by Marcus Loane
Here is a valid argument with a true conclusion:
Premise 1: John is 20 years old
Premise 2: Bob is 30 years old
Conclusion: Bob is older than John
Both premises are true and the conclusion is true if the premises are true.
Here is a valid argument with a false conclusion:
Premise 1: The moon is made of green cheese
Premise 2: Parts of the moon have landed on the earth
Conclusion: These parts must be made of green cheese
Here, the argument is valid because the conclusion is true if both premises are true. However Premise 1 is false so the conclusion is false even though the argument is valid.
Here is a circular argument:
Premise 1: God created Earth
Premise 2: Earth exists
Conclusion: God exists
Here, the conclusion is true if both premises are true. However the conclusion "God exists" is just a repetition of part of Premise 1. Circularity in arguments is called "begging the question". Premise 1 assumes the very thing the argument is setting out to prove.
Here is an invalid argument:
Premise 1: Dogs have 4 legs
Premise 2: Rusty has 4 legs
Conclusion: Rusty is a dog
This argument is invalid because the conclusion is not necessarily true if both premises are true. Rusty could be a dog or a cow.
Here is another invalid argument:
Premise 1: Cars are complex
Premise 2: Cars are designed by beings with minds
Premise 3: Dogs are complex
Conclusion: Dogs are designed by beings with minds
This argument is invalid because it omits a step "all complex things are designed by beings with minds". Let's try again:
Premise 1: Cars are complex
Premise 2: Cars are designed by beings with minds
Conclusion 1: All complex things are designed by beings with
minds
Premise 3: Dogs are complex
Conclusion: Dogs are designed by beings with minds
However Conclusion 1 does not follow from the first two premises. What would follow is that "some complex things are designed by beings with minds"
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Marcus Loane