilosophy.weebly.com

Before we start… If you have any questions about lectures, tutorials or coursework, you can contact me at: chakin@gmail.com

Before we start… • During lectures, every time you see a question or some questions in red, you will be given 2 minutes to think about them. • Don’t sit passively doing nothing. Try to write down some thoughts and ideas of your own. Ask for help if there are things that you don’t understand.

Before we start… Please make sure you have signed up for tutorials. Tutorial dates, times and classroom numbers can be found on the course website under ‘Announcement’.

Recap In last week’s lecture, we looked at the following: • what is philosophy • how to study philosophy • critical thinking skills • the course outline

Recap Basically, philosophy is concerned with: [1] questions that may not have ultimate answers [2] issues that cannot be adequately understood through common sense

Recap We study philosophy by: [1] asking questions [2] analyzing concepts and ideas [3] comparing and evaluating various viewpoints [4] developing arguments through critical thinking

Recap To develop the skills of critical thinking, you should: [1] consider issues from a variety of perspectives (觀點) [2] examine relevant facts and arguments [3] be ready to support your own views with reasoned arguments

Reasoning and arguments • Critical thinking requires the use of reasoned arguments (合理的論據) to support one’s views. • Reasoned arguments are relevant (切題的), valid(有效的), and supported by evidence (facts, observations, statisticsand examples).

Reasoning and arguments • An argument consists of one or more ‘premises’ 前提 (facts or reasons) and a ‘conclusion’ (a claim, a judgment or an assertion). • Premises are statements that support a conclusion. They are supposed to provide the reason, evidence or justification for a conclusion.

Reasoning and arguments • Reasoning is the act of drawing (or deriving) a conclusion from a premise or a set of premises. • An argument is unsound (無效的) or fallacious (錯誤的) if the premise or premises do not support the conclusion. A ‘fallacy’ (謬誤) is an error in reasoning.

Evaluating arguments An important part of philosophy is the evaluation (評估) of arguments. When we evaluate arguments, we should always ask: • Is the evidence/data relevant? • Are the factscorrect? • Is the reasoning logical and valid? • Are there other possibilities? • Are there any counterarguments?

Evaluating arguments “The power is out. You must have forgotten to pay the electricity bill.” What is the problem with this line of reasoning?

Evaluating arguments The question we should ask is: “Are there other possibilities that may lead to power failure?” (e.g. Maybe the fuse is damaged.) If there are other possibilities, the conclusion does not necessarily follow from the premise (i.e. the reasoning may be incorrect).

Deductive reasoning A deductive (演繹的) argument is made up of premises (facts and reasons) and a conclusion. All children love pets. [premise 1] Sue is a child. [premise 2] Sue loves pets. [conclusion]

Deductive reasoning A deductive argument is valid if the conclusion follows necessarily from the premises. All men are mortal (會死的). Socrates is a man. Therefore, Socrates is mortal.

Deductive reasoning • A deductive argument is sound if and only if [1] it is valid, and [2] all of its premises are true. Otherwise, a deductive argument is unsound or fallacious. • We can say that the truth of the conclusion is contained within the truth of the premises.

Deductive reasoning All children are afraid of the dark. Dorothy is afraid of the dark. Dorothy is a child. Is this an example of a valid deductive argument? Why or why not?

Inductive reasoning • Inductive (歸納) reasoning is an act of drawing a general (普遍的) conclusion from particular (個別的) facts or observations. Example: My cat is lazy. My friends’ cats are lazy too. Therefore, all cats are lazy.

Inductive reasoning “I have read 100 comic books. They are all very interesting. Joe just gave me a new comics. I haven’t read it, but I know it must be very interesting.” Do you think this is a valid argument? Why or why not?

Inductive reasoning • Here, the argument can be broken down into 2 parts: [1] The 100 comic books I have read are interesting; therefore, all comic books are interesting. (inductive reasoning); [2] If all comic books are interesting, the one that Joe gave me must be interesting. (deductive reasoning)

Inductive reasoning • Part [1] of the argument (induction) is invalid because the premise about particulars (I have read 100 interesting comic books.) does not necessarily support the general conclusion (All comic books are interesting.) • Part [2] is a valid deductive argument.

Inductive reasoning • An inference (推論) from a number of particular facts and observations to a general rule is called ‘generalization’. • Generalizing from a limited set of facts or observations, however, is not always reliable. This is called ‘the problem of induction’ or ‘the problem of the black swan’.

Inductive reasoning • In the past, people of the West thought that all swans (天鵝) were white. • The 17th century discovery of black swans in Australia showed that the premise ‘All swans are white’ was mistaken.

Inductive reasoning • The existence of ‘black swans’ illustrates the problem of induction. • It draws attention to the limitation of inductive reasoning based on limited experiences (i.e. generalizing from a limited set of facts and observations).

Truth and truth-value • Good reasoning and logic is especially important in the study of philosophy. • The subject matter of logic is the correct connection between ideas. In other words, logic is concerned with the rules or principles (原理) of correct reasoning.

Truth and truth-value • In logic and philosophy, the term ‘truth-value’ means ‘truth or falsehood’. To ask for the truth-value of a propositionp is to ask whether p is true or false. • The concept of truth-value can be applied to propositions (命題), beliefs, theories, etc.

Truth and truth-value • A proposition is a statement. • For example, to ask “What is the truth-value of the proposition ‘Steve is Bob’s brother’?” is the same as asking whether the statement ‘Steve is Bob’s brother’ is true or false.

Truth and truth-value • Beliefs and propositions are ways we make sense of the world. • Merely believing in something, however, does not automatically make it true. A man may firmly believe that he is Jesus Christ or Napoleon, but his belief still cannot possibly be regarded as true.

Truth and truth-value • Beliefs are mental entities – they only exists in people’s minds. • Propositions (statements), on the other hand, can exist independently of the mind as the meaning or content of spoken or written words.

Truth and truth-value • A proposition, however, is different from a sentence (spoken or written words); it is the meaning expressed by a (spoken or written) sentence. • Whenever you say something about something (through speech or writing), the sentence you say or write expresses a proposition.

Truth and truth-value • Two sentences (spoken or written) express the same proposition if they have the same meaning. • For example, “Snow is white” (in English) and “Schnee ist weiß” (in German) are different sentences, but they express the same proposition.

Truth and truth-value • Not everything we say or write or think is a proposition. Questions (e.g. What time is it?) and requests (e.g. Please keep quiet.), for example, are not propositions.

3 logical principles • Now, let us consider some of the most basic principles of logic: 1. The law of bivalence 2. The law of the excluded middle 3. The law of non-contradiction

3 logical principles The law of bivalence: ‘For any proposition p, p is either true or false.’ e.g. The statement ‘Craig is an artist’ is either true or false.

3 logical principles The law of the excluded middle: ‘For any proposition p, either p is true or not-p is true.’ e.g. Either the statement ‘Craig is an artist’ is true, or the statement ‘Craig is not an artist’ is true.

3 logical principles The law of non-contradiction: ‘For any proposition p, it is not the case that both p is true and not-p is true.’ e.g. The statement ‘Craig is an artist and Craig is not an artist’ is false.

3 logical principles • Note that some ideas or concepts are self-contradictory(自相矛盾的). • We know, for example, that there are no round squares, no living dead people, and no largest number because such things violate the law of non-contradiction.

3 logical principles • To summarize: the basic logical principles require that [1] every proposition has exactly one truth-value; [2] a proposition must be either true or false; and [3] no proposition can be both true and false.

Truth and truth-value • In logic and philosophy, it is often assumed that a proposition (statement) must have a truth-value; it must be either true or false. • A sentence that is neither true nor false (i.e. a sentence that does not have a truth-value) does not express a proposition.

Think! Suppose Craig is a computer programmer. He writes songs and draws pictures in his spare time. Some people think that he is an artist, but others do not. Does the statement ‘Craig is an artist’ have a truth-value?

Think! Can you think of any statements that are neither true nor false? In what follows, we willconsider some counterexamples (反例) to the logical principle that ‘every proposition must be either true or false’.

5 problem cases 1. sentences containing non-referring expressions 2. predictions of future events 3. liar sentences 4. sentences containing indexicals 5. sentences about moral, ethical, or aesthetic (美學) values

Non-referring expressions • e.g. ‘The present king of France is bald(秃頭的).’ • Because France has no king in present times, philosopher P. F. Strawson argues that the statement has no truth-value – it is neither true nor false.

Non-referring expressions In a famous dispute (爭論), Bertrand Russell disagreed with Strawson, arguing that the statement ‘The present king of France is bald’ has a truth-value – it is a false proposition. Who is right? Strawson or Russell? Why?

Non-referring expressions Do the following sentences have truth-values? “A unicorn is a horse-like creature with a horn in its forehead.” “Santa Claus keeps reindeers.” “A crocodile ate my homework.”

Future events • Some philosophers think that the sentence ‘It will rain tomorrow’ is neither true nor false at present. • They argue that because the future is not fixed or determined (注定), predictions about the future has no truth-value.

Liar sentences • Examples of liar sentences: ‘I’m lying.’ ‘This sentence is false.’ • By referring to itself, a liar sentence generates a paradox (悖論) when we consider what truth-value to assign to it.

Reasoning and Logic