TD1 - Logic

TD1 - Logic

Arguments | Sound/Unsound

​Properties on the arguments

An argument has at least one premice and exactly one conclusion.

​Arguments can be valid/invalid

• ​​If the truth of all the premises logically guarantees the truth of the conclusion, then the argument is valid.

​Arguments can be sound/unsound

• ​If the premices and the conclusion are both true in real life.

• ​If an argument is invalid, in can't be sound

• ​If an argument is valid, it can be sound or unsound

​Properties on the premices and the conclusion

Premice can be multiple, but the conclusion must be unique.

Premices and conclusion can only be true/false

• ​Premices and conclusion are true if they are logically correct (not necessary in real life, otherwise they are false)

​Knowing this, let's do a quiz

(to test your skills)​

Multiple Choice

An argument has :

• Exactly one premise and one conclusion

• At least one premise and exactly one conclusion

• At least two premises and at least one conclusion

• At least two premises and exactly one conclusion

• Either a premise or a conclusion

​Explanations

This is a course property, which you could read just before :).​

Multiple Select

An argument can be :

• True or false

• Valid or invalid

• Sound or unsound

​Explanations

This is a course property, which you could read just before :).​

Multiple Choice

Premices and conclusion can be :

• True or false

• Valid or invalid

• Sound or unsound

​Explanations

This is a course property, which you could read just before :).​

Multiple Choice

The sky is blue. The grass is green. Therefore tigers are carnivore.

• The argument is valid and sound

• The argument is valid and not sound

• The argument is valid but we cannot know if it is sound

• The argument is not valid and sound

• The argument is not valid and not sound

​Explanations

In this case the argument is not valid because the truth of the premises doesn't logically guarantees the truth of the conclusion (If the sky is blue and the grass is green, it not implies that tigers are carnivore).

​

​Moreover, if an argument is not valid, it cannot be sound.

Multiple Choice

The gasoline price goes up. Therefore, there is a lack of gasoline.

• The argument is valid and sound

• The argument is valid and not sound

• The argument is valid but we cannot know if it is sound

• The argument is not valid and sound

• The argument is not valid and not sound

​Explanations

In this case the argument is not valid because the truth of the premises doesn't logically guarantees the truth of the conclusion (If the price of the gasoline goes up, it doesn't significates that there is a lack of gasoline).

​

​Moreover, if an argument is not valid, it cannot be sound.

Multiple Choice

Chicago is the capital of the United States. The capital of the United States is in Illinois. Therefore, Chicago is in Illinois.

• The argument is valid and sound

• The argument is valid and not sound

• The argument is valid but we cannot know if it is sound

• The argument is not valid and sound

• The argument is not valid and not sound

​Explanations

In this case the argument is valid because the truth of the premises logically guarantees the truth of the conclusion. (If we pretend that Chicago is the capital of the United States and that the capital of the United States is in Illinois, then it logically implies that Chicago is in Illinois).

​

​​However, the argument is not fully valid because the premices and the conclusion are both false in real life (Chicago is not the capital of the USA) so, it cannot be sound.

Multiple Choice

Biden is the president of the United States. Macron is the president of France. Therefore, Merkel is the chancellor of Germany.

• The argument is valid and sound

• The argument is valid and not sound

• The argument is valid but we cannot know if it is sound

• The argument is not valid and sound

• The argument is not valid and not sound

​Explanations

In this case the argument is not valid because the truth of the premises doesn't logically guarantees the truth of the conclusion (If we pretend that Biden is the president of the United States and Macron is the president of France, it doesn't implies that Merkel is necessary the chancellor of Germany ).

​

​Moreover, if an argument is not valid, it cannot be sound.

Multiple Choice

No sea creatures are mammiferous. Dolphins are sea creatures. Therefore dolphins are not mammiferous.

• The argument is valid and sound

• The argument is valid and not sound

• The argument is valid but we cannot know if it is sound

• The argument is not valid and sound

• The argument is not valid and not sound

​Explanations

In this case the argument is valid because the truth of the premises logically guarantees the truth of the conclusion. (If we pretend that No sea creatures are mammiferous and Dolphins are sea creatures, it implies that dolphins are not mammiferous).

​

​​However, the argument is not fully valid because the premices and the conclusion are both false in real life (It exists some mammiferous that are actually sea creatures) so, it cannot be sound.

Multiple Choice

Fred is taller than Kate and Jane is shorter than Kate. So Fred is taller than Jane.

• The argument is valid and sound

• The argument is valid and not sound

• The argument is valid but we cannot know if it is sound

• The argument is not valid and sound

• The argument is not valid and not sound

​Explanations

In this case the argument is valid because the truth of the premises logically guarantees the truth of the conclusion. (If we pretend that Fred is taller than Kate and that Jane is shorter than Kate, it logically implies that Fred is taller than Jane).

​

​​However, the argument is not fully valid because the premices and the conclusion can both be false in real life (we don't know Fred, Jane and Kate, and it might be someone named Fred who is shorter than Jane) so, it cannot be sound.

Multiple Choice

At 2pm, Marc is always either in the office or in the coffee bar. If he's in the coffee bar, he's drinking an expresso. Marc was not in the office at 2pm. So he was drinking an expresso.

• The argument is valid and sound

• The argument is valid and not sound

• The argument is valid but we cannot know if it is sound

• The argument is not valid and sound

• The argument is not valid and not sound

​Explanations

In this case the argument is valid because the truth of the premises logically guarantees the truth of the conclusion. (If we pretend that At 2pm, Marc is always either in the office or in the coffee bar, that If he's in the coffee bar, he's drinking an expresso and that Marc was not in the office at 2pm, then it implies that he was drinking an expresso).

​

​​However, the argument is not fully valid because we can't know if the premices and the conclusion are both be true in real life (we don't if Marc really was in the coffee bar) so, we cannot know if it is sound.

Multiple Choice

Every premise of a valid argument is true.

• True. Explain why.

• False. Give a counterexample.

• None of the above.

​Explanations

As the course indicates, an argument is valid if when its premices are assumed to be logically true, then the conclusion is also valid. But this does not mean that every premice of this valid argument is true.

​

Multiple Choice

Every invalid argument has a false conclusion.

• True. Explain why.

• False. Give a counterexample.

• None of the above.

​Explanations

As the course indicates, an invalid argument can have a true conclusion. If the argument is invalid, it means that if we assume the premises are true, the conclusion is false. Apart from this assumption, the conclusion can be true.

Multiple Choice

Every valid argument has exactly two premices.

• True. Explain why.

• False. Give a counterexample.

• None of the above.

​Explanations

This is false, because as the course indicates, an argument, whether valid or not, has at least one argument, but not necessarily two premices.

Multiple Choice

Some valid arguments have false conclusions.

• True. Explain why.

• False. Give a counterexample.

• None of the above.

​Explanations

It is true, there are valid arguments that have false conclusions because these arguments are valid only under the assumption that the premises are true, which implies that the conclusion is true.

Multiple Choice

Some valid arguments have a false conclusion despite having premises that are all true.

• True. Explain why.

• False. Give a counterexample.

• None of the above.

​Explanations

This is false, as the course indicates, if all the premises of an argument are true, the conclusion is necessarily true.

Multiple Choice

A sound argument cannot have a false conclusion

• True. Explain why.

• False. Give a counterexample.

• None of the above.

​Explanations

A sound argument necessarily has a true conclusion because if an argument is sound, it is valid (which means that the conclusion is true under the assumption that the premises are true) and both the conclusion and the premises are true in real life, whatever the context.