My Notes On 5.1 Beginning The Second Act of the Mind - Categorical and Compound Propositions - From "The Reasonable Person" by Mark Grannis

Here are some of the key take away points from chapter 5.1 in "The Reasonable Person". 

Brief Review

Chapter five is moving from the first act of the mind, simple apprehension (chs. 2, 3, 4), to the second act of the mind, that of judgment. He gives a reminder that "judgment" technically refers to the act in the mind itself, while "proposition" refers to verbal expression of the judgment in speech or writing. He also gives a reminder of the nature of predication. "Predication as the affirmation or denial of some characteristic of a subject so as to produce a meaningful statement about how that subject exists." In other words, to predicate is to say something of a subject. Now while concepts in the first act of the mind are either clear or unclear, propositions in the second act of the mind are either true or false, which depends on their conformity to reality. 

Declarative Sentences

Thus, Grannis offers certain types of sentences that are not making direct claims about reality. He does not classify them as propositions, though I think that they are propositions of a type given that they can be restated into a form which does meet the criteria for a proposition, namely being in a "declarative sentence". Here's how Grannis puts it: "Not all sentences satisfy this requirement. Interrogative sentences, like 'Where are you going?' cannot be true or false because they make no truth claims about reality. Similarly, imperative sentences, like 'Take out the trash, please,' cannot be true or false. Nor can performative sentences, like 'I'll be here to pick you up at 7:00'; not exclamatory utterances, like 'Wow!' Only declarative sentences can be verbal expressions of judgments." 

Categorical Propositions

Grannis then introduces the categorical proposition. "A categorical proposition is a proposition that relates one predicate to one subject, affirmatively or negatively." This is where a proposition has only one subject and one predicate join by the verb to be. This doesn't mean that categorical propositions only have one word subjects and predicates, they certainly can be many worded. This is because a the subject or the predicate can be complex with added attributes like adjectives, adverbs, preposition phrases, etc. 

Grannis points out that you can use brackets {} to show how a complex subject and predicate can be grouped together. For example, "{Home} is {the place where, when you have to go there, they have to take you in}."

Compound Propositions

"A compound proposition is a proposition that comprises two or more different categorical propositions in some logical relation to each other." In other words, a proposition which includes more than one categorical proposition. He lists three examples of compound propositions. 

if... then... Conditional propositions 

either... or... Disjunctive propositions

both... and... Conjunctive propositions