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Frege structures for partial applicative theories

1999
*
Journal of Logic and Computation
*

Due to strictness problems, usually the syntactical definition of

doi:10.1093/logcom/9.5.683
fatcat:4htbjbkr7zflvp3a4735xkrvzi
*Frege**structures*is conceived as a truth*theory**for*total*applicative**theories*. ... To investigate*Frege**structures*in a*partial*framework we can follow two ways. First, simply by ignoring undefinedness in the truth definition. Second, by introducing of a certain notion of pointer. ...*Frege**Structures**for**partial**applicative**theories*4.1 Strictness If we want to define*Frege**structures**for**partial**applicative**theories*, we get in trouble with possibly undefined terms. ...##
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Page 4730 of Mathematical Reviews Vol. , Issue 92i
[page]

1992
*
Mathematical Reviews
*

Three kinds of

*structures*called*Frege**structures*with inductively defined predicates,*Frege**structures*with proof objects, and proof*structures*are also introduced. ... These*structures*are obtained by generalizing certain aspects of RPT and they are all closely related to*Frege**structures*.” ...##
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FREGE'S CONSTRAINT AND THE NATURE OF FREGE'S FOUNDATIONAL PROGRAM

2018
*
The Review of Symbolic Logic
*

$), the requirement that a mathematical

doi:10.1017/s1755020318000278
fatcat:jp2gwmkn5femje6rw5s2nk32u4
*theory*be so outlined that it immediately allows explaining*for*its*applicability*. ... AbstractRecent discussions on Fregean and neo-Fregean foundations*for*arithmetic and real analysis pay much attention to what is called either '*Application*Constraint' ($AC$) or '*Frege*Constraint' ($FC ... objects, places in a*structure*; if they are taken to be univocally specified, they have to be taken to be elements of a particular system exemplifying, possibly*partially*, the*structure*of domains of ...##
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Page 8377 of Mathematical Reviews Vol. , Issue 2000m
[page]

2000
*
Mathematical Reviews
*

The paper under review is concerned with

*Frege**structures*as a truth*theory*over*applicative**theories*. ... Bunder (5-WLG; Wollongong) 03B General logic 2000m:03043 2000m:03042 03B40 03F03 68N18 Kahle, Reinhard (D-TBNG-I; Tiibingen)*Frege**structures**for**partial**applicative**theories*. (English summary) J. ...##
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Page 4711 of Mathematical Reviews Vol. , Issue 87i
[page]

1987
*
Mathematical Reviews
*

The paper is devoted to

*theories*with a*partial*predicate*for*truth (the idea of truth as a*partial*predicate comes from Kripke). ... Salvatore Guccione (Naples) Reinhardt, William N. (1-CO) 87i:03007 Some remarks on extending and interpreting*theories*with a*partial*predicate*for*truth. J. Philos. Logic 15 (1986), no. 2, 219-251. ...##
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Set Theory and Nominalization, Part I

1992
*
Journal of Logic and Computation
*

•

doi:10.1093/logcom/2.5.579
fatcat:mrzvivrh4jcs3kvsg2f2z2dx5y
*Frege**structures**Frege**structures*are not only solutions to the problem of model existence, but are also systems of set*theory*in their own right: they single out that part of Frege's*theory*which ... So in a*Frege**structure*, like in any (Fregean) calculus of functions and objects which has variable-binding (and*application*) through abstraction (resp.*application*) operators one can take functions into ... Set*theory*and nominalisation, Part I, p.26. Set*theory*and nominaIisation, Part II, p.22. The total order assumption, p. 10. A system at the cross-roads of functional and logic programming, p.36. ...##
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Frege's theory of types
[article]

2020
*
arXiv
*
pre-print

*Frege*did not endorse a semantic account of typing, unlike most type theorists who use different types

*for*booleans, natural numbers, products, etc. ...

*Frege*never explicitly advocated a doctrine of types like Russell, but a naive type

*theory*can be found in his concept-script in his 1893 Grundgesetze der Arithmetik. ... (Grundgesetze §4)

*Partial*saturation creates ambiguity in the interpretation of function

*application*and suggests that

*Frege*actually thinks of binary functions as unary functions from objects to unary ...

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Page 1486 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

proof

*theory*with*applications*to computation. ...*Structures*Comput. Sci. 7 (1997), no. 5, 445-452. ...##
###
Set Theory and Nominalization, Part II

1992
*
Journal of Logic and Computation
*

Hence we develop a type

doi:10.1093/logcom/2.6.687
fatcat:kpisjoietffs7e5cl2kchc7vqi
*theory*based on*Frege**structures*and use it as a*theory*of nominalisation. ...*Frege**structures*are more conclusive than a solution to domain equations and can be used as models*for*nominalisation. ... Firstly, Turner can prove at least as much in his*theory*as one can in a*theory*based on*Frege**structures*. ...##
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Our Knowledge of Numbers as Self-Subsistent Objects

2005
*
Dialectica
*

Although

doi:10.1111/j.1746-8361.2005.01024.x
fatcat:tjgwx72d45ae5muqpntgbxirya
*Frege*was undoubtedly concerned with both questions, a goal of the present paper is to argue that his success in securing the objectivity of arithmetic depends on a less contentious commitment ...*Frege*arithmetic and recovering N from a*Frege**structure*, rather than proceeding in the opposite direction by recovering a*Frege**structure*from N. ... ' of number -are recoverable from any model that contains a*Frege**structure*, where the model ·N, s, 0Ò associated with the*Frege**structure*·E, mÒ is defined (see Bell 1999 Bell , 1555 where PE is the ...##
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Page 3499 of Mathematical Reviews Vol. , Issue 84i
[page]

1984
*
Mathematical Reviews
*

The point

*structures*of Part I are strict*partial*orders (7,<), where T is nonempty. ...*Frege*is unable to elucidate what a function is. The price of accepting his*theory*is the view that sentences signify truth-values. ...##
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Page 24 of Mathematical Reviews Vol. , Issue 87a
[page]

1987
*
Mathematical Reviews
*

A model with signature S, also called an S-

*structure*, is given by specifying carrier sets A,*for*every s € ©,*partial*operations*for*every element of P and relations*for*every element of R. ... The treatment of Peirce’s*theory*of signs by introducing into the discussion an*application*of category*theory*is noteworthy. ...##
###
Reform of the construction of the number system with reference to Gottlob Frege

2007
*
ZDM: Mathematics Education
*

Concepts of quantity (ratio-scale) and interval-scale in comparative measurement

doi:10.1007/s11858-006-0003-2
fatcat:y3m5lshcq5cnvcelepwy5zyvi4
*theory*-going beyond*Frege*-show the way how the negative numbers can be ontologically committed and the operations of addition ... Steiner considered Frege's viewpoint of mathematics fundamentals, refined by Tarski's semantics, as suitable*for*math education. ... As already mentioned it would have been more consistent if*Frege*had demanded not only the*application*of numbers*for*measuring but also that the*application*of multiplication and addition*for*measuring ...##
###
Page 4020 of Mathematical Reviews Vol. 58, Issue 6
[page]

1979
*
Mathematical Reviews
*

He gives criteria

*for*two first-order sentences to represent the same scientific law (be nomologically equivalent) and*for*one*theory*to be a reduction of another. ... and triadic semantics in*Frege*. ...##
###
The Breadth of the Paradox

2015
*
Philosophia Mathematica
*

and Entailment" at the Moral Sciences Club, Cambridge University (May 2012) -"Axioms in

doi:10.1093/philmat/nkv038
fatcat:fvwwxbggsfbm5pnru4duw6pmu4
*Frege*" at the Grundgesetze conference, New York University (May 2012) -"Axioms and*Structure*in*Frege*" at the "The ... Analysis in*Frege*," CUNY Logic Workshop, September 2012 -"(*Frege*On) Axioms as Foundations" at the "What are Foundations and What are they*For*?" ...
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