Reason and Argument Lecture 2: Arguments and Validity, Exercises of Design

Download Reason and Argument Lecture 2: Arguments and Validity and more Exercises Design in PDF only on Docsity! Lecture 2 1 Reason and Argument Lecture 2: Arguments and Validity Lecture 2 2 Arguments In an argument, a number of starting claims (premisses) are put forward as, or considered as, supporting a conclusion. Example: There will be talks, or a widespread conflict will break out. There will not be talks. –––––––––––––––––––– A widespread conflict will break out. Lecture 2 5 A Sharpening of Focus We will be concerned primarily with the strongest form of support of this kind. That which occurs in arguments which are such that:– If the premisses are true, then the conclusion must be true also. The truth of the premisses would force or necessitate the truth of the conclusion. Lecture 2 6 Key Concept: (Deductive) Validity Sketch of validity: A DEDUCTIVELY VALID ARGUMENT is an argument such that if its premisses are true then its conclusion must be true also. Validity (the official definition): A DEDUCTIVELY VALID ARGUMENT is an argument such that it is not possible for it to be the case both that its premisses are true and that its conclusion is false. Lecture 2 7 Deductive Invalidity An argument is DEDUCTIVELY INVALID if it could be that its premisses were all true and its conclusion false; otherwise, it is deductively valid. Note: From now on, I’ll just say ‘valid’ to mean ‘deductively valid’, and ‘invalid’ to mean ‘deductively invalid’. Lecture 2 10 George’s salary as a finance officer at the University isn’t big enough to meet payments on a Porsche. George has been seen many times driving a Porsche. George knows a lot about the University computer system. George has been staying late in the office. George seems nervous and on edge. Money seems to have gone missing from University accounts. ––––––––––––––––––––––––––––––––– George is stealing from University funds. Lecture 2 11 If God exists, then there is no unnecessary evil in the world. God exists. ——————— There is no unnecessary evil in the world. If there is a God, then the world will be ordered in ways we’d expect in a product of intelligent design. The world is ordered in ways we’d expect in a product of intelligent design. —————————————————— Therefore, there is a wholly good and all-powerful God. Lecture 2 12 Validity and ‘Good Argument’ Notice, invalid arguments are not always (intuitively) really bad arguments. Some invalid arguments seem to be quite good, in that their premisses (if true) provide quite good reason to believe their conclusions. So … Why focus on validity? Lecture 2 15 Validity and Abstraction In evaluating arguments in terms of validity, we abstract from the actual truth or falsity of the premisses. We say: If the premisses were true, could the conclusion be false? If the answer is ‘yes’, the argument is invalid. If the answer is ‘no’, the argument is valid. Lecture 2 16 (Partial) Independence of Validity from Actual Truth and Falsity There are valid arguments which have one or more false premisses:– David Cameron is Prime Minister of the UK. Whoever is Prime Minister of the UK is universally loved and admired by its people. –––––––––––––––––––––––––––––––– David Cameron is universally loved and admired by the people of the UK. Rene Descartes was an Australian. Every Australian there’s ever been has been a famous philosopher. –––––––––––––––––––––––––––––––––––– Rene Descartes was a famous philosopher. There are invalid arguments which have true premisses and true conclusions:– Whales are not reptiles. The Sun is a giant ball of very hot gas. ––––––––––––––––––––––––––––––––––––– Ulysses is a novel by James Joyce. Lecture 2 17 Validity in Terms of Possible Situations A DEDUCTIVELY VALID ARGUMENT is an argument such that there is no possible situation in which all of its premisses are true and its conclusion false. An argument is DEDUCTIVELY INVALID if there is a possible situation in which all of its premisses are true and its conclusion false; otherwise it’s valid. Lecture 2 20 ‘Inconsistent’ A set of statements (or claims) is inconsistent if and only if it is not possible for all of the statements to be true together. Examples: Set 3 Allen is less than 6 feet 6 inches tall. Allen is more than 6 feet 6 inches tall. Set 4 Mike is clever or buff. Mike is not clever. Mike is not buff. Lecture 2 21 Possibility “Possibility” has more than one sense. In the definition of validity, “possible” is to be understood as relating to logical possibility. Different types of possibility P is EPISTEMICALLY possible (for me): P is consistent with what I know. P is PHYSICALLY possible: P is consistent with the laws of nature/laws of physics. P is LOGICALLY possible: P is consistent with the laws of logic. Lecture 2 22 Logical Possibility and Other Forms of Possibility Notice: Other forms of possibility can be accounted for in terms of logical possibility and consistency. Example Something is physically possible if, and only if, it is (a) logically possible and (b) consistent with the laws of physics Lecture 2 25 Sentences as Components of Sentences (1) Tom is easygoing or Tom is a philosopher. (2) Tom is not easygoing. –––––––––––––––––––– Tom is a philosopher. Tom is easygoing (Part of premiss 1) Tom is not easygoing (Premiss 2) It is not the case that Tom is easygoing. Tom is easygoing or Tom is a philosopher. It is not the case that Tom is easygoing. –––––––––––––––––––––––––––––––––––- Tom is a philosopher. α or β It is not the case that α –––––––––––––––––––––– β Lecture 2 26 Key Concept: Formal Validity (1) Tom is easygoing or Tom is a philosopher. (2) Tom is not easygoing. –––––––––––––––––––– Tom is a philosopher. The FORM of this argument is: Either α or β. It’s not the case that α. So β. This is a VALID FORM OF ARGUMENT. That is, every argument which has this form is valid, whatever the subject matter. Lecture 2 27 Non-Formal Validity …validity which is not simply a matter of the logical structure of the statements involved. This table is brown. Therefore, this table is coloured. Barry is taller than David David is taller than Tom Therefore, Barry is taller than Tom Note: There is debate over where formal validity ends and non-formal validity begins. We’ll largely sidestep these issues by concentrating on the logical powers of particular expressions. Lecture 2 30 Use/Mention & Quotation Marks By putting quotation marks around an expression (a character, a word, or a string of words), we create an expression which stands for that expression. We use the quotation-mark expression when we want to mention the expression. (a) A colon consists of two dots. ‘A colon’ consists of six characters. The expression ‘a colon’ appears at the beginning of sentence (a). Lecture 2 31 Other Uses of Quotation Marks Note that in logic we will be using quotation marks to allow us to talk about (mention) particular expressions. Don’t confuse this kind of use with other kinds of use of quotation marks: —As ‘scare quotes’ to indicate doubts about the concept used or its particular application (e.g. I don’t worry about the “Paradoxes” of Validity. Tom enthused about Christina’s “fantastic vocals”.) —As devices to indicate direct speech (e.g. Tom said he “found Anastacia inspiring”.) Lecture 2 32 Key Points Valid arguments are those where it is not possible for all of the premisses true to be true and the conclusion false. Some arguments are formally valid: they are valid, and their validity depends only upon their form—the way they are built up from logical and non-logical vocabulary. Formally valid arguments depend for their validity on the meaning of the logical vocabulary which appears in them.