3 ;;Quote: Begriffschrift introduced truth-functional propositional calculus, functions instead of subject/predicate, quantification, derivational forms, and a definition of sequence

5 ;;Quote: to see if arithmetic was analytic, Frege reduced ordering in a sequence (number) to logical consequences from the laws of thought

5+;;Quote: Frege developed concept writing to prevent gaps in a chain of inferences; found that language and intuition were inadequate

6 ;;Quote: Frege's ideography will unify the formula languages and extend them to new fields

6+;;Quote: the signs of arithmetic, geometry, and chemistry realized Leibniz's idea of a universal characteristic; the original idea was too gigantic

7 ;;Quote: replace the concepts of subject and predicate with argument and function respectively

7+;;Quote: the meanings of words such as if, and, not, or, all, etc. are connected

12 ;;Quote: when the consequences of two judgments are the same, their conceptual content is what is the same in both

12 ;;Quote: Frege does not use subject/predicate because it is part of the interaction between speaker and listener

12+;;Quote: Frege only considers that which influences the consequences of a judgment, i.e., its affirmation or denial

13 ;;Quote: concept writing provides symbols for implication and negation

15 ;;Quote: concept writing has a format for representing a derivation; e.g., (B->A and B) implies A

17 ;;Quote: Frege only uses detachment to infer consequences; other modes of inference are equivalent

21 ;;Quote: represent what does not change by a function and represent what changes by the function's arguments

22 ;;Quote: the distinction between function and argument is arbitrary

23 ;;Quote: use function notation to indicate a property of an object, a result of a procedure, or a relationship between objects

24 ;;Quote: the function of an argument can itself be regarded as an argument; more general than the concept of function in analysis

24 ;;Quote: universal qualification by indicating that a function is a fact for any replacement of a sign

25 ;;Quote: universal qualification needs to specify its scope

27 ;;Quote: form existential qualification out of negation and universal qualification

28 ;;Quote: need a meta language for an ideography in order to define its basis

28 ;;Quote: a small number of laws and rules can include the content of all the laws, albeit in an undeveloped state

28+;;Quote: derive complex judgments from simpler ones; clarifies relationships

29 ;;Quote: since the number of laws is boundless, need to find a basic set of laws that generates the rest; not unique

29 ;;Quote: two of Frege's basic laws are excluded middle and reduction of implication; substitution rules are unstated

50 ;;Quote: Frege's rule V allows substitution of equivalents

55 ;;Quote: by pure thought can derive propositions about sequences that far surpass in generality those derived by intuition or the senses

55 ;;Quote: use definitions to simplify a derivation; does not change the content of a proposition

57 ;;Quote: Frege defines sequence through hereditary properties that hold for all remaining elements of a sequence