Basic Concepts

Question 0

Proposition

Answer 0

Something that can be asserted or denied. They are either true or false.

Interchangeable with ‘statement’.

Questions, commands, requests, and exclamations do not make claims about the world.

Question 1

Logic is the study of the quality of an argument.

Answer 1

Broadly, an argument is an attempt to provide reasons for accepting the truth of some claim.

Question 2

Inference

Answer 2

The mental process by which one proposition is arrived at and affirmed on the basis of one or more other propositions that are assumed as the starting point of the process.

Question 3

Argument

Answer 3

A collection of propositions in which some propositions, the premises, are given as reasons for accepting the truth of another proposition, the conclusion.

There is no limit to the number of premises, but two is common. There is only one conclusion per argument. No premise by itself constitutes an argument; if there is no conclusion it is not an argument.

Question 4

Deductive argument

Answer 4

An argument that attempts to prove the truth of its conclusion with certainty.

Question 5

Inductive argument

Answer 5

One that attempts to establish its conclusion with some degree of probability.

Question 6

Some conclusion-indicators:

Therefore
Hence
Accordingly
In consequence 
Consequently
Proves that
As a result
For this reason
For these reasons
It follows that
We may infer
Thus 
So
I conclude that
Ergo
Which means that
Which entails that
Which implies that 
Which allows us to infer that
Which points to the conclusion that
Is a reason to believe that
Is a reason to hold that
Is evidence that
Implies that
Means that
Which shows that

Answer 6

Some premise-indicators:

Since
Because
For
As 
Given (that)
Assuming (that)
Due to
In view if the fact that
Inasmuch as
Insofar as
As indicated by
From
Follows from
May be derived from 
May be deduced 
May be inferred from
As shown by
The reason is that

Question 7

Enthymeme

Answer 7

An unstated proposition (premise or conclusion) in an argument.

2 reasons for enthymemes:

1. Enthymemes are rhetorically strong. The reader/hearer is ‘complemented’ by being seen as smart enough to fill in the missing element(s).
2. Leaving a premise unstated can cover defects in the argument.

Question 8

Validity of deductive arguments

Answer 8

Validity asks about what is possible regarding the truth and falsity of the premises and conclusion.

A deductive argument is valid when it is impossible for its conclusion to be false if its premises are true; otherwise, the argument is invalid.

Question 9

Validity and truth

Answer 9

A deductive argument is sound when it is both valid and its premises are true.

Various possibilities include:

1. Some valid arguments contain only true propositions.
2. Some valid arguments contain only false propositions.
3. Some invalid arguments contain only true propositions.
4. Some invalid arguments contain only true premises and have a false conclusion.
5. Some valid arguments can have false premises and a true conclusion.
6. Some invalid arguments can have false premises and a true conclusion.
7. Some invalid arguments contain all false propositions.

Question 10

Deductive conclusions usually contain no information that is not already contained in the premises.

Answer 10

Inductive conclusions provide information that is not contained in the premises.

Question 11

3 types of inductive arguments

Answer 11

Analogy: comparing things directly to reach a conclusion.

Inductive generalization: comparing characteristics of a number of individual things to characteristics of a group.

Argument to the best explanation: considering alternative explanations to determine which is more probable.

Question 12

Analyzing arguments

Answer 12

Paraphrasing: putting the argument’s propositions in clear language and in proper order, listing each premise straightforwardly, restating the conclusion, and simplifying the language (where appropriate).

Diagramming: the propositions are numbered in order, the conclusion is identified. Then the way the premises interact and relate to the conclusion is drawn with arrows.

Question 13

Dependency of premises

Answer 13

Independent premises: each premise, by itself, supplies some reason to accept the conclusion, and it provides this support even in the absence of the other premises.

Dependent premises: when a premise supports the conclusion only in combination.