Philosophy 105
Fall 2005
Lecture Notes - Chapter 3
A. Terms for Evaluating Statements and Terms for Evaluating Arguments
Truth and rationality apply to individual statements. We have a different set of terms to describe whole arguments. Imp. to keep these terms separate. Learn the terminology and its application. Arguments are never true, false, rational or irrational. Those are terms for statements. We'll discuss the terms for whole arguments as we go through Chapters 3 and 4.
B. Elements of Argument Analysis
There are two main elements of argument analysis:
● Reconstruction (putting into standard form)
● Evaluation.
C. Elements of Arguments
Two main elements of arguments
● premises
● conclusions
D. Two Ways Arguments Go Wrong
Consider: “The President said that there were WMD in Iraq. So, there were WMD in Iraq.”
Two ways an argument can go wrong, and so two main components to evaluation
(i) You might reply that he did say it, but Presidents can be mistaken, that they distort things, and so on. This accepts the premise but says that it fails to support the conclusion adequately. This is to say that the arg. is "ill-formed" and not “well-formed. This is just about the connection between the premises and the conclusion.
(ii) You might say that if you look carefully at what the President said, he never quite said this. Now your objection concerns the merits of the premise itself. As we develop things, this will have to do with the soundness (or strength) of the argument. Details to follow, but roughly, soundness for arguments is like truth for statements, and strength is like rationality.
E. Two Kinds of Well-formed Argument
Contrast the following situations:
1) I'm asked if Dave took the test. I know that Dave is on the roster for my class and I look at the roster. I see that there's an entry for a grade beside every name, without focusing on any particular names. I reason:
1. Everyone in the class took the exam
2. Dave is in the class
3. Dave took the exam.
There is no possible way in which those premise could be true and the conclusion false. This is a deductively valid argument.
2) I'm standing in line eagerly waiting to see a movie. I believe that I will enjoy the movie. Why? It’s one of a series and I liked the first 59, others say it was good. Formulate argument.
1. I liked the first 59 movies in the Batman series.
2. Others who like the first 59 Batman movies liked this movie
3. I will like this movie.
Notice two things: (i) it is possible for the premises to be true and the conclusion false; (ii) if I learn that the conclusion is false, by watching the movie, I don't come to think that I didn't like the first 59 or that the others didn't like this one. I don't reject the premises. Contrast what would happen if somehow I learned that the conclusion in the earlier argument was wrong - I then must reject one of the premises. This second argument is an example of an inductive argument, one that makes its conclusion probable. We'll say that arguments like this are cogent.
F. Arguments and Evidence
You can think of arguments as precise ways of spelling out evidence bearing on a proposition. The premises state some evidence - either evidence that is new to you or evidence you already were aware of. The argument says, in effect, since you have these premises among your evidence, your conclusion is justified for you. .
A. Preliminary Definition
See p. 61.
B. Four Crucial Points
1. The validity of an argument does not depend upon the truth value of its premises. Consider
1. All members of the UR faculty are over 6 feet tall.
2. RF (me) is a member of the UR faculty.
3. RF is over 6 feet tall.
This is valid! That’s not to say that it is a good argument. The premises are bad ones since we know that (1) is false. But that’s a different defect. It has nothing to do with validity.
First crucial point: An argument can be valid even if it has premises that are obviously false. All that matters is the connection between the premises and the conclusion.
2. The argument just discussed has a conclusion that you know to be false. It is still valid.
Second point: An argument can be valid even if it has a conclusion that is obviously false.
3. Incomplete arguments are invalid.
1. Smith is a good student.
2. Smith has a brain.
This is not valid. It is an incomplete argument. A premise is left out.
1. Smith is a good student.
2. All good students have brains.
3. Smith has a brain.
The lesson to be drawn is that
Third point: An argument is valid only if its premises by themselves guarantee the truth of the conclusion. If some other premise, even if it is obvious, is needed to guarantee the truth of the conclusion, then the argument is invalid.
4. Probably the hardest thing about this is the idea of impossibility, which is used in the definition. Things that are extremely unlikely are nevertheless possible. Things that you may know to be false can still be possible. Something is possible provided there is some way things could have worked out so that it is true. Thus, if I’ve bought a ticket in a zillion ticket lottery, it’s still possible that I’ll win. So, an argument from premises describing that situation to the conclusion that I won’t win is not valid. In contrast, look at Argument 3.4, p. 61. There is no possible way for those premises to be true and the conclusion false.
Also possible, in the relevant sense, are things we know to be false. Consider the proposition that no one is in this room right now. We know it’s false, but it is still possible. That is, things could have worked out in such a way that it was true.
Here is a proposition that is not possible:
Bush is president and ~(Bush is president).
Notice that you can tell that this is false without knowing who Bush is, what presidents do, etc. Just from the form, it follows that this is not true. Another impossibility:
All American presidents are male and Hilary is not a male and Hilary is president.
Consider next:
No American president is from Texas and George W. Bush is from Texas.
This is possible, since Bush could have failed to be president and could have been from somewhere other than Texas. Thus:
Fourth point: Something is impossible only when there is no way at all that things could have worked out so that it was true. An argument is valid only when there is no way that things could have worked out so that its premises were true and its conclusion false.
C. A Complication and a Revised Definition
The simple idea of validity is not quite right. Consider
George is a son
George is male
Does this argument satisfy our original definition of validity? This turns out to be a complicated
matter, turning on exactly how we understand the concept of necessity involved in the definition.
It does seem right to say that by definition a son must be male. You cannot come up with a case
in which the premise is true and the conclusion false, given the meanings of the words. At the
same time, this argument does not seem to follow a good pattern. What's the pattern here?
P
Q
We could stick with (D1) and count these arguments as valid. But the core idea of validity has to do with form or structure. Arguments that are valid are ones in which the conclusion follows just in virtue of form, not partly on the basis of the meaning of the (non-logical) terms like ‘son’ or ‘male’. So, we’ll revise the definition to the one on p. 75. The argument above definitely is not valid according to this definition. But if we add a premise yielding
George is a son
All sons are male
George is male
we get a valid argument.
Key point: validity is a matter of form. The revised definition makes use of this idea, but the original definition did not.
D. Sentential Logic and Predicate Logic
The ability to recognize patterns of argument is crucial to learning to formulate and evaluate arguments. You can recognize patterns by identify recurring elements.
Examples - go over exercises 1-9 (skip 5) on pp. 72-3; 1-7 on p. 74.
Sometimes the important structural elements are complete sentences. Sometimes they involve smaller units - subjects and predicates. It is relatively easy to do this in cases where the arguments are simple and the elements are right there for you pick out of the reconstruction. It’ll be much tougher later on.
When I ask for patterns of argument, I mean the logical structure, not the names of the patterns.
E. Testing for Validity
1) Find a counterexample.
This is an example in which the premises are all true and the conclusion is false.
Three comments on this:
1. The example must really be possible. See text, p. 77 for examples of this.
2. The premises must all be true together. Suppose you just say, in response to the example about the height of UR faculty members, "Well, suppose the premises are true, but RF isn't that tall." But the premises can't both be true if he isn't that tall. They must all be true at the same time.
3. Failure to find an example does not prove validity.
2) Find a counterexample to the pattern.
Find an argument following exactly the same pattern to which you can find an obvious
counterexample. But you have to be careful with this - you have to pick the best potential pattern
for the original argument. Suppose you took Argument 3.13 to have a pattern from sentential
logic. You’d then say it is invalid. And you’d be wrong.
3) Use the charts in the text.
Again, this works only if you pick the right pattern.
F. Rewording Arguments
Consider
1. It always rains when we have a picnic scheduled.
2. We have a picnic scheduled for Saturday.
3. It will rain on Saturday.
This is the all A’s are B’s pattern. Reword to make this obvious:
1. All days that we have a picnic scheduled are rainy.
2. Saturday is a day that we have picnic scheduled.
3. Saturday is [will be] rainy.
Note: (1) as stated is about all days, past and future. So it’s ok that (3) is about a future day. It still falls under (1).
Another example:
1. The winner is the team that gets the most points.
2. Philadelphia scored the most points.
3. Philadelphia wins.
Reword as:
1. All teams that get the most points are winners.
2. Philadelphia is a team that got the most points.
3. Philadelphia is a winner.
Key idea: reword arguments to make them follow standard patterns as closely as possible.
This is not just my own pickiness. Seemingly valid arguments may not be quite right. And following the forms carefully will help you to see that.
G. Some Examples
This will be a good review for the quiz - Exercises on pp. 78-80. State patterns for and evaluate p. 79-80, 2a, c, d, f-i, n. 3b, d.
III. Cogency
A. Comparison to Validity
1) The basic idea is that cogent arguments are invalid arguments that nevertheless provide good
support for their conclusions. Like validity, cogency is a matter of the form or structure of the
argument, not the actual truth value of the premises. Intuitively, in a cogent argument, if all you
knew was that the premises were true, then it would be reasonable for you to believe the
conclusion. Thus, this is cogent:
1. PHL 105 is a 100 level class at the UR.
2. Almost all 100 level classes at the UR meet on either Mon. or Tues.
3. PHL 105 meets on either Mon. or Tues.
2) Background information does not convert a cogent argument into an ill-formed argument. In the argument above, information against (1), (2), or evidence that PHL 105 is one of the few classes with a different schedule does not show that the argument is not cogent. When you think about that stuff, you are not considering what would be reasonable if all you knew was that the premises were true. You are adding additional information.
3) Similarly, background information does not convert an otherwise ill-formed argument into a cogent argument. To be cogent an argument must include the key assumptions that make it work. Incomplete arguments are not cogent. See definitions in text.
4) Cogency comes in degrees. We won't make a big fuss about that.
B. Some Examples
Cogency is trickier than validity. Go over p. 87, 1b, d, e; p. 88, 2a, c, e.
Go over 1, pp. 92-3.
© Richard Feldman, 2005