Whenever we find one thing passing over into its opposite through a gradual series of borderline cases, we can construct (a) an argument from the heap and (b) a conceptual slippery-slope argument by...

Whenever we find one thing passing over into its opposite through a gradual series of borderline cases, we can construct (a) an argument from the heap and (b) a conceptual slippery-slope argument by using the following method: Find some increase that will not be large enough to carry us outside the borderline area. Then use the patterns of argument given above. Applying this method, formulate arguments for the following claims. Then explain what is wrong with these arguments.

1. a. There are no heaps. b. There is no difference between a heap and a single grain of sand.

2. a. Nobody is tall. b. There is no difference between being tall and being short.

3. a. Books do not exist. b. There is no difference between a book and a pamphlet.

4. a. Heat is not real. b. There is no difference between being hot and being cold.

5. a. Taxes are never high. b. There is no difference between high taxes and low taxes.

6. a. Science is an illusion. b. There is no difference between science and faith.