1. Other Info on Making Arguments
Deductive vs. Inductive
Sound vs. Unsound
Cogent vs. Uncogent
Valid vs. Invalid

2. Deductive vs. Inductive
Deductive Reasoning
Inductive Reasoning
Argument in which the arguer claims that it was impossible for the premise to be true and the conclusion false.
Conclusion is claimed to follow necessarily, or absolutely, from the premise
EX: Barbara is taller than Carol, and Carol is taller than Denise. Therefore, it necessarily follows that Barbara is taller than Denise.
ALL ABOUT “NECESSARY REASONING”
Arguer claims that it is improbable that the premise be true and the conclusion false.
Conclusion has a ‘level of certainty’ in relation to the premises.
EX: 90% of the nurses in St. Luke’s Hospital are women. Therefore, since Anderson is a nurse in that hospital, it probably follows that she is a woman.
ALL ABOUT “PROBABLISTIC REASONING”

3. To distinguish the difference…
Look for special indicator words.
Address the actual strength of the link between the premises and conclusion.

4. Deductive Indicator Words Inductive Indicator Words
Necessarily
Definitely
Certainly
Absolutely
*Sometimes language is used only for the rhetorical purposes and to add to the impact of the conclusion. Much like indicators in syllogistic arguments can be prepositional phrases, ensure that the language used would work within an argument.
Probably
Likely
Plausibly
Reasonable to conclude
*The word “must” is ambiguous. It can signify either necessity or probability.

5. To determine the link…
This is the “actual strength” of the link between the premises and the conclusion.
This does not require indicator words
Deductive: the conclusion does, in fact, follow necessarily, from the premises
Inductive: if the conclusion does not necessarily follow the premises, but it does follow probably, then apart from other criteria, the argument is inductive

6. This is called “substitution instance of the form”.
Valid Arguments
This is determined by form.
A = B
B = C
A = C
If terms are uniformly substituted in place of the letters, it can still be valid.
This is called “substitution instance of the form”.

7. Invalid Arguments
Not every set of terms result in an argument having two premises and a false conclusion – but it is always possible to find terms that give this result.
INVALID = true premises, false conclusion
A = B
C = B
A = C

8. Random Note The word “some” in logic means “at least one”
You’ll have to watch the language within arguments more than anything. People use charged words to confuse and mislead.

9. SOUND = VALID + ALL TRUE PREMISES
Sound vs. Unsound
Sound = if the argument is valid and all premises are true
SOUND = VALID + ALL TRUE PREMISES
All cats are mammals.
All mammals are animals.
All cats are animals. SOUND

10. Sound vs. Unsound
Unsound = the argument is invalid (or) has one or more false premises (or both)
All cats are mammals.
All cats are animals.
All mammals are animals. UNSOUND

11. Therefore, true conclusion
Sound Arguments
Good deductive argument:
True premises
Good reasoning
Therefore, true conclusion

12. To evaluate sound.. Check for validity.
If valid, check to ensure that all premises are true.

13. Strong vs. Weak
Strong = Inductive arguments
It is improbable that the premises be true and the conclusion false.
It’s an assumed truth, based on that assumption, it is probable that the conclusion is true.
All previously discovered emeralds have been green. Therefore, probably the next emerald to be discovered will be green.
STRONG

14. Degrees of Strength with Probability
If the probability is more than 50% likely, it is a STRONG argument.
If the probability is less than 50%, it is a WEAK argument.
Determine the relationship between premises and conclusion, not by truth or falsity of the premise.

15. Therefore, probably true conclusion
Cogent vs. Uncogent
Cogent = strong + all true premises (inductive)
Cogent =
True premises
Good reasoning
Therefore, probably true conclusion
Uncogent = is weak or has one or more false premises (if either is missing, it is uncogent)

16. Apply this in your own writing…
This is not formulaic writing.
It’s all common sense, which relies on you doing simple math to ensure that one point leads smoothly to the next point. But more importantly, the idea is that you show and prove a logical and accurate point is made.