Logical Constants and Arithmetical Forms

被引:0
作者
Speitel, Sebastian G. W. [1 ]
机构
[1] Univ Bonn, Inst Philosophy, Bonn, Germany
关键词
logical constants; logical form; criterion of logicality; formality; INVARIANCE;
D O I
10.12775/LLP.2023.012
中图分类号
B81 [逻辑学(论理学)];
学科分类号
010104 ; 010105 ;
摘要
This paper reflects on the limits of logical form set by a novel criterion of logicality proposed in (Bonnay and Speitel, 2021). The interest stems from the fact that the delineation of logical terms according to the criterion exceeds the boundaries of standard first-order logic. Among 'novel' logical terms is the quantifier "there are infinitely many". Since the structure of the natural numbers is categorically characterisable in a language including this quantifier we ask: does this imply that arithmetical forms have been reduced to logical forms? And, in general, what other conditions need to be satisfied for a form to qualify as "fully logical"? We survey answers to these questions.
引用
收藏
页码:495 / 510
页数:16
相关论文
共 26 条
  • [1] Logicality and invariance
    Bonnay, Denis
    [J]. BULLETIN OF SYMBOLIC LOGIC, 2008, 14 (01) : 29 - 68
  • [2] Invariance and Definability, with and without Equality
    Bonnay, Denis
    Engstrom, Fredrik
    [J]. NOTRE DAME JOURNAL OF FORMAL LOGIC, 2018, 59 (01) : 109 - 133
  • [3] Compositionality Solves Carnap's Problem
    Bonnay, Denis
    Westerstahl, Dag
    [J]. ERKENNTNIS, 2016, 81 (04) : 721 - 739
  • [4] Bonnay Denis, 2021, The Semantic Conception of Logic: Essays on Consequence, Invariance, and Meaning, P55
  • [5] Carnap Rudolf., 1943, Formalization of Logic
  • [6] Ebbinghaus H.-D., 2017, Model-Theoretic Logics, Perspectives in Logic, P25
  • [7] Feferman S., 1999, Notre Dame Journal of Formal Logic, V40, P31, DOI [10.1305/ndjfl/1039096304, DOI 10.1305/NDJFL/1039096304]
  • [8] Feferman S, 2015, SYNTH LIBR, V373, P19, DOI 10.1007/978-3-319-18362-6_2
  • [9] Set-theoretical Invariance Criteria for Logicality
    Feferman, Solomon
    [J]. NOTRE DAME JOURNAL OF FORMAL LOGIC, 2010, 51 (01) : 3 - 20
  • [10] Studies on logical closing.
    Gentzen, G
    [J]. MATHEMATISCHE ZEITSCHRIFT, 1935, 39 : 176 - 210