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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
necessary, possible,
contingent
tautology, contradiction
ergo, follows, entails,
antecedent, consequence,
premiss, conclusion
not, 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
equals
some, 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.
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