PHIL: General Logic- The Basics

Unit 1

argument 

what are the two classification of an argument ?

An inductive argument and a deductive argument

what is the difference between the two categories of an argument

has to do with the strength of the argument's inferential claim.

what is an inferential claim?

what is an deductive argument?

the conclusion is claimed to follow from the premises by necessity. This means that if a deductive argument is a good one, it is impossible for the conclusion to be false when the premises are all true

what is an inductive argument ?

In an inductive argument, the conclusion is claimed to be only probably true given the premises. This means that if an inductive argument is a good one, then when the premises are all true, the conclusion is probably also true (but not definitely).

what does the Aristotelian tradition say regarding the particularity and generality in deductive and inductive reasoning?

deductive arguments proceed from the general  to the particular, while inductive arguments proceed from the particular to the general  

Do all deductive arguments support there conclusion ?

not all deductive arguments are actually successful in supporting their conclusions with necessity

what are the different kinds of deductive forms ?

1. Arguments based on mathematics

2. Arguments from definition

3. categorical syllogism

4. hypothetical syllogism

5. disjunctive syllogism

what is an deductive arguments based on mathematics

(excluding statistical reasoning, which deals with probabilities) are those arguments whose conclusions rely on mathematical reasoning.

what is an deductive argument from definition

those arguments whose reasoning depends solely on the definition of some word or phrase in the argument.

what is deductive syllogism

an argument form consisting of exactly two premises and one conclusion

what is an deductive argument of categorical syllogism

an argument whose two premises deal with the relationship between categories of objects.
made up of statements beginning with words such as "all," "no," and "some.

what is an deductive argument of hypothetical syllogism 

a syllogism with an "if... then..." statement as one or both of its premises

what is an deductive argument of disjunctive syllogism?

"either... or..." statement as one of its premises.

what are the different kinds of inductive forms ?

1. A prediction

2. argument from analogy

3. generalization

4. argument from authority

5. argument based on signs 

6. causal inference 

what do all inductive argument forms have in common?

their conclusions are intended to follow from their premises with probability.

how do inductive arguments differ from deductive arguments?

the premises do not guarantee that the conclusion has to be true.

what is an inductive argument based on a prediction?

an argument that makes a conclusion about the future based on facts about the past.

what is an inductive argument from analogy?

an argument whose conclusion is based on a comparison between two similar objects or states of affairs.

what is an inductive argument based on generalization?

an argument that draws a conclusion about a whole group based on a sample of members of that group.

what is an inductive argument from authority

an argument whose conclusion is based on the claims of an expert or on eyewitness testimony

what is an inductive argument based on signs?

an argument that draws a conclusion based upon any kind of message (usually visual) produced by an intelligent being.

what is an inductive argument based on causal inference

an argument that draws a conclusion about the effect of a given cause, or about the cause of a given effect.

are indicators reliable to determine if an argument is deductive or inductive?

Deductive indicators and inductive indicators are a useful but unreliable way to determine whether an argument is deductive or inductive.

what is a particular statement?

makes a claim about one or more particular members of a class

what is a general statement?

 makes a claim about all members of a class.

what does the Aristotelian tradition hold about deductive and inductive arguments?

It was formerly held that deductive arguments involved reasoning from general statements to particular statements, while inductive arguments went from particular to general

Is a scientific reasoning deductive or inductive ?

may be either deductive or inductive.

what is validity?

the concept used to evaluate the internal reasoning of a deductive argument. in terms of possibility and impossibility (specifically in terms of a certain combination of impossible truth values) instead of actual truth values.

what is a valid deductive argument?

A deductive argument in which the conclusion really does follow from the premises with necessity

If a deductive argument is valid, then it is impossible for the premises to be true and the conclusion to be false simultaneously.

what is an invalid detective argument ?

a deductive argument in which the conclusion does not follow from the premises with necessity, even though it is claimed to follow

what is one way to evaluate whether an argument is valid?

1. to assume that the premises are true (even if they are actually false)

2. then determine whether the conclusion would therefore also have to be true.

does the argument have to actually be true ?

NO

the premises and conclusion do not have to actually be true for the argument to be valid

What is the one exception that the actual truth or falsity of the premise and conclusion is adequate for determining an arguments validity?

If a deductive argument is valid, then it is impossible for the premises to be true and the conclusion to be false simultaneously

what is a sound argument?

a deductive argument that is valid and has all true premises.

In order to be sound, an argument must meet both conditions.

what is an unsound argument?

not sound; invalid; one or more premises are false

how do you evaluate an argument for soundness

1. determine whether the argument is valid

2. if valid, then you must determine if the premises are all true

what if you don’t know if the premises are all true; how would you detect for soundness

If you do not know whether a premise is true, then you will not know whether the argument is sound or unsound until you learn the truth values of the argument's premises

what is strength in an argument?

the concept used to evaluate the internal reasoning of an inductive argument

what is a strong inductive argument?

An inductive argument in which its premises really do give reason to think that its conclusion is probably true

unlikely that the conclusion is false, given the assumed truth of the premises.

It is important to recognize that the premises and conclusion do not have to actually be true for the argument to be strong

what is a weak inductive argument?

an inductive argument in which the conclusion does not follow from the premises with probability

what is one way inductive arguments differ from deductive arguments?

There are degrees of inductive strength, whereas deductive arguments are simply valid or invalid, with no degrees of validity.

what is one way to evaluate the strength of an inductive argument

1. is to assume that the premises are true (even if they are actually false

2. determine whether the conclusion would therefore also probably be true

what’s an inferential claim in an inductive argument?

its conclusion follows by probability from its premises.

what is a cogent argument?

an inductive argument that is strong, has all true premises, and has not ignored an important piece of evidence that entails a different conclusion.

what is a total evidence requirement in a cogent argument?

In order to be cogent, an argument must meet all three conditions of
1. strong inductive argument

2. all true premises

3. has not ignored an important piece of evidence that entails a different conclusion

what is an uncogent argument?

a weak inductive argument, contains at least one false premise, fails to meet the total evidence requirement

how to evaluate an argument for cogency?

1. determine whether the argument is strong? (if weak = uncogent)

2. If strong, you then must determine whether the premises are all true (everything component of the argument must be true)

what is an argument form?

a representation of the logical relationship between terms in an argument

replace the content terms in the argument, whether statements or noun terms, with capital letters (A, B, C, and so on)while leaving alone the connecting phrases such as "either... or..." and "not."

what is a substitution instance?

any argument that is produced by uniformly substituting specific terms or statements in place of the letters in an argument form.

Can a single argument be a substitution instance of more than one form?

yes.

An argument's specific wording can simultaneously match a narrow, specific form and a broader, more generic one — it isn't locked to just one template.

If an argument form is valid, what do we know about every substitution instance of it?

Every instance is also valid, regardless of the actual content

Validity is a property of the form itself. Once a form is shown valid, it carries over automatically to every instance, even ones with absurd or false content, like the moon-cheese-cows example.

An argument is a substitution instance of an invalid form. What's the ONE condition under which it might still be a valid argument?

If it is also a substitution instance of some valid form

Matching an invalid form only guarantees invalidity when that's the only form the argument fits. If the same argument also happens to match a valid form, that valid form guarantees validity instead.

If it's raining, the ground is wet. The ground is wet. Therefore, it's raining." What form is this, and is it generally valid?

Affirming the consequent — generally invalid

This matches "If P then Q. Q. Therefore P." — affirming the consequent. It's invalid because the ground could be wet for reasons other than rain, so the conclusion doesn't follow necessarily.

Why does logic care about argument form rather than the specific content of an argument?

Because validity depends on structure — a pattern guarantees the same validity status across all its instances, regardless of content

Classifying by shape lets you judge a whole family of arguments at once: prove one form valid or invalid, and you instantly know the status of every argument sharing that shape.

Counterexample

a substitution instance of a given argument form in which the premises are actually true and the conclusion is actually false.

what is a successful counterexample?

must have the same argument form as the argument to which it is put forward as a counterexample

what are form words in a deductive argument?

words to indicate the relationships between terms or statements within the argument

words such as "if," "not," "all," "none," and "either"