Example of an argument

In natural language:

Since all humans are mortal, and Socrates is human, it follows that Socrates is mortal

In standard form:

(1) All humans are mortal.

(2) Socrates is human.

(3) :. Socrates is mortal.



Logic: the study of arguments

Premise: a statement which is intended to be used as evidence for a conclusion

Conclusion: a statement which is intended to be supported by at least one premise

Argument: at least one premise accompanied with a conclusion.

The premises are only intended to prove or provide some evidence for the conclusion, but they do not need to actually prove the conclusion

The premises and conclusion of an argument are always propositions

Propositions: assertion that is either true or false

Non-propositional utterances: questions, commands, or exclamations, are neither true nor false




Inference indicators: words or phrases used to signal the presence of an argument

Two types: conclusion indicators and premise indicators

Inference indicators often have other functions in other contexts; no hard and fast rule


Since [premise indicator] all humans are mortal, and Socrates is human, it follows that [conclusion indicator] Socrates is mortal


Premise Indicators

As shown by the fact that

Assuming that



For the reason that

Given that

Granted that

In view of the fact that

Inasmuch as

It is a fact that

One cannot doubt that

Seeing that


The reason is that

This is true because


Conclusion Indicators


As a result


For this reason

From which we can infer that


In conclusion

It follows that


The moral is


This being so

This proves that


We can conclude that

Which means that

Which proves that




Three types of argument inferences

Joint Inference: premises must be taken together to produce the conclusion; each premise independently will not do that

Example Argument: [1] The roof is sagging [2] but it is propped up. [3] Therefore, the roof will not collapse any time soon.

Diagram: 1 + 2 → 3

Example Argument: [1] Everyone at this party is a biochemist, and [2] all biochemists are intelligent. Therefore, since [3] Sally is at this party, [4] Sally is intelligent.

Diagram: 1 + 2 + 3 → 4


Independent inference: each premise by itself leads to the same conclusion; distinct arguments for the same conclusion, each of which stands independently of the other

Example Argument: [1] The roof is sagging [2] and it has been leaking for many years. [3] Therefore, the roof will collapse soon.

Diagram: (1 → 3) and (2 → 3)

Example Argument: [1] the grass is way too high, [2] the weeds are out of control, [3] the neighbors think our yard looks shabby, thus [4] itís time to mow the lawn.

Diagram: (1 → 4) and (2 → 4) and (3 → 4)


Inference chain: conclusion of one argument becomes the premise of another

Example Argument: [1] Because I am a human being [2] I am rational; [3] therefore, I am no idiot.

Diagram: 1 → 2 → 3

Example Argument: [1] She could not have known that the money was missing from the safe since [2] she had no access to the safe itself. Thus, [3] there was nothing she could have done and so [4] she bears on guilt in the incident.

Diagram: 2 → 1 → 3 → 4


Symbols for diagraming

Plus sign: together with

Arrow: intended as evidence for


Analyzing the Original Argument

Implicit Statements

Implicit statements: hidden statements in arguments that are incompletely expressed

e.g., the author may intend for the reader to draw the conclusion

Principle of charity: give the arguer the benefit of the doubt, and make the argument as strong as possible while remaining faithful to the arguer's thought

Goal is to minimize misinterpretation

Compound sentence: sentence that contains two or more statements

Breakable compounds: it is helpful to break apart some compound statements into two separate ones, such as those that include ďandĒ

Unbreakable compounds: should not be split into separate statements and treated as complete statements (e.g., either-or, if-then, which are not inference indicators)

Steps for diagraming arguments

Bracket each statement in a way that best reveals the argument structure

Circle clue words (and, but, therefore)

Number each statement sequentially

Identify conclusion; if conclusion is implied, supply it and number it

Work backwards from conclusion to premises

Determine if any premise leads independently to a conclusion

Determine if there are any intermediate conclusions

Determine which premises need to be taken together