SSH 105 Study Guide - Quiz Guide: Modus Tollens, Modus Ponens, Hypothetical Syllogism
19 Jun 2018
School
Department
Course
Professor
SSH105 Quiz #3
Five senteial connectives
(1) Conjunction – A and B
(2) Disjunction - A or B
(3) Negation – not A
(4) Conditional – If A then B
(5) Biconditional – A if and only if B
Eleven valid argument patterns
(1) Argument by elimination – 1. A or B 2. Not A 3. Therefore, B
(2) Conjunction – 1. A 2. B 3. Therefore, A and B
(3) Simplification – 1. A and B 2. Therefore, A
(4) Affirming the antecendent (modus ponens) - 1. If A, then B 2. A 3. Therefore, B
(5) Denying the consequent (modus tollens) – 1. IF A, then B 2. Not A 3. Therefore, Not B
(6) Hypothetical syllogism – 1. If A then B 2. If B then C 3. Therefore, If A, then C
(7) Contraposition – 1. If not B 2. The not A
(8) Universal modus ponens – 1. All As are Bs 2. X is an A 3. Therefore, X is a B
(9) Universal modus tollens – 1. Alls As are Bs 2. X is not a B 3. Therefore, X is not an A
(10) Universal hypothetical syllogism – 1. Alls As are Bs 2. All Bs are Cs 3. all As are
Cs
(11) Universal ruling out – 1. No As are Bs 2. X is not an A 3. X is not a B
Invalid argument patterns
(1) Denying the antecedent – 1. If A then B 2. Not A 3. Not B
(2) Affirming the consequent – 1. If A then B 2. B 3. A
Cogency- if premises are true, conclusion is likely
Validity- if premises are true, conclusion must follow
Well-formed- the premises if true make the conclusion guaranteed to be true or probably true
Ill-formed- the premises do not make the conclusion true or likely
Deductive strength- valid, r/j/r
Deductively weak- invalid, not r//j/r to believe and both invalid and not r/j/r
Inductive strength- cogent, r/j/r, argument is not defeated
Inductively weak- not cogent, not r/j/r, argument is defeated or any combination of above
Components of “standard form”:
- Individually numbered premises and conclusions
- Only one premise or conclusion per line
- The word “therefore” or the equivalent symbol (.:) before the conclusion
- The word “probably” before the conclusion, if it is an inductive argument
- After the conclusion, in brackets, should be the justification:
(a) The numbers of the premises that support the conclusion
(b) The name of the argument pattern (if it has a name)
find more resources at oneclass.com
find more resources at oneclass.com
Example:
1. Most politicians are talented communicators
2. Donald trump is a politician
Therefore, probably
3. Donald Trump is a talented communicator (from 1,2)
Principle of charity
- Try to make the argument strong- valid or cogent and r/j/r premises
- In simple terms
- DON’T: twist other people’s words (either for the better or for the worse)
- DO: be fair when you express somebody’s position
- Slightly more technically
PC: When reconstructing an argument, try to formulate a reconstruction that is well-formed, has
premises that are reasonable/justified/rational, for the author/speaker, and (in the case of
inductive arguments) that is undefeated. In other words, make the argument as strong as
possible…
… consistent with what you, upon careful and fair-minded reflection, take to be the author or
speaker’s intention
How to recognize arguments:
- Look for a conclusion (a statement that is being supported), and look for premises (the
statements offering support)
- Ask yourself: is the author trying to get me to believe something by giving me reasons in
support of it?
- If yes: it is probably an argument
- If no: it is probably not an argument
Some contrasts:
1) Descriptive writing
2) Rhetorical writing. This merely asserts one of more conclusions, without offering
reasons.
E.g.: “We hold these truths to be self-evident, that all men are created equal, that they are
endowed by their creator with certain unalienable rights…”
Compare
- “Work is underway to build a bridge over the river. It is hoped that this bridge will solve
our traffic problems.” – descriptive writing of facts
- “We ought to build a bridge over the river. And we should limit the cars that go on it.
And let’s fix the park while we are at it.” – rhetorical writing, states what we should do
without reasons
- “We ought to build a bridge over the river, because doing that is the best way to solve the
traffic problems.” – argument, has a premise and claim
find more resources at oneclass.com
find more resources at oneclass.com
- Note: a long text or speech might well contain all three kinds of writing (and perhaps
more)
- The key thing is to zero in on the argument or arguments it contains, and to ignore
everything else
Some techniques for identifying conclusions
1) Try to ignore non-argumentative material (such as descriptive writing and rhetorical
writing)
2) Remember that any proposition, on any topic, expressed by any person, at any time, can
be a conclusion
3) Ask yourself: what’s the overall point of the (argumentative portion of the) text/speech?
That will likely be the main conclusion
Be careful with these common expressions:
“My argument is that…”
“I would argue that…”
Typically, what comes next isn’t an argument at all- it’s just the conclusion
4) Remember that one text/speech may well contain
- Several independent arguments
- Sub-arguments
5) Look for conclusion-indicators, such as:
- Thus
- Therefore
- Hence
- Entail(s)
- Implies
- …it follows that…
- … we may conclude…
- … this proves that…
- Consequently
- So
- Establishes
- Shows
6) Remember that conclusion-indicators aren’t always present
7) Remember that conclusions don’t always come last in actual texts/speeches, even though
we put them last in standard form
8) Sometimes conclusions aren’t explicitly stated at all
- Suppose a doctor says: “Look, everyone who has high cholesterol is at risk of having a
heart attack, and you have very high cholesterol…”
- Doctor did not state the conclusion but based on principle of charity we can say doctor is
intending to say “you’re at a high risk of having a heart attack”
9) Sometimes the conclusion that is explicitly stated isn’t the one the speaker/author is
really arguing for
10) Conclusions can be stated in unclear or obscure ways. When reconstructing the argument
in standard form, try to state the conclusions as clearly and simply as possible
- Changing the words is not the same as changing argument provided
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Five senteial connectives (1) conjunction a and b (2) disjunction - a or b (3) negation not a (4) conditional if a then b (5) biconditional a if and only if b. Eleven valid argument patterns (1) argument by elimination 1. Therefore, a (4) affirming the antecendent (modus ponens) - 1. Therefore, b (5) denying the consequent (modus tollens) 1. Therefore, not b (6) hypothetical syllogism 1. Therefore, if a, then c (7) contraposition 1. The not a (8) universal modus ponens 1. Therefore, x is a b (9) universal modus tollens 1. All bs are cs 3. all as are. Invalid argument patterns (1) denying the antecedent 1. Not b (2) affirming the consequent 1. Cogency- if premises are true, conclusion is likely. Validity- if premises are true, conclusion must follow. Well-formed- the premises if true make the conclusion guaranteed to be true or probably true. Ill-formed- the premises do not make the conclusion true or likely.
