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Philosophy

PP201

Nicholas M Ray

Fall

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Chapter 1: The Parts of Public Thinking: Deductive Argument
Assertions and Arguments
-assertion; to present something as if it were true
-argument; the fundamental units of rational exchange; the presentation of reasons; an argument is
premises given in support of a conclusion
-soundness; the property of an argument that succeeds in supporting its conclusion; a sound argument
proves that its conclusion is true
What Makes an Argument Good?
Two ways of approaching the study of arguments and arguing:
(1) Argumentation is a rational practice
-reflects the idea that a good argument is supposed to be an effective one
-reasonableness of an argument has to be measured, at least in part, by the effects the argument has, or
would have, on a basically reasonable person
-stresses the fact that arguing is a process, one that occurs in a communicative context
-argumentation is a practice by which we aim to show the reasonableness of an assertion, up to
whatever standard of reasonableness is called for in that context
-a good argument is the presentation of a collection of premises that jointly are rationally persuasive of
a conclusion
-together, the premises make it reasonable to believe the conclusion
(2) Arguments are linguistic or logical objects
-makes no mention of effectiveness
-argument being sound does not mean that anyone believes, or even ought to believe ,that it is sound
-idealization represented only captures the virtues of deductive arguments
-a good argument defined in terms of the truth of the premises and their logical relation to the
conclusion, without any allusion to speakers or hearers or context
-it doesn’t matter if the audience finds the premises reasonable
-means that first, it must be valid (premises relevant to its conclusion in such a fashion that if the
premises are true, then the conclusion must be true), and it must have all true premises (essential
premises/ones that would remain if all irrelevancies were removed must be true)
Some Basic Vocabulary of Communication and Argumentation
Assertion: the act of stating something as if it were true
Proposition, statement ,sentence, claim: what you say in order to make an assertion
Premise: a statement intended to provide rational support for some other statement (A conclusion),
often in conjunction with other premises
Conclusion: a statement intended to be rationally support by a set of premises
Argument: a collection of premises that justify, or are supposed to justify, a conclusion
Validity: a structural property of argument; an argument is valid just in case there is no way for the
conclusion to be false if all the premises are true
Soundness: a two-fold property of arguments; an argument is sound if it (a) is valid and (b) has all true premises; by definition, a sound argument proves its conclusion
Inference: the act of reaching a conclusion on the basis of some premises
Is Good Argumentation a Matter of Being Logical?
‘The Laws of Thought’;
(1) The Law of Identity; for any proposition P:P if and only if P
(2) The Law of Non-Contradiction (Not both P and not-P)
(3) The Law of Excluded Middle (P or not-P)
Examples;
Intuitionistic Logic: a well-developed formal system that does not include the Law of the Excluded
Middle as an axiom; may tolerate vagueness and fuzzy boundaries better than classical logic, which
tends to idealize and sharpen distinctions conveniently but (potentially) inaccurate; you need DIRECT
proof in intuitionistic logic
Dialetheic Logic: keeps the Law of the Excluded Middle, but gives up/restricts the Law of Non-
Contradiction; tells you that if a collection of propositions contains a contradiction, the collection is
incoherent
-what counts as logic is not a settled question
-logic is not monolithic
-there is a great deal of variety and many live philosophical issue involving logic and logics
-it is probably safer to think of ‘Laws of Thought’ as weaker and less absolute than the name suggests
-we won’t refer to statements or arguments as ‘logical’ because it is a sloppy way of classifying and
understanding
What Isn’t an Argument?
-lines are blurry between good instances, bad instances and non-instances
-bad arguments aka fallacious arguments
-mere assertions are not arguments
Explanation vs. Argument
-arguments; given in the form of premises to defend a conclusion
-explanations; appeal to some facts in order to rationalize, or make sense of, some other fact
-explanation is a form of reasoning that is broadly distinct from argument while often overlapping with it
-arguments aim at showing some statement to be worth believing, while explanations aim to make
better sense of something already believed
Implicit elements: parts that are supposed to be understood from the context
-both arguments and explanations are meant to teach us something
Understanding Valid Argument Forms
-validity is a structural property of arguments
*Modus Ponens;
(1) If P then Q (2) P
Therefore,
(3) Q
-the argument is valid because this is a valid FORM of argument
-to say the structure is valid is to say that any choice of sentences for P and Q that makes both premises
true also makes the conclusion true
-NOTE; having true premises does not necessarily mean having trues Ps and Qs!
-as long as we pick P and Q in such a way that it’s true both that P, and if P then Q, then Q will also be
true
-the property remains even if P and Q don’t happen to make the premises true
*Modus Tollens;
(1) If P then Q
(2) Not Q
Therefore,
(3) Not P
-in both cases, arguments are valid but not sound
-there is no way for the conclusion to be false if the premises are true
-the idea is for the conclusion to be supported by the premises
-a lousy argument with a true conclusion is a lousy argument
-categorical terms; matter of how the categories (premises) are related to one another (ex. Vixen, Fox,
Mammal)
-conditional reasoning; ‘if P then Q’
-quantifier expression; ‘some’ and ‘every’
*Disjunctive Syllogism
(1) P or Q
(2) Not Q
Therefore,
(3) P
-argument has a valid form
Checking an Argument’s Validity: The Method of Counter-Example
0quick and useful way of testing for invalidity is called the Method of Counter-example
-our definition of validity tells us that there is no way for the conclusion of a valid argument to be false if
all the premises are true; means that we can tell that an argument is invalid aif we can think of ways for
the premises all to be true while the conclusion is false
Valid Argument Forms
Argument forms recognized/classified as valid;
(1) Simplification
P and Q Therefore,
P
example-“Eric and Ellen are both doctors. Therefore, Ellen is a doctor.”
(2) Conjunction
P
Q
Therefore,
P and Q
example-“Eric is a doctor. Ellen is a doctor. Therefore, Eric and Ellen are both doctors.”
(3) Addition
P
Therefore,
P or Q
example-“Foxes are mammals. Therefore, either foxes are mammals or cows are mammals.”
“Foxes are mammals. Therefore, either foxes are mammals or lizards are mammals.”
-the resulting statement is true as long as at least one of the sub-statements is true; if we already know
that P is true, this guarantees that “P or Q” is true, no matter what Q is
(4) Hypothetical Syllogism
If P then Q
If Q then R
Therefore,
If P then R
example-“If the dollar is devalued, exports will rise. If exports rise, the unemployment will fall.
Therefore, if the dollar is devalued, unemployment will fall.”
(5) Constructive Dilemma
P or Q
If P then R
If Q then S
Therefore,
R or S
example-“Either it will snow tomorrow or there will be a quiz in class. If it snows tomorrow, classes will
be cancelled. If there’s a quiz in class tomorrow, I’ll fail it. SO either classes will be cancelled tomorrow
or I’ll fail a quiz tomorrow.”
(6) Destructive Dilemmas
If P then R
If Q then S
Not R or not S
Therefore, Not P or not Q
example-“If Zainab called her mother, the answering machine took a message. And if her brother called
her mother, the line was busy. But the machine didn’t take a message, or the line wasn’t busy. So Zainab
didn’t call her mother, or her brother didn’t.”
Other Structural Properties of Arguments
-linked arguments; their premises essentially tie together to support a single overall conclusion (ex.
Modus Ponens); the most fundamental sort of argument
-convergent argument; a range of independent grounds for a conclusion assembled together as
premises; no premise requires the other premises in order to support the conclusion, instead, each
premise directly supports the conclusion
-sequential arguments; cases in which premises establish intermediate conclusions which then serve as
premises for some further conclusion
Truth Conditions
-first element of soundness is validity
-second element= what does it mean to say that a premise is true?
-truth conditions; how things would have to be in order for the statement to be true
Truth and Reasonableness
-arguments, NOT single statements that are valid/invalid, sound/unsound
-statements, NOT arguments that are true or false
-‘reasonableness’ applies to individual statements rather than arguments
-statements are either true or not true, no middling cases
-bivalent truth; having only two possible truth values
Necessary Truths and Definitional Truths
-contingent truth; things might have turned out differently
-necessary truths; they would be true no matter how things might have turned out (ex. propositions of
mathematics)
Truth Conditions of Compound Sentences
Simple (or atomic) statement: a sentence that does not contain another sentence as one of its parts
ex. “My dog has fleas”, and “Continent drift”
Conjunctive statement, or conjunction: a compound statement containing two or more sub-statements
(called conjuncts), usually joined with the words “and” or “but”; a conjunction is true if and only if its
conjuncts are true
Disjunctive statement, or disjunction: a statement of the form “P or Q” is true just in case at least one of
P or Q is true; a compound statement containing two sub-statements (called disjuncts), joined with the
word “or” or near-equivalents like “alternatively”; true if and only if one of its disjuncts is true ;
particularly easy to be true
“or”=inclusive or exclusive
inclusive; AT LEAST one of the listed disjuncts is true; disjunction is also true if BOTH its disjuncts are true
exclusive; applies when one and only one of the disjuncts is true
Conditional statements: a statement of the form “If P then Q” is true unless P is true but Q is false; with
an ‘if-then’ form
antecedent; the ‘if’ part
consequent; the ‘then’ part
Two kinds of conditional statement in natural language;
(1) indicative conditionals; If P then Q
(2) subjunctive conditionals; If it were to be the case that P, then it would be the case that Q
Negation: a statement of the form ‘Not-P’ (that, is “It is not the case that P”) is true if and only if P is
false
Chapter 2: Evidence Adds Up
Cogency and Ampliativity
-argument is cogent just in case it makes its conclusion rationally credible (rationally believable)
-strongly cogent argument provides a high degree of justification for its conclusion
-weakly cogent argument might provide only a tentative or easily overturned justification for its
conclusion
-deductive arguments=strongly cogent arguments (true premises and valid structure, demonstrating
truth of its conclusion)
Valid, Invalid, and Ampliative Arguments
-logical fallacies; arguments th

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