4.2 Propositions

A proposition is an assertion about a factual state of nature. This means that it is capable of being either true or false. Although not always correct, we will speak of propositions as not only capable of being either true or false, but as being either true or false.

The truth of propositions does not depend upon any individual’s or consensus belief about them (unless the proposition is specifically about their belief). Consider the following:

  1. The Earth orbits the Sun.
  2. The Earth is flat.

Proposition 1 is true and proposition 2 is false, and we have scientific evidence to prove this. At a certain time in history, however, common belief about those propositions was false: people thought that the Sun orbited the Earth, and that the Earth was flat. It was true that the Earth orbits the Sun both before and after humans had enough evidence to believe it was true.

Propositions can still evoke epistemic uncertainty; they are true or false but we might not know which. This means we can apply the tools of probability theory to them. Consider another example:

  1. Poker Player B is holding an ace in this round.

In this hypothetical poker game, the proposition is true if Player B is holding an ace and it is false if Player B is not holding an ace in this round. If you are Player B then you will know the truth of this and the proposition is trivial. However, if you are not Player B then you will not know the truth of this - you have epistemic uncertainty.

To play this round well, you require a reasonable belief about this proposition (and others) in order to make decisions which account for your uncertainty. Note that in this example you might never know the truth of this proposition. Player B might never turn over their cards nor reveal the answer. The proposition is still either true or false regardless of this.

The truth of some propositions may be conditional on other factors. Consider the following:

  1. Boris Johnson’s Conservative party govern the UK.

At the time of writing this, the proposition is true. The UK still exists, the Conservative party exist under that same name and are led by Boris Johnson, and his party governs the UK. This proposition will not be true forever, and may not even be true by the time you are reading this. It is useful to be more specific when formulating propositions so that important factors (e.g. time) are made explicit. Doing this makes propositions less ambiguous. Changing the previous proposition to:

  1. On 20th May 2020, Boris Johnson’s Conservative party govern the UK,

gives a more specific proposition whose truth is now clear to anyone with the knowledge of who governed the UK on that specific date. However, the proposition is now less general since it only refers to one specific day. Whether this reduced generality is worth the increased clarity or not depends on the question at hand. When case information is provided by investigators to forensic scientists, then the scientists have to balance these factors in order to formulate appropriate propositions for the case (if they are not given them).