Lecture Notes by Christopher Lay

Los Angeles Pierce College

Department of History, Philosophy, and Sociology

Mathew Van Cleave's 2016 Introduction to Logic and Critical Thinking

https://open.umn.edu/opentextbooks/BookDetail.aspx?bookId=457

Chapter 2 "Formal Methods of Evaluating Arguments," § 1 "What are formal methods of evaluation and why do we need them?" 

The Informal Test of Validity, and its Limits

Recall "the informal test of validity" from Chapter One.  "According to that test, in order to determine whether an argument is valid we ask whether we can imagine a scenario where the premises are true and yet the conclusion is false." 

"The informal test relies on our ability to imagine certain kinds of scenarios as well as our understanding of the statements involved in the argument." 

"Because not everyone has the same powers of imagination or the same understanding, this informal test of validity is neither precise nor objective." 

Precision and Objectivity

"[[W]hile one person may be able to imagine a scenario in which the premises of an argument are true while the conclusion is false, another person may be unable to imagine such a scenario."

"As a result, the argument will be classified as invalid by the first individual, but valid by the second individual."

"[O]ur standard of evaluation of arguments (i.e., validity) to be as precise and objective as possible, and it seems that our informal test of validity is neither."

Absence of Precision

"It isn’t precise because the concept of being able to imagine x is not precise—what counts as imagining x is not something that can be clearly specified."

"What are the precise success conditions for having imagined a scenario where the premises are true and the conclusion is false?"   

Absence of Objectivity

Objectivity is lacking "since it is possible that two different people who applied the imagination test correctly could come to two different conclusions about whether the argument is valid."   

"[P]eople’s understanding of the statements differ and partly because people have different powers of imagination."

Formal Evaluation and Precision and Objectivity

"The goal of a formal method of evaluation is to eliminate any imprecision or lack of objectivity in evaluating arguments." 

Achieving Precision and Objectivity with the Removal of Imagination and Meaning

Methods of formal evaluation can be applied "without having to utilize imagination at all." 

Methods of formal evaluation can be applied "without really having to understand the meanings of the concepts used in the argument." 

("In general, a formal method of evaluation is a method of evaluation of arguments that does not require one to understand the meaning of the statements involved in the argument.")

Form, not Content

A formal method of evaluation "evaluate[s] an argument by its form, rather than its content." 

A "[F]oretaste" E.G.

Consider this:  Kamaiyah is effervescent and talented. 

"This statement is a conjunction because it is a complex statement that is asserting two things:"

Kamaiyah is effervescent. 

Kamaiyah is talented. 

Conjunctions / And

"These two statements are conjoined with an 'and.' So the conjunction is really two statements that are conjoined by the 'and.'"

"Thus, if I have told you that" Kamaiyah is effervescent and talented, "it follows logically that" Kamaiyah is effervescent.   

Here is that simple argument in standard form:

1) Kamaiyah is effervescent and talented. 

2) Kamaiyah is effervescent (from 1). 

"This is a valid inference that passes the informal test of validity." 

"But we can also see that the form of the inference is perfectly general because it would work equally well for any conjunction, not just this one." 

Placeholders / Symbols

"This inference has a particular form that we could state using placeholders for the statements," Kamaiyah is effervescent and Kamaiyah is talented. 

"1. A and B"

"2. Therefore, A" 

"We can see that any argument that had this form would be a valid argument."

Even When You Don't Understand the Meanings

1) Kweego is a foeshiggler and poncy. 

2) Therefore, Kweego is poncy (from 1).  

"Regardless of whether you know what the statements in the first premise mean, we can still see that the inference is valid because the inference has the same form ... pointed out above."   

You should now understand that "what it means for an argument to be valid" stems from the argument's form.