Topic: analytic truth

topics > philosophy > Group: meaning and truth

philosophy of mathematics
philosophy of science

empirical truth
mathematical proof
mathematics as a formal system
necessary truth
number and arithmetic as part of language
object and value equivalence
problems with analytic truth
sentences, propositions, and truth
set definition by extension or intension
what is a number
what is truth


Kant distinguishes analytic truth from synthetic truth. Analytic truth is a priori, necessarily true, independent of reality. It is what is true by how we understand and communicate. For example, a=a is analytic. Analytic truth is closely tied to equivalence, contradiction, definition, logic, and mathematics. Analytic truths are exact because they are about concepts. Since concepts are created, they can satisfy an exact relationship.

It is tempting to think of analytical truth as absolute truth, because it is not contingent on the world. Analyticaly truth is tied to mathematics which has a ring of permanence that other fields may lack. (cbb 3/94)

Subtopic: perfect truth up

Quote: intensive knowledge, e.g., mathematics, equals the Divine in objective certainty because the knowledge is necessary
Quote: our mathematical knowledge is the same as Divine wisdom but we reason by steps while His is one of simple intuition [»galiG_1632]
Quote: knowledge by deduction from first principles without contingent facts [»ockhW_1310]
Quote: by verification theory, an analytic statement is confirmed no matter what
Quote: necessary and contingent propositions; what is (so) either is or is not (so) vs. something exists [»leibGW_1666]

Subtopic: analytic as axiomatic up

Quote: infinite things can be compounded out of the combination of a few; e.g., numbers from digits [»leibGW_1679]
Quote: since derivative concepts arise from primitive ones, nothing exists in things except through the influence of God
Quote: an a posteriori truth depends on facts; an a priori truth depends on general, primitive laws that neither need nor admit to proof [»fregG_1884]
Quote: a primitive concept is its own sign; is part of the thing which is conceived through itself, that is, God [»leibGW_1679]

Subtopic: analytic as syntactic up

Quote: the principles of logic and mathematics are true because they arise from the rules that govern the use of language; they are analytical [»ayerAJ_1956]
Quote: mathematics and logic are part of the apparatus of language, not part of its application; allows us to use "900" in our daily life [»wittL_1939]
Quote: analytical propositions are necessary because they record our determination to use words in a certain fashion [»ayerAJ_1956]
Quote: theory of meaning for recognizing synonymy of linguistic forms and analyticity of statements [»quinWV1_1951]
Quote: analytic statements are true by virtue of linguistic rules alone, without recourse to empirical investigation [»searJR_1958]
Quote: an analytic proposition gives no information about any matter of fact; only how we use certain symbols [»ayerAJ_1956]
Note: analytical truths such a 'p or not-p' is known by the rules of language; not via behavior

Subtopic: analytic as logic up

Quote: a subject is defined by its predicates; hence except for existence, every true statement is analytic
Quote: Kant's analytic truths and Leibniz's truths of reason are those that can not be false [»quinWV1_1951]
Quote: a proposition is true a priori when it is reducible to identical propositions; its reason always appears [»leibGW_1679]
Quote: the highest criterion for abstraction is that it should be an identity or reducible to identities [»leibGW_1679]
Quote: a theory of meaning must include sentences that owe their truth to those constants that give the theory its grip on structure; a logic [»daviD_1967]
Quote: empiricism--a sentence is either true or false if it is analytic (logical meaning) or tested by experiential evidence [»hempCG_1951]

Subtopic: logical truth up

Quote: the meanings of words such as if, and, not, or, all, etc. are connected
Quote: words such as "two" and "and", and rules such as "2+2=4" have many uses but not much of a meaning [»wittL_1939]
Quote: if A is the subject and B the predicate, B can be substituted for A without destroying the truth; i.e., primitive terms in B are also primitive terms in A [»leibGW_1686]
Quote: A and A are the first coincidents [»leibGW_1686]
Quote: 'p or not p' is logically true while 'no bachelor is married' is true by the nature of language; both analytical

Subtopic: logical contradiction up

Quote: mathematics is independent of the existence of material objects; mathematical existence means free from contradiction [»poinH_1908, OK]
Quote: those propositions are necessary whose contrary implies a contradiction [»leibGW_1679]
Quote: A and non-A are the first disparities; i.e., it is false that some A is B
Quote: if A is B, it is false that A is non-B

Subtopic: analytic as numeric up

Quote: Frege's concept of Number extends our knowledge even though it is analytic; like the seed produces the plant
Quote: Frege's definition of 1 does not presuppose, for its objective legitimacy, any matter of observed fact
Quote: Frege's definition of successor is objectively definite; something independent of the laws that govern the movements of our attention [»fregG_1884]
Quote: a universal characteristic strengthens the mind; as certain as arithmetic; avoids objections and emotional decisions [»leibGW_1679a]
Quote: analyze categories as mutipart numbers; e.g. 'Interval' is 2.3.10 where 2 is space, 3 is between, and 10 is whole [»leibGW_1666]

Subtopic: mathematics as analytic up

Quote: mathematical knowledge is virtually included in the definition of all things
Quote: it is absurd to say that "12*12=144 may be wrong" because agreement is the justification for this technique; calculation is based on agreement [»wittL_1939]
Quote: saying two pieces of chalk are the same could mean different things; but saying everything is the same as itself seems utterly unambiguous [»wittL_1939]
Quote: showed that arithmetic laws are analytic judgments (a priori) [»fregG_1884]
Quote: to see if arithmetic was analytic, Frege reduced ordering in a sequence (number) to logical consequences from the laws of thought [»fregG_1879]

Subtopic: analytic truth up

Quote: an analytic statement follows from intensions; a synthetic statement is verified with extensions [»sowaJF_1984]
Quote: a statement about a database is analytic if it follows from constraints and synthetic if need to query the database

Subtopic: concepts as analytical up

Quote: concepts can accurately represent man-made structures that originated as concepts; e.g., chess [»sowaJF_1984]

Subtopic: time, space, existence up

Quote: time and space are a priori; both are necessary conditions for the possibility of appearances [»kantI_1781, OK]
Quote: time is nothing but the form of our internal intuition; it has empirical reality but not absolute reality [»kantI_1781, OK]
Quote: analytic vs. synthetic by (not) asserting existence at particular times
Quote: except for God's existence, every existential proposition is synthetic; the subject need not exist

Subtopic: problems with analytic truth up

Quote: the dogmas of empiricism are ill-founded (i.e., analytic vs. synthetic and reductionism) [»quinWV1_1951]
Quote: analyze categories to their indefinable terms; Aristotle--we must not seek a definition of everything
Quote: measurement belongs to science while eternal truth belongs to faith; e.g., Ptolemy's astronomy vs. Plato's philosophy

Related Topics up

Group: formalism   (9 topics, 478 quotes)
Group: philosophy of mathematics   (11 topics, 330 quotes)
Group: philosophy of science   (10 topics, 406 quotes)

Topic: empirical truth (47 items)
Topic: mathematical proof (23 items)
Topic: mathematics as a formal system (30 items)
Topic: necessary truth (25 items)
Topic: number and arithmetic as part of language (30 items)
Topic: object and value equivalence (60 items)
Topic: problems with analytic truth (20 items)
Topic: rules (43 items)
Topic: sentences, propositions, and truth (23 items)
Topic: set definition by extension or intension (18 items)
Topic: what is a number (55 items)
Topic: what is truth
(67 items)

Updated barberCB 2/06
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