1. Introduction to logic Lecture 6 Clear Thinking and Clear Writing By David Kelsey

2. Guidelines Here are some general guidelines for writing a philosophy paper: 1. Your philosophy paper will make an argument. 2. The philosophy paper you will write in this course will be of 2 kinds: –a. The positive approach: –b. The negative approach:

3. Keep it modest & starting the writing process 3. Keep the scope of your paper modest. 4. How do you start the paper writing process? –Read and think about it –Work backwards

4. Start early & be simple 5. Start the paper early, at least a few weeks in advance of the due date. –Finding your thoughts on a subject can be difficult. 6. Be Simple: –Simple straightforward prose

5. Make the structure obvious and Be concise yet fully explain 7. Make the structure of your paper obvious: 8. Be concise yet fully explain –Cover one or two small points but do fully explore them

6. Chuck out what’s unnecessary 9. Chuck out unnecessary paragraphs: –Each paragraph should be necessary in making your argument –Each sentence should be a necessary part of its paragraph –Each word should be a necessary part of its sentence

7. Avoid vagueness and ambiguity, anticipate objections & editing your draft 10. Avoid vagueness and ambiguity. 11. Anticipate objections:Imagine the reader of your paper is a devil’s advocate in the worst kind of way. 12. Read and re-read your draft

8. Vagueness A vague statement is one whose meaning is indistinct, imprecise or lacks details. Degrees: Vagueness isn’t all or nothing. It comes in degrees. –Apartment example

9. Clarifying vagueness Desirable vagueness: sometimes vagueness is actually desirable. –Being Romantic Clarify: If we come across a vague statement we can simply try to clarify the lack of detail or indistinct-ness. –Job example

10. Vagueness and Propositions A vague statement –it is unclear what proposition the sentence asserts at all. –It could be any one of a number of propositions

11. Ambiguous Claims An ambiguous claim is one that is subject to more than one interpretation. Claim x   –P1 P2

12. Semantic Ambiguity A sentence that is semantically ambiguous is one which contains an ambiguous word or phrase. For example: What do you do when you have a semantic ambiguity?

13. Syntactic Ambiguity A sentence is syntactically ambiguous when it is ambiguous because of its grammar or the way it has been structured or put together. When you have come across a semantic ambiguity what do you do?

14. Analytical Definitions: their form An Analytical definition is composed of a definiendum and a definiens. –The definiendum: –The definiens: Form: the form of a definition is this: –X =df _____ Which is the definiendum and which is the definiens? –For example, Bachelor =df unmarried adult male

15. Necessary and sufficient conditions We can think of a definition as a set of necessary and sufficient conditions. X is a necessary condition of Y if and only if (or iff) we cannot have Y without also having X. –Oxygen and Combustion X is a sufficient condition of Y iff X is all that is needed to get Y. –Being born in the US and citizenship

16. Necessary and Sufficient Conditions #2 X is both a necessary and sufficient condition of Y iff both –1) we cannot have Y without also having X & –2) X is all that is needed to get Y. Bachelorhood and being an unmarried adult male

17. Correct Definitions For a definition to be adequate the definiendum and definiens must be co-extensive. For the defiendum and definiens of any definition to be co-extensive it must be the case that: –Everything in the extension of the definiendum is in the extension of the definiens and vice versa… –What is the extension of a concept?

18. Co-extensiveness: An example So if your definition of BACHELOR as UNMARRIED ADULT MALE is correct then: –Everything in the extension of BACHELOR is in the extension of UNMARRIED ADULT MALE and vice versa.

19. Testing definitions To determine if a definition is adequate: –determine if its definiendum and definiens are co-extensive. –Is there any item in the extension of one that isn’t in the extension of the other? Example: Car =df 4 wheeled vehicle one can drive –All Cars are 4 wheeled vehicles one can drive. –All 4 wheeled vehicles one can drive are Cars. Universal generalizations and counterexamples –A counterexample: a case that violates a universal generalization.

20. Counterexamples 2 examples: Defining Car as 4 wheeled vehicle one can drive: –We need to find either a Car that isn’t a 4 wheeled vehicle one can drive –Or a 4 wheeled vehicle one can drive that isn’t a Car –Thoughts? Defining Knowledge as true belief: –We need to find either –a case of knowledge that isn’t what? –Or a case of true belief that isn’t what? –A counterexample: The Belief Game:

21. Counterexamples #2 Love: Say I define Love as a deep seated feeling composed of compassion & care which one can have for another human being. –Can anyone find a counterexample to this definition? We are looking for either: –a case of love that isn’t ____________ –a case of having this feeling for another human which isn’t ______________ –Any thoughts?