BIG Brain KidLokSe- Truth, Validity, and Soundness

Symbologics Part 3

Alola, KidLokers! Let’s get right into some definitions that are used in the standard use of proofs-

argument- an example of reasoning in which certain statements (premises) are used to offer support or evidence for another statement (conclusion).

premise- the statement used to support an argument; what you assume to be true

conclusion- the end goal of an argument; what is being supported

validity- an argument is valid if:

• the truth of its premises logically guarantees the truth of the conclusion

• The conclusion must be true if it is assumed that the premises are true

• It is impossible for the conclusion to be false while all the premise are true

• The conclusion can be deduced from the premises by following certain rules

soundness- when the argument’s premises are realistically true and their reasoning is valid.

Examples:

1. Invalid-Unsound

Premises:

• Cats are mammals

• Dogs are mammals

Conclusion:

• Cats are dogs

This argument is invalid and unsound, because using the venn method we cannot conclude this. It is unsound because Cats can never be Dogs.

2. Valid-Sound

Premises:

• Cats are mammals

• Tigers are cats

Conclusion:

• Tigers are mammals

This argument is valid and sound, because using the venn method we can conclude this. It is sound because the entire argument is valid and realistically true.

3. Valid-Unsound

Premises:

• Dogs are cats

• Cats are birds

Conclusion:

• Dogs are birds

This argument is valid and unsound, because using the venn method we can conclude this. However, it is unsound because the entire argument is valid but realistically false.

I hope you all can sort of understand the above. Don’t worry, in the next post we will go over truth tables, a very logical way to solve these situations. Sayonara!