Clt Notes

• Conditional sentences

If p, then q

p- antecedent

q- consequent

• The original conditional is: “If p, then q.”

• The converse of the original conditional is: “If q, then p.”

• The inverse of the original conditional is: “If it is not the case that p, then it is not the case that q.”

• The contrapositive of the original conditional is: “If it is not the case that q, then it is not the case that p.”

• Modus Ponens

If p, then q

P

Therefore, q

• Modus Tollens

If p, then q

Not q

Therefore, not p

• Rights

in the strict sense (that is, claim-rights) always refer to someone else’s action: they refer to the duty holder’s action

If I have a right, all that means is that someone else has a duty: my right is a right that they do something, which means that they have the duty to do it

• Liberties

always refer to the liberty-holder’s own actions (or omissions)

e.g. I am not at liberty to disclose…

If I have a liberty, all that means is that I do not have a duty: my liberty is a liberty to do something, which means that I do not have a duty not to do it

• Negations

It is not the case that p. Not p.

• Conjunctions

P and q

• Disjunctions

P or q

• Hypothetical Syllogism

• Disjunctive Syllogism

• Fallacy

a fallacy is an argument which is (a) in some respect not a good one, but which is (b) likely to look (at least at first sight) as a good argument

So, a fallacy is an argument that is flawed in some crucial respect, but whose flaw is not readily apparent

Formal- validity (form)

Informal- soundness (content)

• Formal Fallacy

Internally flawed

Flaw affects the validity of the argument

Flaw lies in their structure

“Non sequitur” (“it does not follow”)- Conclusion does not follow from the premises

Argumentative flaw that once exposed reveals the argument not to be valid

• Equivocation

Using an ambiguous term in more than one sense, thus making an argument misleading.

In logic,equivocation('calling two different things by the same name') is a formal fallacy resulting from the use of a particular word/expression in multiple senses throughout an argument leading to a false conclusion.

I want to have myself a merry little Christmas, but I refuse to do as the song suggests and make the yuletide gay. I don't think sexual preference should have anything to do with enjoying the holiday.

The word, “gay” is meant to be in light spirits, joyful, and merry, not in the homosexual sense

• Denying the antecedent

If it barks, it is a dog.

It doesn’t bark.

Therefore, it’s not a dog.

Since it doesn’t bark, we cannot conclude with certainty that it isn’t a dog -- it could be a dog who just can’t bark.

The arguer has committed a formal fallacy, and the argument is invalid because the truth of the premises does not guarantee the truth of the conclusion.

If I have cable, then I have seen a naked lady.

I don’t have cable.

Therefore, I have never seen a naked lady.

The fallacy is more obvious here than in the first example. Denying the antecedent (saying that I don’t have cable) does not mean we must deny the consequent (that I have seen a naked lady).

The arguer has committed a formal fallacy, and the argument is invalid because the truth of the premises does not guarantee the truth of the conclusion.

• Affirming the Consequent

An error in formal logic where if the consequent is said to be true, the antecedent is said to be true, as a result.

If taxes are lowered, I will have more money to spend.

I have more money to spend.

Therefore, taxes must have been lowered.

I could have had more money to spend simply because I gave up crack-cocaine, prostitute solicitation, and baby-seal-clubbing expeditions.

• Summary

• Disjunctions: exclusive vs inclusive

Disjunctions – sentences of the form “p or q” – can be either exclusive or inclusive

That is because the word “or” in English can be used in two different ways

• Sometimes it means “p or q but not both”: this is the exclusive reading

  • “Wanted: dead or alive”

• Sometimes it means “p or q or both”: this is the inclusive reading

• Validity and Soundness

Of course, we want our arguments both to be valid and to have true premises: we want our arguments to be sound

Which is why when you are assessing someone’s argument you should be ready to challenge both its validity and the truth of the premises

Charitable Reading- rendering of an argument ehich accurately describes what the person arguing I actually saying.

• Informal Fallacy

Does not affect the validity

Externally flawed

Informal fallacies are arguments that, although formally valid (and perhaps also sound), are flawed in some other respect

• Begging the question

Assuming what you must prove

Any form of argument where the conclusion is assumed in one of the premises.

Claim X assumes X is true.

Therefore, claim X is true

The reason everyone wants the new "Slap Me Silly Elmo" doll is because this is the hottest toy of the season!

Everyone wanting the toy is the same thing as it being "hot," so the reason given is no reason at all—it is simply rewording the claim and trying to pass it off as support for the claim

• Straw man fallacy

Substituting a person’s actual position or argument with a distorted, exaggerated, or misrepresented version of the position of the argument.

Zebedee: What is your view on the Christian God?

Mike: I don’t believe in any gods, including the Christian one.

Zebedee: So, you think that we are here by accident, and all this design in nature is pure chance, and the universe just created itself?

Mike: You got all that from me stating that I just don’t believe in any gods?

Mike made one claim: that he does not believe in any gods. From that, we can deduce a few things, like he is not a theist, he is not a practicing Christian, Catholic, Jew, or a member of any other religion that requires the belief in a god, but we cannot deduce that he believes we are all here by accident, nature is chance, and the universe created itself. Mike might have no beliefs about these things whatsoever. Perhaps...

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