PARTS OF ARGUMENTS
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
As shown by the fact that
For the reason that
In view of the fact that
As a result
For this reason
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:  The roof is sagging  but it is propped up.  Therefore, the roof will not collapse any time soon.
Diagram: 1 + 2 → 3
Example Argument:  Everyone at this party is a biochemist, and  all biochemists are intelligent. Therefore, since  Sally is at this party,  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:  The roof is sagging  and it has been leaking for many years.  Therefore, the roof will collapse soon.
Diagram: (1 → 3) and (2 → 3)
Example Argument:  the grass is way too high,  the weeds are out of control,  the neighbors think our yard looks shabby, thus  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:  Because I am a human being  I am rational;  therefore, I am no idiot.
Diagram: 1 → 2 → 3
Example Argument:  She could not have known that the money was missing from the safe since  she had no access to the safe itself. Thus,  there was nothing she could have done and so  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: 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