# From Logic to Probability

Consider the following arguments:

- Ann with get an A or B in PHIL 171. Ann will not get a B in PHIL 171. So, Ann will get an A in PHIL 171.
- Ann brought her laptop to class the first 5 lectures. So, Ann will bring her laptop to the next class.
- The witness said that John stole the laptop. So, John stole the laptop.
- Two independent witnesses claimed John stole the laptop. John was seen on video leaving the classroom. John confessed to stealing the laptop. So, John stole the laptop.

The first argument is valid: It is impossible that both premises are true while the conclusion is false. Arguments 2, 3, and 4 are not valid. This is not hard to see since none of the statements involved in the arguments 2, 3, and 4 involve Boolean connectives or quantifiers. Nonetheless, the premises in arguments 2, 3, and 4 do seem to provide *some* support for their conclusions. In the remainder of this book, we will introduce probability theory as a tool to study reasoning and inductively strong arguments, where:

An argument is **inductively strong** when it is *improbable* that its conclusion is false while its premises are true.

- Lecture
- Slides