The Philosopher’s Toolkit

Write as a thinker, think as a writer.

Basic Tools for Argument 1.1Nit-picking through

Arguments Premises Conclusions

Argument: precise reasoningAn inference from one or more starting

points (premises) leading to an end point (conclusion).

Arguments show that something is true.Arguments are rational.

Premises and Conclusions Premises make truth claims that imply

conclusions.

All men are mortal (1st premise) Socrates is a man (2nd premise) Socrates is a mortal (conclusion)

If the premises are true, then it follows that the conclusion is true.

Grounds for PremisesPremises may be settled (basic)

conclusions to a solid argument. “I think, therefore I am.”

Premises may need no further justification. “All bachelors are unmarried.”

Basic Tools for Argument 1.2Deduction

True premises guarantee the certainty of the conclusion.

The murder of King Hamlet was planned. Claudius had the most to gain by killing

King Hamlet. Claudius killed King Hamlet.

1.2 Deduction: ambiguous premises My late husband Laius was killed at a

crossroads in a right-of-way dispute. My new husband Oedipus killed a man once

at a crossroads in a right-of-way dispute. Oops!

We must not jump to conclusions because the premises may seem true.

Basic Tools for Argument 1.3 Induction

Premises make the conclusion necessary and with probable certainty.

Below: induction or deduction? The sun always rises. The sun rose today. The sun will always rise.

Misleading Similarities Below is an induction:

Some elephants like chocolate. This is an elephant. This elephant likes chocolate.

Below is a deduction:

All elephants like chocolate. This is an elephant. This elephant likes chocolate.

1.3 Induction: Nature’s Uniformity

If nature’s laws are observed as uniform, then the past is a reliable predictor of the unobserved future.

However, we must admit to a limited knowledge of the observed uniformity of nature.

Basic Tools for Argument 1.4Validity: what creates conviction.

Everyone at Wuthering Heights is a block of cheddar.

Heathcliff lives at Wuthering Heights. Heathcliff is a block of cheddar.

The above argument is valid, but not true. Validity is content-blind. A ridiculous argument can be valid.

1.4 Continued…SausageThe Truth Machine

Deductive arguments are best because they demand good ingredients (true premises).

These create sound arguments. But sound arguments rest on validity or

invalidity.

Invalid Arguments: UnsoundPut in false premises

Get out true or false conclusion.Put in true premises

Get out true or false conclusion.

Valid Arguments: SoundPut in false premises

Get out true or false conclusion.Put in true premises.

Get out only true conclusion.

SoundnessWhen a valid argument and true

premises are combined and lead to a true conclusion we have a sound argument.

We must accept a sound argument.All sound arguments must be valid.

In Reasoning We Must…Attack the premises from which

someone reasons.Show that the argument is invalid,

whether or not the premises are true.

1.5 Invalidity If premises of an invalid argument are

true, the conclusion may be false. Vegans do not eat sausages. Gandhi did not eat sausages. Therefore, Gandhi was a vegan.

All three propositions are true, but...

It is invalid to say that, because

All cats are carnivores.President Bush is a carnivore.Therefore President Bush is a cat.

True premises/false conclusion

Therefore, Invalidity is…Not settled by truthfulness of premises.But by logical relations among them.

Thus, good thought and writing

Make truthful claims that are grounded in good arguments.

Gain veracity or weight by showing how the truth claim comes about.

1.6 ConsistencyThe cornerstone of rationality.The property of two or more statements.Apparent or real.

Murder is wrong. Abortion is not murder. Abortion is not wrong.

Consistency continuedExceptions to Rule?

It is raining and it is not. My home is not my home.

Paradox Jesus was God and a man.

Philosophy God is good. God allows evil to occur.

1.7 Fallacies Instances of poor reasoning.

Faulty inference.All invalid arguments are fallacious.Not all fallacies are invalid arguments.

Formal Fallacies: faulty form. If Mr. B won the lottery, he’ll be driving a

yellow Mini today.Mr. B is driving a yellow Mini today.Mr. B won the lottery!

Informal Fallacies: faulty content

If I’ve tossed seven heads in a row with my coin, I am due to toss tails for # 8.

I’ve tossed seven heads. I will probably toss a tail this time.

No: the odds are always 50:50. The first premise is false.

1.8 Refutation & ToolsTo show that an argument is wrong, you

must demonstrate That the argument is invalid.

Conclusion does not follow from premises. That one or more premises is false. That the conclusion must be false.

Refutation: Inadequate Justification

Dubious Premise: There is intelligent life elsewhere in the

universe. There can be no adequate justification for this

claim, so it is dubious (doubtful), and we may ignore it.

Refutation: Conceptual Problems

Vague concepts used as precise concepts lead to distortion. Argument

Government is only obliged to provide assistance to those who do not have enough to live on.

How much is that? Please define this vague concept.

The use of vague concepts in precise arguments we end up with distortions.

Axioms & Indeterminacy Initial claims that need no justification.No rational person could deny them.

Premises true by definition (obvious)Primitive sentences (lines/points)Universal? (unalienable)

Definitions IAgreement on terms necessary.Clear conclusions more likely.Problems leading to confusion:

Too narrow Too broad

Rules of thumb necessary Problem of language

Certainty and ProbabilityRene Descartes’ Method of Doubt

“I think, therefore I am” cannot be doubted. Everything else must be doubted unless it

is clear and distinct. It is possible to arrive at certainty, but only

by doubting everything first.

Certainty and Probability 2Ludwig Wittgenstein: (1899-1951)

It makes no sense to doubt certain things. We can figure things out with certain

degrees of probability. Caveat: we must give thought to our concepts.

What is Certainty?A feeling or mental state where the

mind believes X without doubt.A mental admission of the necessarily

true or false.

The Problem of SkepticismAbsolute certainty may not be attainable

in any or all cases. Probability is our only recourse to

skepticism. Objective Probability: radioactive decay Subjective Probability: coin flipping

Certainty and Validity In a sound deductive argument, the

conclusion must follow with certainty, but must also be true. All humans are mortal. Socrates was a human. Therefore, Socrates is a mortal.

Tautologies, self-contradictions, and the law of non-contradiction

Tautology: a sentence that is necessarily true. P or Not-P

“Today is Xday.” “Atoms are invisible.” “Monkeys make great lasgna.”

All valid arguments are tautologies.

Tautologies, self-contradictions, and the law of non-contradiction Law of non-contradiction is a tautology.

Not (P and Not-P) Whether P is true or false, the statement is

true. Attempts to break the law of non-contradiction

are themselves contradictions and are therefore always wrong.

One cannot claim that something is true and not true at the same time.

“What is is and cannot not be.” (Parmenides) “It is what it is what it is.” (Scott)