Notes on Introduction to Logic --
Phil A101
William Jamison - Instructor
Notes for
Logic by Robert Baum
Lecture 2:
CHAPTER 1
As soon as you get the text and have some time, please read through the Introduction and do the exercise on page 5. Don't write in the answers in the text! The suggestion Baum makes is to time your self at this and then retake the exercise after the course is over. Compare your times. See if there is a difference. More thoughts on lecture 1?
In class lectures begin with Chapter 1.
Chapter 1
Informal Analysis of Statements 30
1.1 Sentences 31
We distinguish the physical aspects of our language from the meaning it has for us. To talk about the meaning we use the words “statement” or “proposition” instead of “sentence.” More on this in 1.3.
Exercises 31
These are to help clarify the above difference. Do you see why this is an important difference?
1.2 Cognitive and Noncognitive Uses of Sentences 32
Is the sentence used to make a statement that is true or false? Can the sentence be used in any other way? It seems that what we call declarative sentences can be used to make statements that are true or false. Imperatives, exclamations, and questions are not true or false. Why is this the case?
Exercises 33
These show that a sentence may be of non-declarative form but still used to make a statement that is declarative and have truth value (that is be true or false). What kind of intonation does the speaker have to use to utter a sentence that is non-declarative in form to use it to make a declarative statement?
1.3 Statements 34
What about recordings of statements? Is the difference in verbalizing the sentence or something else? Think about the difference between brain states and thoughts. I wonder if there is something common here about the way we want to think about our subjective experience of objective phenomena. To keep it simple, statements or propositions will be true or false. (But see Pierce to make it complicated).
1.4 Recognizing Sentences Used to Express Statements 35
You might think about who determines what a statement means at this point. It seems to me that the audience determines what you meant regardless of what you intended to mean! The speaker must receive feedback and decide if the feedback is what was expected. If not, a different way must be tried to transmit that message until the audience reacts the way the speaker expects. Is this how we communicate?
Exercises 37
Here would be a good place to discuss the “Boo-Hooray” theory of meaning.
1.5 Self-Evident and Supported Statements 38
Syntactically analytic statements seem to be free of the critique Quine gives analyticity in his work. Semantically analytic statements do not.
“Call an observation categorical analytic for a given speaker if, as in 'Robins are birds', the affirmative stimulus meaning for him of the one component is included in that of the other. Otherwise synthetic. Call a sentence or set of sentences testable if it implies some synthetic observation categoricals. Call two observation categoricals synonymous if their respective components have the same stimulus meanings. Then the empirical content of a testable sentence or set of sentences for that speaker is the set of all the synthetic observation categoricals that it implies, plus all synonymous ones. I add the synonymous ones so that merely verbal variation will not obstruct sameness of content.” (Quine, Pursuit of Truth pp. 16-17). We will see the source of these relationships when we look at the square of opposition.
Exercises 40
(X or Y for sentences, A or B for words from above.)
Have you ever heard a politician say something semantically analytic? Wouldn’t that be psychologically persuasive to those that did not mull it over? They can say a lot this way, without saying anything we would disagree with! The trick is saying contingent or synthetic statements and still finding an agreeable audience. But if the main reason we speak to one another is to voice disagreement, how much better off a speaker is that sticks to analytic statements!
1.6 Logical Relationships between Two (or More) Propositions 44
This is why the set of beliefs a person has can be coherent or incoherent. Each belief can be voiced as a statement. Do all the statements we accept go together or are there conflicts? If there are conflicts, do we experience cognitive dissonance?
1.7 Consistency 45
Aristotle argues that the person who denies they have to be consistent in their arguments cannot argue his point. Yet it does seem like we can believe contrary things without breaking down. Imagine a computer trying to operate with contradictory instructions! A dialectical interpretation of the nature of things suggests that each “thing” implies its opposite! An interesting book here is John Barrow’s Impossibility. Another issue: Does the religious mind require an ability to think incoherent views together?
Exercises 48
1.8 Real versus Apparent Disagreements 49
In light of this, are most disagreements real or only apparent? Imagine people speaking with one another but using words in different ways in different contexts. If they do not mean the same things, how can they have a real disagreement?
Exercises 52
Why would we agree that #5 is consistent?
1.9 Verbal Disagreements 52
What would you consider poor?
Exercises 53
Does it help us if we determine that a disagreement is merely verbal?
1.10 Implication 54
We will do much more with this through out the course.
1.11 Logical Equivalence 55
Implication both ways? We are not talking necessarily about the same sets of things, but the truth value of the statements!
1.12 Independence 56
Are we talking about completely different sets of things?
Exercises 57
Summary 60
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