*In your own words, explain the difference between deductive and inductive logic.*

Inductive logic reaches a general conclusion based on a series of observations (recognising patterns), whereas deductive logic uses a set of known premises to reach its conclusion (using facts to create more facts). Inductive logic is inherently uncertain, since its conclusion relies on perfect continuity and reliability, neither of which exist in the real world. Deductive logic, on the other hand, can be perfectly certain and reliable. For example, if we know for a fact that all corgis are dogs, and all dogs are animals, then we know that all corgis are animals. Deductive conclusions can still, however, be incorrect, if the premises are uncertain or the reasoning is done incorrectly.

*What are the problems with each of these kinds of logic and what we can do to overcome some of these problems?*

A popular example of inductive logic notes that since all the swans we’ve seen are white, we may conclude that all swans are white. This is not, however, necessarily true, and it can never be proven without some level of doubt. All inductive claims can be disproven (e.g. finding a black swan), but they cannot be completely proven.

The fault in deductive logic arises when the premises are uncertain (as they usually are in the real world). An example may be claiming that since all men are mortal, and John is a man, then John is mortal. Although the reasoning is perfectly sound, we do not know that all men are mortal (since this is an inductive claim: all men we’ve seen are mortal, not necessarily all men), and so we cannot know with certainty that John is mortal. Not all premises, however, are uncertain. The broadest set of premises that comes to mind are those found in math: since we, as humans, invented math, there is no way it can be false.