chapter 4 (1.2)

Question 1

Any deductive inference is either

Answer 1

valid or invalid. A valid deductive argument cannot be made more valid, or rendered invalid, by adding more premises

Question 2

Monotonicity

Answer 2

Reasoning is monotonic of the addition of new information never invalidates an inference or forces the conclusion to be retracted.

For this reason, deductive arguments are rock-solid; you might be wrong about a starting point one or more of your premises might be false but if you have a valid inference, you can be absolutely certain that your premises if true guarantee your conclusion

Question 3

affirming the antecedent of a conditional statement (also known by its latin name modus ponens)

Answer 3

This is when a conditional statement and its antecedent are used as premises for concluding the consequent must be true

For example:

1) If a star is more than 10 billion years old, then the universe must be more than 10 billion years old

2) This star is more than 10 billion years old

3) the universe must be more than 10 billion years old

Question 4

Denying the consequent of a conditional statement (also known by its latin name modus tollens)

Answer 4

When a conditional statement and the negation of its consequent are used as premises for concluding the antecedent must be false

For example:

1) if the universe is in a steady state, then astral bodies remain the same distance from one another

2) It is not the case that astral bodies remain the same distance from one another

3) IT is not the case that the universe is in a steady state

Each of the previous two arguments is deductively valid. The premises may not be true.
But if they were true, they would logically guarantee that the conclusion must also be
true. This holds for every other instance of these general patterns of inference. No matter
how long and deep you think, you will not be able to find an instance of either pattern
that is invalid

Question 5

The two main criticisms that can be made of a deductive argument are that

Answer 5

Its premises are false and

The conclusion isnt validly inferred from the premises

When evaluating a deductive argument, one should determine whether either or both of these criticisms apply.

Question 6

Denying the antecedent

Answer 6

occurs when a conditional statement and the negation of its antecedent are used as premises for concluding that the consequent must be false as well. here is an argument that commits the error of denying the antecedent

1) if a star is more than 15 billion years old, then the universe is more than 15 billion years old

2) No star is more than 15 billion years old

3) Its not the case that the universe is more than 15 billion years old

This argument is invalid. Even if the first two premises are true that does not guarantee the conclusion is also true

Question 7

Affirming the consequent

Answer 7

occurs when a conditional statement and its consequent are used as premises for concluding that the antecedent must also be true. Here is an argument that commits the error of affirming the consequent

1) If the andromeda nebula is 13.8 billion light years away, then the universe is at least 13.8 billion years old

2) The universe is at least 13.8 billion years old

3) The andromeda nebula is 13.8 billion light years away

This is invalid argument. Both premises are true but they dont guarantee the truth of the conclusion

Question 8

Counterexamples

Answer 8

situations that you can describe whether real or imagined, in which the premises of an argument are true but the conclusion is false ar ecalled counterexamples

Question 9

informal fallacy

Answer 9

which is a faulty inference pattern where the defect in reasoning lies with the inference content rather than its form and which goes beyond just merely having false premises

Question 10

Strawman fallacy

Answer 10

involves carcaturing someones thoughts in order to criticize the caricature rather than the actual thoughts

Here is an example:

1) Evolutionary theory claims that humans recently evolved from monkeys

2) The idea that humans recently evolved from monkeys is clearly wrong

3) Evolutionary theory is clearly wrong

This argument seems to be an instance of affirming the antecedent, which is a valid inference pattern. But the argument misrepresents evolutionary theory, so premise 1 is false (evolutionary theory instead posits among other things, that humans and apes share a common ancestor

Question 11

Appeal to irrelevant authority

Answer 11

For example, the pseudoscientific pronouncements of scientologists – a warning religious cult from the 1950s – often appeal to L.R.Hubbards book dianetics. Hubbard, however, has no expertise in any academic subject whatsoever. Appeals to his booka re poor grounds for scientific conclusions about well-being, mind or the cosmos

Question 12

Appeal to ignorance

Answer 12

Another informal fallacy. Arguments that commit this fallacy conclude that a certain statement is true because there is no evidence proving that it is not

E.g.

There is no compelling evidence that pyramids were not built by extraterestrial creatures

The pyramids were built by extraterrestrial creatures