PHILOSOPHICAL STUDIES
Logic

(Introduction to Logic by Copi)

CHAPTER 2: ANALYZING ARGUMENTS

2.1 Paraphrasing Arguments

The most common, and perhaps the most useful technique for analysis is paraphrase We paraphrase an argument by setting forth its propositions in clear language and in logical order. . . . great care must be taken to ensure that the paraphrase put forward captures correctly and completely the argument that was to be analyzed.

"Peter Abelard . . . General germs (e.g., justice, yellow, smooth plainly do exist, but are there abstract objects that actually exist, beneath or behind those terms, in some non-physical world? Abelard held that there are no such entities, but that we are sometimes misled by the words we use for the common properties of things. His position came to be known as nominalism . . . In logic, Abelard explored the relations of premises and conclusions in deductive arguments. He was one of the first to emphasize the syntactic nature of validity. An argument is valid, he pointed out, not because of the semantic content of its propositions, but because of the formal relations among those propositions.

2.2 Diagramming Arguments

With a diagram we can represent the structure of an argument graphically; the flow of premises and conclusion is displayed in a two-dimensional chart, or picture, on the page. . . . When an argument is complex, with many premises entwined in various ways, a diagram can be exceedingly helpful.

. . . . first number all the propositions it contains, in the order in which they appear, circling each number. Using arrows between the circled numbers, we can then construct a diagram that shows the relations of premises and conclusions without having to restate them. . . . a conclusion always appears on the space below the premises . . . coordinate premises are put on the same horizontal level.

When the several premises of an argument are not all coordinate--that is, when some premises give direct support not to the conclusion but to other premises that support the conclusion:
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Another strength of diagrams is their ability to exhibit relations between the premises . . . In some arguments, however, the premises support the conclusion only when they are considered jointly[:}.
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Some complications may be revealed more clearly using paraphrase. When an argument has a premise that is not stated explicitly, a paraphrase allows us to formulate the tacit premise and then add it to the list explicitly. A diagram requires the representation of the tacit premise in some way that indicates visually that it has been added (a broken circle around a number is commonly used) . . .

The number of arguments in a passage is determined, most logicians agree, by the number of conclusions it contains.

Two conclusions (and hence two arguments) may have a single stated premise.

A single argument means an argument with a single conclusion, regardless of how many premises are adduced in its support.

. . . the same proposition can serve as a premise where it occurs as an assumption in an argument; or as a conclusion where it is claimed to follow from other propositions assumed in an argument. "Premise" and "conclusion" are always relative terms.

Multiple arguments . . . [N.B. multiple arguments require multiple conclusions.]

"William of Ockham, sometimes spelled Occam, (c. 1288-c. 1348) . . . The great intellectual theme of William's life was simplification. . . . 'Ockham's Razor' . . .; one should not multiply entities beyond necessity. [Simplification led him to accept nominalism.] nominalism; what exists in the universe are only individuals. The universals, or Platonic forms, of which some philosophers write, he believed to be no more than the products of abstraction by the human mind."

2.3 Complex Argumentative Passages

Analyzing passages in which several arguments are interwoven, with some propositions serving as both premises and subconclusions while other propositions serve only as premises, and still others are repeated in different words, can be a challenge. . . . More than one plausible interpretation may be offered, and in that case more than one diagram, can reasonably be used to show the logical structure of that passage.

Repetition complicates the task of analysis. Individual propositions are sometimes repeated within an argument in differently worded sentences, sometimes for emphasis and at other times by oversight. . . . we can assign the same number to different formulations of the same proposition.

. . . a premise may appear in compressed form, sometimes as a short noun phrase.