Chapter Six, Tutorial Two
Basic PL Symbolization

This tutorial provides an introduction to symbolization for PL. We now know enough about PL to begin symbolizing simple quantified sentences of natural language. But beware! We have not yet spelled out the details of what counts as a sentence of PL, that's the next tutorial, and we have not yet provided a semantics for PL, that we do in the next chapter. So, we are only scratching the surface for now. A more comprehensive account of symbolization will come soon.

Names

We will use lower case letters, 'a' - 'u', to refer to objects. These are the "names" of PL. They can be used to symbolize proper names of English, as we have seen from the last tutorial. So, our names take the place of "Clinton", "Earth", or "Seven". We might use 'c','e',and 's' respectively to be mnemonically correct. But any association of names of PL to the English proper names will do.

Names of PL can also be used to symbolize any singular referring expression of natural language. So, "the winner of the OU election" and "that woman in the front row" are English expressions which are used to pick out one specific individual. So, these too are represented in PL with a name. (Names of PL are often called "individual constants" so that it is clear that they may represent more than proper names.)

The following English expression are typically used to signify a specific individual and so can be symbolized with PL names:

Proper Nouns like "Paris", "Earth", "Mary", "Oakland University", "Waiting for Godot", "tomorrow", etc.

Kind Names like "oxygen", "Homo Sapiens" (the species), "logic", etc.

Pronouns
like: "this", "that", "he", "she", "it", "who", "what", "there", etc.

Definite Descriptions like: "the boy in the field", "Smith's murderer", "the square root of 4", "my son", etc.

Other tags or symbols, e.g., '(*)' as used so often in the Café to name a sentence or example.

But be careful. Other apparently similar expressions are not about a particular individual and cannot be symbolized with a PL name. For example, "A boy in the field" is not generally about a particular individual. The sentence

(*) There is a boy in the field

need not be about any particular boy. Why? Because the sentence in question, (*), is properly uttered by one who might also say "I'm not sure who is in the field, but from the noise there's at least one boy out there!". So, "a boy" is too general to be symbolized with a PL name.

Which of the following noun phrases should probably be symbolized in PL with a name?

  1. The first person in line
  2. My friend
  3. The left fielder
  4. Anyone you know
  5. A friend in need
  6. Human Kind
  7. Universe