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

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:

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

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

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

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

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

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

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

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

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

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?

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?

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

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

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

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?

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.

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.

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:

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?