# Wetzel's 'occurences'

I was reading this often quoted article by Linda Wetzel (1993) where she discusses the 'occurence' of expressions in others and Quine's issues with the idea, she describes an expression as a sequence of symbols. If an expression can be a sequence of other expressions as well as a sequence of letters, how can both of these be true, defining a sentence as two separate things, mathematically speaking I would not define a sequence of letters as being also a sequence of words (a sequence with a sequence of letters at each position).

Perhaps I am misunderstanding here, but is she drawing a distinction between occurences in the string and occurences in the sentence as a type? I don't see how a sequence of letters and a sequence of words can be the same object as the function is different.

A function that takes a natural number to a letter, is different to a function that takes a natural number to a sequence of letters.

If 'expressions' are both strings of symbols how can one 'occur' within another? I find it a contradiction that an expression can occur within the other with the other retaining the same 'occurences' of symbols as it had before.

How can an 'expression' be a sequence of letters and a sequence of other sequences?

• I haven't read Wetzel's papers but IMO there is no issue here... We start with an alphabet, i.e. a collection (usually finite) of symbols: a,b,c,...,w,x,y,z. Then we define expression i.e. a string (usually finite) of symbols: mother. If we work in a formal setting, we use also the empty space " " ("blank") as a symbol. In this way we have single words, like mother and yes and "complex" expressions (sentences), like Ann is the mother of John and Yes. Nov 30, 2022 at 14:42
• IMO there is no contradiction: what counts as a sentence is defined by the rules of the syntax (the grammar). Compare with logic: in propositional logic an atom p (a single symbol) can be a formula (a sentence), while in predicate logic a term x (a variable, i.e. a symbol) cannot be a formula. Nov 30, 2022 at 14:42
• Maybe useful: Linda Wetzel, Types and Tokens: On Abstract Objects (MIT Press, 2009) Nov 30, 2022 at 14:54
• As often (alas!) in philosophy we have to try to avoid discussing about "words", i.e. I prefer to start with clearly (as much as possible) defined terms. We have symbols and we have strings of symbols; if we think like natural language, we call expressions those strings that are meaningful, i.e. well-formed according to the rule of the grammar. Thus, abc is a string but not an expression while one is a string that is also an expression. Nov 30, 2022 at 15:29
• The Types vs Tokens introduced by Peirce is interesting but also problematic... It does not coincide with Universal-Particular, also if types are presumably universal and tokens must be particulars. In addition, it seems to me difficult to apply it outside the context of language: me and you are particulars (individuals) and we may assume for the discussion that we are both instances of the universal man; but I'm not a token of a "Mauro-type". Dec 1, 2022 at 10:25

I can't find your aforementioned quotes about sentences, but if we take what Wetzel says on p218: "An expression is any sequence of letters; the wffs will be a proper subset of them" then this should be fairly simple. Now it is easy to realize that every sequence of words naturally gives rise to a sequence of letters over the typical alphabet + whitespace/delimiters.

So Wetzel is not defining a sentence as two contradictory things, she is realizing a subset relation. However, you should also in general be aware of the following:

Suppose we wish to form all words. We fix a base class of letters and close it under the proper grammatical rules. This process is entirely analagous to fixing a base class of words, and, using the grammatical rules for sentences, obtaining all the sentences. So when dealing with formal expressions, it is common to conflate the words "word", "sentence", "wff", etc.

This allows Wetzel to define a notion of occurence for both word and sentence, allowing context to determine which is the case. This is standard in mathematics and philosophy, although less common in linguistics, where the distinction actually matters.

Lastly, with respect to your last point, there is no contradiction in a word occuring in another, whilst both retain the same association with whatever sequence they have been associated with. In fact, it has to be this way. Example:

Bob said "Sarah is a bad person".

Both of these are sentences, one containing the other. The fact that one is embedded in the other should not change eithers order at all.

• @Confused can you please provide the exact page number where Wetzel says that "sentences are sequences of words"? I think this will help clarify our discussion. Dec 2, 2022 at 17:33
• Maybe page 215: "is. In On Universals Wolterstorff says that "occurrences of sentences [words or sequences of words] are Peirce's tokens"." Dec 2, 2022 at 17:42
• @MauroALLEGRANZA its unclear to me that Wetzel endorses this view, since that very same paragraph then deduces an impossibility from Wolterstorffs view in conjunction with Pierces. Further, I don't see the word 'sentence' anywhere else in her paper, which leads me to think Confused is referencing some other paper. Dec 2, 2022 at 17:49
• @Confused - but yes, letters form words and words form sentences and sentences form texts. Dec 2, 2022 at 18:04
• If you equate expression with finite string of symbols, then words and sentences and texts are all expressions. Dec 2, 2022 at 18:06