Review Deductive Arguments:

Argument from a Categorical, from a universal generalization, “All” “No” “Some” “Not”
Argument from a Conditional, from an unqualified “if-then”

Deductive Fallacies:
—— “All” does not imply only
—— “If” does not imply only if

Fallacy of Denying the Antecedent
Fallacy of Affirming the Consequent

Deductive fallacies are the common reasoning errors that result in an invalid deductive argument — one capable of having true premises with a false conclusion.

Argument by elimination

Argument by Elimination (process of elimination) takes the form:

A or B (a disjunction)
not B
Therefore, A

The conclusion follows from the definition of ‘or’ as “at least one is true.”
This type of argument is sometimes called Disjunctive Syllogism, because ‘or’ is a disjunction.

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AVOID THE XOR ERROR:

A or B
B is true
Therefore, not A

The ‘or’ does not imply only one is true!
OR ≠ XOR (Inclusive ‘or’ is not exclusive). For example

Rami is sleeping or he’s at work
He is at work
Therefore, he’s not sleeping

No! He could be both! ‘OR’ is not exclusive. This argument is invalid, capable of having true premises with a false conclusion.

A well-known and popular puzzle, Sudoku, works by process of elimination, but the “or’s” involved are exclusive or’s. Each square contains only one digit from 1 to 9. If the row or column or 3x3 sub group of a particular square contains, say, an 8, one can eliminate 8 as the digit for any vacant square. If a player can eliminate all digits except one, the player knows the one remaining digit goes in that square.

This XOR mistake often shows up in social decision-making situations. People can fall into thinking a group must choose between, say, policy A and policy B, when in fact it is possible to combine the best elements of both.

To avoid the XOR ERROR in social situations, it is often helpful to recognize when it’s “not an either/or (an exclusive ‘or’) but can be a both/and.”

BEWARE of FALSE ALTERNATIVES: an Argument by Elimination with a false, or likely to be false, premise. The problem of False Alternatives is the problem of a first premise that leaves out some options.

Kamala must be a Democrat or a Republican
I know she’s not Republican
Therefore, she’s a Democrat

The first premise is false. Kamala might be a Libertarian!

Even though this argument is deductively valid (if the premises were true, the conclusion would have to be true), it has a false, oversimplified premise. It is often classified as a fallacy even though it is logically correct, because of the factual error in the disjunctive premise. Review the discussion of validity, logical assessment, and factual assessment in the chapter on Argument from a Conditional.

This is one particular example of the more general phenomenon of oversimplified thinking.

Conjunction

The term “and” is another important logical connective. If one has logically supported two or more claims, one can take their conjunction as supported.

A
B
Therefore, A & B

Also, given a conjunction as a premise, one can conclude any of the conjuncts separately.

A & B
Therefore, A

This should be obvious. Just be aware that “and” can be used for something other than simple conjunction. “Put metal in the microwave and you will regret it,” for example, means, “if you put metal in a microwave, you will regret it.”

Argument by Mathematics

Any argument claiming in effect that the conclusion follows as a matter of mathematical necessity from the premises is an Argument by Mathematics.

Invalid arguments would be any containing mathematical errors.

Argument by Definition

Any argument in which the conclusion follows by definition of a term in the premise(s) OTHER THAN:

or (disjunction)
and (conjunction)
mathematical terms
Categorical
Hypothetical

Example of correct argument, “Saanvi is a cardiologist. Therefore, Saanvi is a medical doctor.”

Avoid the Mis-def (misdefining) Mistake! “The Lonely Walk Bridge is a bridge. Therefore, it must span body of water.”

The deductive arguments we are studying:

Argument from a Categorical,
Argument from a Conditional,
Argument by Elimination,
Conjunctive Argument,
Mathematical Deduction,
Argument by Definition.

Logical consistency, inconsistency

A critical thinker aims to have beliefs that are logically (deductively) consistent with one another. Inconsistent claims cannot possibly both be true. Holding beliefs that are logically inconsistent guarantees that one is holding at least one false belief.

Talking about consistency over time is very different. Beware of people claiming to be “consistent” by clinging to a belief over time even though new evidence undermines the belief. This use of the word “consistent” is just a euphemism meant to put a positive gloss over what is actually dogmatism, or cognitive inflexibility.

the problem of circular argument

Circular Reasoning consists in stating or assuming in your premises what you set out to prove in the conclusion.

—> The deductive arguments we are examining technically are guilty of Circular Argument. “Tom is a bachelor, therefore Tom is unmarried” is circular, but might be useful, as it pulls out and emphasizes one part of the definition of a bachelor. The deductive arguments we are examining can be seen as explicating concepts, hence they are non-ampliative, meaning that they do not intent to extend beyond (amplify on) the information already present in the premises.<--

For INDUCTIVE ARGUMENTS, Circular Argument is useless, because anyone who does not already believe your conclusion will not accept your premises. Inductive arguments are ampliative, intending to expand (amplify) our knowledge.

The common name, Begging the Question, is confusing, so we’ll avoid it.

Circular Argument amounts to simply repeating your claim over in a disguised way, but this doesn’t work as an argument because just “saying it doesn’t make it so!” It usually just amounts to a disguised unsupported assertion.

Assuming in the argument anything that needs to be argued in the current context of discussion commits this mistake.

A good argument typically aims to have premises that are already established and widely accepted leading to a conclusion that was initially controversial or disputed. There should be many people who don’t initially accept your conclusion but do find the premises acceptable. So, …

A GOOD TEST for CIRCULAR ARGUMENT: Ask yourself, “could there be anyone who disagrees with my conclusion but would allow the premises?” If not, then it is probably circular reasoning.

examples of circular argument

Skipper: How do we know that the Howells are really that rich?
Gilligan: Of course they're rich. They have a whole trunk full of money. We saw it.
Skipper: How do we know they didn't steal that money?
Gilligan: Skipper, when you're as rich as the Howells you don't have to steal.

“Grade-school children should not receive any homework, because the time a grade-school teacher has during the course of the school day to instruct children and work with them should be enough for everything they need to do.” [the premise really just makes the same claim as the conclusion.]

“Their arguments are bad, because they do not follow from the premises.” Quoted from a student paper. (– “they do not follow (non sequitur)” means the same as “the arguments are bad.”)

“Some skeptics claim that people who report seeing flying saucers are not really careful observers and probably were mistaken about what they thought they saw. But in fact, of course, people who report seeing flying saucers are careful observers—for if they weren’t careful observers they wouldn’t have seen the flying saucers at all, would they?” (from Bruce N. Waller, Critical Thinking: Consider the Verdict, 5e)
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