Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or
forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called "logical constants."[
1] Thus, for example, the sentences
Every boy loves some girl.
and
Some boy loves every girl.
are thought to differ in logical form, even though they share a common syntactic and semantic structure, because they differ in the placement of the logical constants "every" and "some". By contrast, the sentences
Every girl loves some boy.
and
Every boy loves some girl.
are thought to have the same logical form, because "girl" and "boy" are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the "logical constants" of a language from its nonlogical expressions.
While it is generally agreed that signs for negation, conjunction, disjunction, conditionality, and the first-order quantifiers should count as logical constants, and that words like "red", "boy", "taller", and "Clinton" should not, there is a vast disputed middle ground. Is the sign for identity a logical constant? Are tense and modal operators logical constants? What about "true", the epsilon of set-theoretic membership, the sign for mereological parthood, the second-order quantifiers, or the quantifier "there are infinitely many"? Is there a distinctive logic of agency, or of knowledge? In these border areas our intuitions from paradigm cases fail us; we need something more principled.
However, there is little philosophical consensus about the basis for the distinction between logical and nonlogical expressions. Until this question is resolved, we lack a proper understanding of the scope and nature of logic, and of the significance of the distinction between the "formal" properties and relations logic studies and related but non-formal ones. For example, the sentence
If Socrates is human and mortal, then he is mortal.
is generally taken to be a logical truth, while the sentence
If Socrates is orange, then he is colored.
is not, even though intuitively both are true, necessary, knowable
a priori, and analytic. What is the significance of the distinction we are making between them in calling one but not the other "logically true"? A principled demarcation of logical constants might offer an answer to this question, thereby clarifying what is at stake in philosophical controversies for which it matters what counts as logic (for example, logicism and structuralism in the philosophy of mathematics).