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]

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]

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

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]

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

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

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]

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]

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

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

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

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