(12th Edition, e-Logic)

Copi &Cohen

Arguments are constructed from propositions.

A proposition is something that may be asserted or denied, and is therefore to be distinguished from a question, command, request, or exclamation. Only propositions (statements) assert that something is (or is not) the case, and therefore can be true or false.

Propositions are different from the sentences by means of which they are asserted. Two different sentences may have the same meaning and can be used to assert the same proposition. Propositions are what declarative sentences are typically used to assert.

The component proposition: Many propositions are compound, containing other propositions within themselves. For examples:

Conjunction: A compound statement that asserts two or more simple statements at the same time is called a conjunction. For this kind of statement to be true, all of the component simple propositions must be true.

Disjunction: An alternative or disjunctive proposition is a compound proposition in which the component simple propositions are not individually asserted. For a disjunctive proposition to be true all that is required is for one of its component simple propositions to be true.

Conditional Proposition:In hypothetical, or conditional propositions the component simple propositions are likewise not being asserted. Only the "if-then" proposition is asserted by the conditional statement, and that conditional statement might be true even though both of it components were false.

Inference: The term inference refers to the process by which one proposition is arrived at and affirmed on the basis of one or more other propositions accepted as the starting point of the process. This set of propositions constitutes an argument, and thus, there is an argument corresponding to every inference.

Argument: An argument is any group of propositions of which one is claimed to follow from the others, which are regarded as providing support or grounds for the truth of that one.

Premises and Conclusion: The conclusion of an argument is the proposition that is affirmed on the basis of the other propositions of the argument. These other propositions, which are affirmed (or assumed) as providing support or reasons for accepting the conclusion, are the premises of that argument.

Arguments can take many forms. The conclusion might be stated at the beginning or at the end. Separate premises might be combined into one sentence, or the premises and conclusion all stated in a single sentence.

No single proposition can, by itself, be an argument. Some compound statements may look like arguments but they are not.

    A deductive argument:  A deductive argument makes the claim that its conclusion is supported by its premises conclusively. 

    Valid and Invalid: A deductive argument is valid when, if its premises are true, its conclusion must be true. Deductive arguments that fail to do so are invalid.

    From classical logic to modern symbolic logic: They differ in the methods and their interpretation if some arguments, but agree that the fundamental task of    deductive logic is to develop the tools to distinguish valid arguments from those of invalid.

An inductive argument: An inductive argument makes claim that their premises support their conclusions with probability, which always falls short of certainty.  The terms validity and invalidity do not apply to inductive arguments.

    The difference between validity and truth: The validity of a deductive argument refers to the relation between its propositions.  The validity can never apply to any single proposition by itself.  Truth and falsity, on the other hand, are attributes of individual propositions. Truth is the attribute of a proposition that asserts what really is the case.

An argument may be valid even when its conclusion and one or more of its premises are false.

1.6. Deduction and Validity

1. Two techniques used to analyze argumentative passages are paraphrasing and diagramming.

2.1.A. Paraphrasing

We paraphrase an argument by setting forth its propositions in clear language and logical order, listing each premiss straightforwardly, restating the conclusion, and simplifying the language. Paraphrasing an argument often helps us understand the argument better. Many arguments contain tacit premisses—premisses that are implied but not stated—and a paraphrase can make these explicit.

2.2.B. Diagramming

We diagram an argument by exhibiting its structure using spatial relations in two dimensions. To do this we number each proposition in the argument in the order it appears, circling the numbers. We then exhibit the logical relations of premisses and conclusion using arrows as "conclusion-indicators" between the circled numbers.

The diagram can exhibit, as a paraphrase may not, the way in which the premisses support the conclusion.

The premisses may support the conclusion either independently or dependently. In diagrams, each independent premiss has its own arrow linking it to the conclusion. In diagrams, dependent premisses are connected with brackets. A single arrow links the bracketed premisses to the conclusion.

2.3. C Arguments Interwoven

The number of arguments in any passage is determined by the number of conclusions. A passage with a single premiss that supports two conclusions, for example, would contain two arguments.

Ordinarily, by a "single argument," we mean an argument to a single conclusion, regardless of how many premisses are used to support that conclusion. However, the same proposition that serves as a conclusion in one argument may serve as a premiss in a different argument.

As these examples make clear, a proposition, taken in isolation, is neither a premiss nor conclusion. It is a premiss only where it occurs as an assumption in an argument. It is a conclusion where it is claimed to follow from other propositions assumed in an argument. "Premiss" and "conclusion" are relative terms.

2.1.A Conclusion- and Premiss-indicators

Certain words or phrases, called "conclusion-indicators," are helpful because they typically serve to introduce the conclusion of an argument. Here is a partial list of conclusion-indicators:

therefore hence

thus so

accordingly in consequence

consequently proves that

as a result for this reason

for these reasons

Other words or phrases typically serve to mark the premisses of an argument, and are called "premiss-indicators." Here is a partial list of premiss-indicators:

since because

for as

follows from as shown by

inasmuch as

2.2.B Arguments in Context

Although words and phrases like those above often signal an argument and identify premisses and conclusions, some argumentative passages lack them. In such cases the context and meaning of the passage by themselves signal its argumentative function.

Passages containing arguments often contain additional material that serves neither as premiss nor conclusion. Such material may, in some cases, be extraneous, but in other cases may supply background information helping us understand what the argument is about.

2.3.C Premisses Not in Declarative Form

Questions can function as premisses when they are rhetorical. That is, a question may suggest or assume a premiss when the question is one to which the author believes the answer is obvious or inescapable.

Since questions assert nothing, they can be neither true nor false. Authors sometimes rely upon a question whose answer is supposed to be obvious, when in fact, the assumed answer is actually dubious or even false.

The use of a genuinely rhetorical question as a premiss can be a very clever argumentative technique. By suggesting the desired answer, one can increase the persuasiveness of an argument.

2.4.D Unstated Propositions

One of the premisses of an argument may be left unstated because the arguer supposes that it is common knowledge, or that it will be readily granted for other reasons. Arguments that rely upon some proposition that is not expressly formulated are called enthymemes, and they depend heavily on context.

 

3.  Arguments and Explanation

Many passages that appear to be arguments are in fact not arguments at all but explanations.

If the aim is to establish the truth of some proposition, Q, and to do that we offer some evidence, P, in support of Q, we may appropriately say "Q because P." We are in this way presenting an argument for Q, and P is our premiss. But suppose, instead, that Q is already known to be true. In that case we don’t have to give any reasons to support its truth, but we may want to offer an account of why it is true. We may still say "Q because P" but in this case we are not giving an argument in support of Q, rather we are providing an explanation of Q.

 

4. Complex Argumentative Passages

[Advanced Material]

Complex passages may be subject to varying plausible interpretations and more than one reasonable diagram of their logical structure.

To analyze a complex passage we must strive to understand the flow of the author’s reasoning and to identify the roles of the several elements of the passage.

Diagramming helps because it exhibit the logical structure of arguments.

1.11 Reasoning

[Advanced Material]

Logic is the study of the methods and principles used to distinguish correct from incorrect reasoning. Reasoning is the process with which one advances, with arguments, from known or affirmed premisses to conclusions.

Skill in reasoning is of enormous value that can be improved with practice on logical games and puzzles.