Matthias Schirn - Academia.edu (original) (raw)
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Papers by Matthias Schirn
Acta Analytica, Jan 10, 2024
In this essay, I critically analyze Wittgenstein's dispensation with " = " in a correct concept-s... more In this essay, I critically analyze Wittgenstein's dispensation with " = " in a correct concept-script. I argue inter alia (a) that in the Tractatus the alleged pseudo-character of sentences containing " = " or =-sentences remains largely unexplained and propose how it could be explained; (b) that at least in some cases of replacing =-sentences with equivalent identity-sign free sentences the use of the notion of a translation seems inappropiate; (c) that in the Tractatus it remains unclear how identity of the object as that which is expressed by identity of the sign should be understood specifically; (d) that there are =-sentences which have no obvious equivalent in Wittgenstein's novel notation; (e) that Wittgenstein's adherence to (non-relational) identity, although he dispenses with " = ", is probably motivated by his desire to ensure that the expressive power of an identity-sign free concept-script of first-order is on a par with standard first-order logic containing " = ". In the concluding section, I critically discuss some claims in Lampert and Säbel (The Review of Symbolic Logic, 14, 1-21, 2021) and defend Wehmeier's account of pseudo-sentences in the Tractatus (2012) against the objections they raise.
Theoria-revista De Teoria Historia Y Fundamentos De La Ciencia, Mar 1, 1999
In this article, I discuss some important aspects of Frege's treatment of non-extensi... more In this article, I discuss some important aspects of Frege's treatment of non-extensional contexts. I focus on the analysis of belief sentences and of oratio obliqua. In the first part, I describe two types of theory within Fregean semantics and assess the analyses of non-extensional sentences of first and of second evel which can be carried out in the theories ofboth types. In the second part, I examine to what extent one can establish an infinite hierarchy of indirect senses. In the third and final part, I examine Frege's principle of substitutivity salva veritate of coreferential terms. I conclude with critica observations on articles of Tyler Burge and Jaakko Hintikka which deal with this principle.
... that the chief difficulty for everyone who wishes to un-derstand Hilbert’s conception of fini... more ... that the chief difficulty for everyone who wishes to un-derstand Hilbert’s conception of finitist mathematics is this: to specify the sense of the provability of general statements about the natural numbers without presupposing infinite totalities. Tait further argued that all finitist reasoning is essentially primitive re-cursive. In our paper, we attempt to show that his thesis “The finitist functions are precisely the primitive recursive functions ” is disputable and that another, likewise defended by him, is unten-able. The second thesis is that the finitist theorems are precisely those Π0 1-sentences that can be proved in (QF-IA).
DOAJ (DOAJ: Directory of Open Access Journals), Oct 1, 2010
Allgemeine Zeitschrift für Philosophie (AZP)
Reports Math. Log., 2005
... that the chief difficulty for everyone who wishes to un-derstand Hilbert’s conception of fini... more ... that the chief difficulty for everyone who wishes to un-derstand Hilbert’s conception of finitist mathematics is this: to specify the sense of the provability of general statements about the natural numbers without presupposing infinite totalities. Tait further argued that all finitist reasoning is essentially primitive re-cursive. In our paper, we attempt to show that his thesis “The finitist functions are precisely the primitive recursive functions ” is disputable and that another, likewise defended by him, is unten-able. The second thesis is that the finitist theorems are precisely those Π0 1-sentences that can be proved in (QF-IA).
Fregesche Variationen, 2020
Theoria-revista De Teoria Historia Y Fundamentos De La Ciencia, 1999
In this article, I discuss some important aspects of Frege's treatment of non-extensional con... more In this article, I discuss some important aspects of Frege's treatment of non-extensional contexts. I focus on the analysis of belief sentences and of oratio obliqua. In the first part, I describe two types of theory within Fregean semantics and assess the analyses of non-extensional sentences of first and of second evel which can be carried out in the theories ofboth types. In the second part, I examine to what extent one can establish an infinite hierarchy of indirect senses. In the third and final part, I examine Frege's principle of substitutivity salva veritate of coreferential terms. I conclude with critica observations on articles of Tyler Burge and Jaakko Hintikka which deal with this principle.
The British Journal for the Philosophy of Science, Dec 1, 1981
tained that the chief difficulty for everyone who wishes to understand Hilbert’s conception of fi... more tained that the chief difficulty for everyone who wishes to understand Hilbert’s conception of finitist mathematics is this: to specify the sense of the provability of general statements about the natural numbers without presupposing infinite totalities. Tait further argued that all finitist reasoning is essentially primitive recursive. In our paper, we attempt to show that his thesis “The finitist functions are precisely the primitive recursive functions” is disputable and that another, likewise defended by him, is untenable. The second thesis is that the finitist theorems are precisely those Π1-sentences that can be proved in (QF-IA). . 1 Tait’s interpretation of finitism In his influential essay ‘Finitism’ (1981), W.W. Tait set himself the task (a) of explicating the notion of finitism by explaining a sense in which one can prove general statements about the natural numbers without assuming
Synthese
In this article, I try to shed new light on Frege’s envisaged definitional introduction of real a... more In this article, I try to shed new light on Frege’s envisaged definitional introduction of real and complex numbers in Die Grundlagen der Arithmetik (1884) and the status of cross-sortal identity claims with side glances at Grundgesetze der Arithmetik (vol. I 1893, vol. II 1903). As far as I can see, this topic has not yet been discussed in the context of Grundlagen. I show why Frege’s strategy in the case of the projected definitions of real and complex numbers in Grundlagen is modelled on his definitional introduction of cardinal numbers in two steps, tentatively via a contextual definition and finally and definitively via an explicit definition. I argue that the strategy leaves a few important questions open, in particular one relating to the status of the envisioned abstraction principles for the real and complex numbers and another concerning the proper handling of cross-sortal identity claims.
Frege: Importance and Legacy
teaches classical languages and literature at Sarah Lawrence College. She holds an AB from Dartmo... more teaches classical languages and literature at Sarah Lawrence College. She holds an AB from Dartmouth College and a PhD in classical philology from Yale University. Her publications include Solon the Singer: Politics and Poetics (Rowman & Littlefield, 1993) as well as articles on the poetics of metaphor in Homeric epic poetry. Her new book on the critique of rage in ancient Greek myth is forthcoming from Yale University Press. For their suggestions and advice regarding this translation, she is extremely grateful to Ann Lauinger of Sarah Lawrence College and to Transference's editor David Kutzko and the anonymous referee.
Grazer Philosophische Studien, 1985
Acta Analytica, Jan 10, 2024
In this essay, I critically analyze Wittgenstein's dispensation with " = " in a correct concept-s... more In this essay, I critically analyze Wittgenstein's dispensation with " = " in a correct concept-script. I argue inter alia (a) that in the Tractatus the alleged pseudo-character of sentences containing " = " or =-sentences remains largely unexplained and propose how it could be explained; (b) that at least in some cases of replacing =-sentences with equivalent identity-sign free sentences the use of the notion of a translation seems inappropiate; (c) that in the Tractatus it remains unclear how identity of the object as that which is expressed by identity of the sign should be understood specifically; (d) that there are =-sentences which have no obvious equivalent in Wittgenstein's novel notation; (e) that Wittgenstein's adherence to (non-relational) identity, although he dispenses with " = ", is probably motivated by his desire to ensure that the expressive power of an identity-sign free concept-script of first-order is on a par with standard first-order logic containing " = ". In the concluding section, I critically discuss some claims in Lampert and Säbel (The Review of Symbolic Logic, 14, 1-21, 2021) and defend Wehmeier's account of pseudo-sentences in the Tractatus (2012) against the objections they raise.
Theoria-revista De Teoria Historia Y Fundamentos De La Ciencia, Mar 1, 1999
In this article, I discuss some important aspects of Frege's treatment of non-extensi... more In this article, I discuss some important aspects of Frege's treatment of non-extensional contexts. I focus on the analysis of belief sentences and of oratio obliqua. In the first part, I describe two types of theory within Fregean semantics and assess the analyses of non-extensional sentences of first and of second evel which can be carried out in the theories ofboth types. In the second part, I examine to what extent one can establish an infinite hierarchy of indirect senses. In the third and final part, I examine Frege's principle of substitutivity salva veritate of coreferential terms. I conclude with critica observations on articles of Tyler Burge and Jaakko Hintikka which deal with this principle.
... that the chief difficulty for everyone who wishes to un-derstand Hilbert’s conception of fini... more ... that the chief difficulty for everyone who wishes to un-derstand Hilbert’s conception of finitist mathematics is this: to specify the sense of the provability of general statements about the natural numbers without presupposing infinite totalities. Tait further argued that all finitist reasoning is essentially primitive re-cursive. In our paper, we attempt to show that his thesis “The finitist functions are precisely the primitive recursive functions ” is disputable and that another, likewise defended by him, is unten-able. The second thesis is that the finitist theorems are precisely those Π0 1-sentences that can be proved in (QF-IA).
DOAJ (DOAJ: Directory of Open Access Journals), Oct 1, 2010
Allgemeine Zeitschrift für Philosophie (AZP)
Reports Math. Log., 2005
... that the chief difficulty for everyone who wishes to un-derstand Hilbert’s conception of fini... more ... that the chief difficulty for everyone who wishes to un-derstand Hilbert’s conception of finitist mathematics is this: to specify the sense of the provability of general statements about the natural numbers without presupposing infinite totalities. Tait further argued that all finitist reasoning is essentially primitive re-cursive. In our paper, we attempt to show that his thesis “The finitist functions are precisely the primitive recursive functions ” is disputable and that another, likewise defended by him, is unten-able. The second thesis is that the finitist theorems are precisely those Π0 1-sentences that can be proved in (QF-IA).
Fregesche Variationen, 2020
Theoria-revista De Teoria Historia Y Fundamentos De La Ciencia, 1999
In this article, I discuss some important aspects of Frege's treatment of non-extensional con... more In this article, I discuss some important aspects of Frege's treatment of non-extensional contexts. I focus on the analysis of belief sentences and of oratio obliqua. In the first part, I describe two types of theory within Fregean semantics and assess the analyses of non-extensional sentences of first and of second evel which can be carried out in the theories ofboth types. In the second part, I examine to what extent one can establish an infinite hierarchy of indirect senses. In the third and final part, I examine Frege's principle of substitutivity salva veritate of coreferential terms. I conclude with critica observations on articles of Tyler Burge and Jaakko Hintikka which deal with this principle.
The British Journal for the Philosophy of Science, Dec 1, 1981
tained that the chief difficulty for everyone who wishes to understand Hilbert’s conception of fi... more tained that the chief difficulty for everyone who wishes to understand Hilbert’s conception of finitist mathematics is this: to specify the sense of the provability of general statements about the natural numbers without presupposing infinite totalities. Tait further argued that all finitist reasoning is essentially primitive recursive. In our paper, we attempt to show that his thesis “The finitist functions are precisely the primitive recursive functions” is disputable and that another, likewise defended by him, is untenable. The second thesis is that the finitist theorems are precisely those Π1-sentences that can be proved in (QF-IA). . 1 Tait’s interpretation of finitism In his influential essay ‘Finitism’ (1981), W.W. Tait set himself the task (a) of explicating the notion of finitism by explaining a sense in which one can prove general statements about the natural numbers without assuming
Synthese
In this article, I try to shed new light on Frege’s envisaged definitional introduction of real a... more In this article, I try to shed new light on Frege’s envisaged definitional introduction of real and complex numbers in Die Grundlagen der Arithmetik (1884) and the status of cross-sortal identity claims with side glances at Grundgesetze der Arithmetik (vol. I 1893, vol. II 1903). As far as I can see, this topic has not yet been discussed in the context of Grundlagen. I show why Frege’s strategy in the case of the projected definitions of real and complex numbers in Grundlagen is modelled on his definitional introduction of cardinal numbers in two steps, tentatively via a contextual definition and finally and definitively via an explicit definition. I argue that the strategy leaves a few important questions open, in particular one relating to the status of the envisioned abstraction principles for the real and complex numbers and another concerning the proper handling of cross-sortal identity claims.
Frege: Importance and Legacy
teaches classical languages and literature at Sarah Lawrence College. She holds an AB from Dartmo... more teaches classical languages and literature at Sarah Lawrence College. She holds an AB from Dartmouth College and a PhD in classical philology from Yale University. Her publications include Solon the Singer: Politics and Poetics (Rowman & Littlefield, 1993) as well as articles on the poetics of metaphor in Homeric epic poetry. Her new book on the critique of rage in ancient Greek myth is forthcoming from Yale University Press. For their suggestions and advice regarding this translation, she is extremely grateful to Ann Lauinger of Sarah Lawrence College and to Transference's editor David Kutzko and the anonymous referee.
Grazer Philosophische Studien, 1985