Maarten Maartensz:    Philosophical Dictionary | Filosofisch Woordenboek                      

 L  - Logical Terms

Logical Terms: Terms that are used for reasoning that may occur in statements about any kind of subject-matter, and that are supposed to come with rules or axioms that specify their valid and proper use.

What are the logical terms is not a matter of universal agreement, not even for a specific natural language. But it is useful to have the notion, to add a further characteristic and to provide a list.

The further characteristic is that logical terms are often supposed to be syncategorematic i.e. to have no meaning on their own, but only in combination with terms that have meaning. Whether this is generally so is doubtful, e.g. if 'class' or 'set' is a logical term, but it is useful in reminding that at least many terms that have been deemed logical are syncategorematic.

Here is a list of logical terms, or at least of terms that have been widely regarded as logical and occurred as such in logical texts:

true, false
, possible, contingent
, contradiction

, follows, entails, antecedent, consequence, premiss, conclusion

, and, or, implies, if and only if

equals, such that

predicate, relation, tuple

every, some, no

part, element

set, subset, class, collection, structure

inference, proof, hypothesis, assumption, axiom, rule of inference

As I indicated, there is no universal agreement on what are and are not logical terms but a minimal set on which there is wide agreement concerns the terms that are commonly used in propositional and predicate logic, which is a subset of the one given above

not, and, or, implies, if and only if

equals, such that

every, some, no

The simplest set of basic logical terms that is widely accepted as such seems to be this:

not, and, or

, entails

which may be simplified again to four by using the Sheffer-stroke. (Note that entailment is implication styled as inference: We need a writing or asserting rule in order to write proofs and arguments.)

This minimal set is suffficient for first-order logic, and may also be used for second-order logic. (Set theory or mereology require another primitive each, namely respectively element or part.)

All logic books give rules of reasoning, or rules of inference and axioms, to lay down how to validly reason with statements involving these terms.


See also: Basic Logic, Logic Notation


Bochenski, Carnap, Cartwright, Hamilton, Hasenjäger, Hilbert & Bernays, Shoenfield, Slupecki & Borkowski, Tarski, Tennant,

 Original: Apr 4, 2005                                                Last edited: 6 Jan 2011.   Top