Following Chisholm, I have been identifying propositions with states of affairs. A proposition is a subset of the set of states of affairs. The state of affairs of John grasping a doorknob at time t_0 in Chicago is a state of affairs that always occurs (or always fails to occur). States of affairs like this one are propositions. The truth (falsity) of a proposition is nothing but a certain state of affairs occurring (failing to occur). I am ignoring the question, which is pestering me right now, of why then it seems so awkward to talk about a ‘true’ (‘false’) state of affairs. From The Stanford Encyclopedia of Philosophy article on Roderick Chisholm:
Consider the state of affairs that is expressed by the sentence ‘Someone is walking’. Chisholm wanted to say that this state of affairs occurs whenever someone walks, and fails to occur at times when no one is walking. Other states of affairs are not like this. For them, it is impossible to sometimes occur and sometimes fail to occur. Chisholm claims that this provides the opportunity for an ontological reduction. We can define a proposition as a state of affairs of this latter sort — it is impossible for there to be times when it occurs and other times when it does not occur. A true proposition is thus one that occurs; and afalse proposition is one that does not occur. Chisholm thinks that we may understand the principles of logic to be about these propositions. By saying that a fact is a true proposition, Chisholm gains yet another ontological reduction ([P&O], 123).
Chisholm thought that in some cases it makes sense to speak of the location at which a state of affairs occurs. Suppose John walks in Chicago at a certain time. Then Chisholm would be willing to say that the state of affairs of John’s walking occurs in Chicago and at that time.
Those states of affairs that are not propositions are events. I am going through this stuff a bit impressionistically; the chances of my making an error someplace are high.
The tuples in the body of a database relation are propositions. That is to say, they are states of affairs. In a conventional database, these are always states of affairs occurring now, and now, and now…. John is an employee of WIDGETS_R_US now, the ‘now’ being implicit in the presence of that tuple in the relation. In a temporal database as described by Date and Darwen (TEMPORAL DATA AND THE RELATIONAL MODEL), these are states of affairs that occurred during a time period, or are occurring now (“Since t_0….”), the relevant time periods being explicitly stated in the tuple.
Since propositions are nothing but states of affairs of a certain kind, the operations of the Relational Algebra are operations on states of affairs of that kind. On the relation ‘Standing_To_The_RIGHT_Of’, for example, we can perform a RESTRICT operation that delivers to us the state of affairs of Don standing to the right of Genghis Khan, then perform a PROJECT operation on that derived relation to obtain just Don.
We will figure out later what to do with Don now that we have him.
My homage to Plato’s SYMPOSIUM for this post will be Matt Damon. This time we are a bit further along on the way towards eros for mathematical beauty:
But let’s not forget it all originally stems from eros for gorgeous young men.