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ThesaHelp:
references e-f
Topic:
history of mathematics
Topic:
logic
Topic:
analytic truth
Topic:
number as a progression for counting and 1-1 relations
Group:
formalism
Topic:
natural language as a system
Topic:
mathematics as a formal system
Group:
function
Topic:
meaning by language as a whole
Group:
grammar
Topic:
natural language as communication
Topic:
sentences, propositions, and truth
Group:
parameters
Topic:
change
Topic:
fundamental concepts such as type, attributes, relationships are all the same
Topic:
rules
Topic:
what is truth
Topic:
number as the extension of a class of equinumerous classes

#### Reference

Frege, G., Begriffschrift, a formula language, modeled upon that of arithmetic, for pure thought, Halle, 1879. Google

#### Other Reference

p. 5-82 in J. van Heijenoort, From Frege to Godel, Cambridge Massachusetts: Harvard University Press, 1967, translated by Stefan Bauer- Mengelberg

Quotations
 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

Related Topics

ThesaHelp: references e-f (168 items)
Topic: history of mathematics (57 items)
Topic: logic (84 items)
Topic: analytic truth (51 items)
Topic: number as a progression for counting and 1-1 relations (22 items)
Group: formalism   (9 topics, 473 quotes)
Topic: natural language as a system (43 items)
Topic: mathematics as a formal system (30 items)
Group: function   (12 topics, 232 quotes)
Topic: meaning by language as a whole (26 items)
Group: grammar   (8 topics, 180 quotes)
Topic: natural language as communication (29 items)
Topic: sentences, propositions, and truth (23 items)
Group: parameters   (10 topics, 145 quotes)
Topic: change (28 items)
Topic: fundamental concepts such as type, attributes, relationships are all the same (37 items)
Topic: rules (43 items)
Topic: what is truth (66 items)
Topic: number as the extension of a class of equinumerous classes (23 items)

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