Logical truth is one of the most fundamental
concepts in logic, and there are different
theories on its nature. A logical truth is
a statement which is true, and remains true
under all reinterpretations of its components
other than its logical constants. It is a
type of analytic statement. All of philosophical
logic can be thought of as providing accounts
of the nature of logical truth, as well as
logical consequence.Logical truths (including
tautologies) are truths which are considered
to be necessarily true. This is to say that
they are considered to be such that they could
not be untrue and no situation could arise
which would cause us to reject a logical truth.
It must be true in every sense of intuition,
practices, and bodies of beliefs. However,
it is not universally agreed that there are
any statements which are necessarily true.
A logical truth is considered by some philosophers
to be a statement which is true in all possible
worlds. This is contrasted with facts (which
may also be referred to as contingent claims
or synthetic claims) which are true in this
world, as it has historically unfolded, but
which is not true in at least one possible
world, as it might have unfolded. The proposition
"If p and q, then p" and the proposition "All
married people are married" are logical truths
because they are true due to their inherent
structure and not because of any facts of
the world.
Later, with the rise of formal logic a logical
truth was considered to be a statement which
is true under all possible interpretations.
The existence of logical truths has been put
forward by rationalist philosophers as an
objection to empiricism because they hold
that it is impossible to account for our knowledge
of logical truths on empiricist grounds. Empiricists
commonly respond to this objection by arguing
that logical truths (which they usually deem
to be mere tautologies), are analytic and
thus do not purport to describe the world.
== Logical truths and analytic truths ==
Logical truths, being analytic statements,
do not contain any information about any matters
of fact. Other than logical truths, there
is also a second class of analytic statements,
typified by "no bachelor is married". The
characteristic of such a statement is that
it can be turned into a logical truth by substituting
synonyms for synonyms salva veritate. "No
bachelor is married" can be turned into "no
unmarried man is married" by substituting
"unmarried man" for its synonym "bachelor".
In his essay Two Dogmas of Empiricism, the
philosopher W. V. O. Quine called into question
the distinction between analytic and synthetic
statements. It was this second class of analytic
statements that caused him to note that the
concept of analyticity itself stands in need
of clarification, because it seems to depend
on the concept of synonymy, which stands in
need of clarification. In his conclusion,
Quine rejects that logical truths are necessary
truths. Instead he posits that the truth-value
of any statement can be changed, including
logical truths, given a re-evaluation of the
truth-values of every other statement in one's
complete theory.
== Truth values and tautologies ==
Considering different interpretations of the
same statement leads to the notion of truth
value. The simplest approach to truth values
means that the statement may be "true" in
one case, but "false" in another. In one sense
of the term "tautology", it is any type of
formula or proposition which turns out to
be true under any possible interpretation
of its terms (may also be called a valuation
or assignment depending upon the context).
This is synonymous to logical truth.
However, the term "tautology" is also commonly
used to refer to what could more specifically
be called truth-functional tautologies. Whereas
a tautology or logical truth is true solely
because of the logical terms it contains in
general (e.g. "every", "some", and "is"),
a truth-functional tautology is true because
of the logical terms it contains which are
logical connectives (e.g. "or", "and", and
"nor"). Not all logical truths are tautologies
of such a kind.
== Logical truth and logical constants ==
Logical constants, including logical connectives
and quantifiers, can all be reduced conceptually
to logical truth. For instance, two statements
or more are logically incompatible if, and
only if their conjunction is logically false.
One statement logically implies another when
it is logically incompatible with the negation
of the other. A statement is logically true
if, and only if its opposite is logically
false. The opposite statements must contradict
one another. In this way all logical connectives
can be expressed in terms of preserving logical
truth. The logical form of a sentence is determined
by its semantic or syntactic structure and
by the placement of logical constants. Logical
constants determine whether a statement is
a logical truth when they are combined with
a language that limits its meaning. Therefore,
until it is determined how to make a distinction
between all logical constants regardless of
their language, it is impossible to know the
complete truth of a statement or argument.
== Logical truth and rules of inference ==
The concept of logical truth is closely connected
to the concept of a rule of inference.
== Logical truth and logical positivism ==
Logical positivism was a movement in the 20th
century and was followed to a great extent
in Europe and the United States. It is a structured
method of determining how valid the knowledge
is. It introduced mathematics and the natural
sciences into the field of philosophy. It
is also known as scientific empiricism. Logical
positivism considers philosophy as an analytical
inquiry. Philosophy was deciphered as an activity
rather than a theory. Logical positivists
worked to explain the language of science
by showing that scientific theories could
be broken down to logical truths along with
the experience of the five senses. The concepts
created in this movement are very closely
followed today in the West. Logical positivism
was a way to decipher whether a statement
was truly a logical truth by means of relating
it to a scientific theory or mathematics.
It determined the validity of the statement
as well as gave it the rank of a logical truth
or a false truth.
== Non-classical logics ==
Non-classical logic is the name given to formal
systems which differ in a significant way
from standard logical systems such as propositional
and predicate logic. There are several ways
in which this is done, including by way of
extensions, deviations, and variations. The
aim of these departures is to make it possible
to construct different models of logical consequence
and logical truth.
== See also ==
Contradiction
False (logic)
Satisfiability
Tautology (logic) (for symbolism of logical
truth)
Theorem
Validity
== References ==
== External links ==
Zalta, Edward N. (ed.). "Logical Truth". Stanford
Encyclopedia of Philosophy.
Logical truth at the Indiana Philosophy Ontology
Project
Logical truth at PhilPapers
