Reference no: EM133508279

Translate the following arguments into symbolic form, then use conditional proof and/or the eighteen rules of inference to derive the conclusions of each.

1. If being a platonist entails rejecting empiricism, then Quine is not a platonist. Being a platonist entails being an apriorist. Not rejecting empiricism entails not being an apriorist. So, Quine is not a platonist.

2. If the common interest is imposed on individuals, then they are alienated or not self-determining. But people are self-determining. So, if people are not alienated, then the common interest is not imposed.

3. Either it is not the case that nothing is certain or we have unmediated access to our mental states. If we have unmediated access to our mental states and our basic beliefs are not secure, then either our mental states are potentially misleading or we lack mental states. But if we lack mental states, then our basic beliefs are secure. So, if nothing is certain and our basic beliefs are not secure, then we have unmediated access to our mental states, but they are potentially misleading.

4. Either some objects are beautiful or we impose cultural standards on artifacts. It's not the case that some particular proportions are best. So, if some objects being beautiful entails that some particular proportions are best, then if something is aesthetically moving, then we impose cultural standards on artifacts.

5. lf suicide is not legal, then we lack autonomy and the least powerful people do not have self-determination. If education is universal and free, then the least powerful people have self-determination. If only the privileged are educated, then suicide is not legal. Either education is universal and free or only the privileged are educated. So, suicide is legal if, and only if, the least powerful people have self-determination.