Individuals, Properties and Relations

With the set of resources now at your disposal for translation, you can do a much better job of representing the logical structure of natural language sentences than you could earlier before we introduced relations and multiple quantifiers. Translation with all these resources can be a challenge, however. So It's important to think carefully about which resources to use, and when to use them. As always, when you begin a translation, formulate the dictionary.  Identify the names, the monadic predicates, and the relations expressed in the sentence, and abbreviate them appropriately.

Let's look at some examples.

This sentence refers to an individual, Ignat. It also mentions two kinds of things, wine and caviar. It further posits a relation between Ignat and these two kinds of things, the "enjoying" relation.  So our dictionary will be as follows:

We've identified individuals, properties, and relations. The individual is Ignat, the properties are the properties of being wine and being caviar. One common mistake is to treat "wine" and "caviar" as names. But wine and caviar are not individual things. Put differently, "wine" and "caviar" are not names! Wine is a kind of thing, and so we must use a propositional function to express it. The same goes for caviar. Finally, we have the relation of enjoying which we express with the two place propositional function "Exy".

Notice that this sentence has an "and". This suggests that we rewrite the sentence as:

Now we can translate each conjunct, and conjoin them. We do this by specifying the kind of thing Ignat enjoys, and then expressing the fact that Ignat enjoys that kind of thing. So we can translate:

as

and thus the whole conjunction as:

Notice that we did not translate as follows:

This says that Ignat enjoys that which is both wine and caviar! Perhaps Ignat would enjoy such a concoction, but that's not what sentence (1) says!

However, the following wff is logically equivalent to the correct translation above:

Note another incorrect translation:

At this point, you should be able to say with confidence why this is an incorrect translation.

Let's try another translation.  Consider:

In this sentence, what are the individuals, properties and relations? We notice right off that there are no individuals. The sentence talks about scouts, marshmallows, and the relation of toasting. So our dictionary is:

We also notice that this is really an A categorical proposition: All scouts toast marshmallows. So our translation is:

Let's look at one more:

Again, there are no individuals. This sentence refers to farmers, failing crops, and the relation of rotating. What are the relata of the rotating relation? Farmers and crops:

This is an E categorical sentence. The subject is "farmers who rotates crops" and the predicate is "those who fail."  So our translation is:

In all these translations, we began by asking what individuals, properties and relations are expressed. We formulate our dictionary guided by that question. Then we look for the structure of the sentence, finding categorical structure in many cases, and we translate as appropriate.