Explain the difference between each pair of terms and support your explanation with your own examples. (3 points each, 15 points total)

(a) The difference between genus and species.

Genus: a relatively larger class; genus Panthera, species Panthera tigris
Species: a relatively smaller class; species Panthera tigris, genus Panthera

(b) The difference between deductive and non-deductive arguments.

Deductive arguments: If the argument is valid and if the premises are true, the truth of the conclusion follows with absolute certainty.

If the sun rises, daytime follows. The sun rises. Therefore, daytime
follows.

Non-deductive arguments: In a strong non-deductive/inductive argument, the conclusion follows with high probability from the premises; typically probabilistic arguments.

These critical thinking problem sets have all been interesting. It is likely
the next one will be interesting as well.

(c) The difference between modus ponens and modus tollens.

MP: If p âŠƒ q, p, âˆ´q. If the sun rises, daytime follows. The sun rises. Therefore,
daytime follows.

MT: If p âŠƒ q, ~q, âˆ´~p. If the sun has risen, itâ€™s daytime. Itâ€™s not daytime.
Therefore, the sun has not risen.

(d) The difference between a reportive definition and a stipulative definition.

Reportive: lexical, existing meaning of a term; captures/reports correct usage of the term defined. E.g. what a â€œHiggs bosonâ€ is in physics.

Stipulative: establishes the meaning of a term, assigns a meaning to a term. E.g. what was done when â€œHiggs bosonâ€ was first used as a term and assigned the meaning of â€œparticle responsible for Higgs field.â€

(e) The difference between a sound argument and a valid argument.

An argument can be valid but unsound, i.e. its form can be such that the truth of its conclusion will follow from the truth of its premises, but it just so happens the premises are not true. Soundness is about the truth of premises; validity is about an argumentâ€™s form. For example, during the day, the following argument would be valid but unsound: If the sun has risen, itâ€™s daytime. Itâ€™s not daytime. Therefore, the sun has not risen.

2 â€“ Explain why the following definitions are problematic, if we regard them as reportive definitions. (2 points each, 10 points total)

(a) A crime is any act committed by a criminal, and a criminal is anyone who has committed a crime.

As a reportive definition, it is too narrow; it is not clear whether it makes sufficient room for crimes without criminals or criminals without crimes. (if this were stipulative, it would be circular)

(b) A table is a piece of furniture that has four legs.

Too wide. Too many things are pieces of furniture with four legs but are not tables (chairs, for example).

(c) Rain is the precipitation of cumulus bodies of atmospheric dihydrogen monoxide in accord with the dictums of gravitation.

Too narrow, both ways. â€œRainâ€ need not refer to only precipitated H2O, and â€œprecipitations of cumulusâ€¦â€ need not refer to only rain (hail or snow, for example).

Question 2 Name: (i) translate the argument into the symbolic lan...