On theory dependence of truth in measurement

Measurement results are stated in terms of sentences ascribing measured values, as obtained via measurement processes, to measurands, as defined by measuring agents. Since both the definition of the measurands and the characterization of the processes depend on models constructed on the basis of relevant theories, the issue arises of the theory dependence of the truth of those sentences. This paper aims at assessing the question by introducing suitable distinctions about the sense and reference of the terms used to refer to individual and general quantities, in a framework where measurement is construed as an agent-dependent, model-based, purpose-driven activity.

Kripke, Perry eta “ni”

Artikulu honetan, lehen pertsonako “ni” izenordainari buruz Kripkek dituenikuskerez ari naiz. Nire asmoa da erakustea Saul Kripkeren geroagoko ikuskera nola urruntzenden Naming and Necessityn esplikatu zituenetatik, eta John Perryren azalpenarekinalderatzea; gertuago dago Perryrena Kripkeren hasierako baieztapenetatik. Kripkeren biartikulu eztabaidatzen ditut, “Frege’s Theory of Sense and Reference” eta “The First Person”.Hasteko, argudiatzen dut Fregez egiten duen interpretazioa ez dela egokia, eta gero erakustendut Kripkeren beraren ikuskera nola eratortzen den interpretazio horretatik. Kripkerenikuskera Perryrenarekin alderatzen dut, batez ere “Frege erakusleez” (1977 [2018]) laneanaurkezten duenarekin. Kripkeren proposamenak bi suposizio ditu oinarrian: Fregeren ikuskerainterpretatzean, Kripkek ez du arazorik ikusten Pentsamendu komunikaezinetan, eta kartesiarnira jotzen du berak “ni”ren erabilerak esplikatzean. Bi suposizio horiek ez ditu egiten Namingand Necessityn, eta ez dira beharrezkoak “ni” lehen pertsonako izenordainaren azalpensemantikorako.

Hegel, Peirce and us

Historically, our theme is situated within the triangle of three of Kant's students: Hegel (1770-1831), Bolzano (1781-1848) and Peirce (1839-1914). All three wanted to change Kant's strict separation of philosophy and science by developing a new conception of logic. Bolzano inaugurated the so-called linguistic turn of philosophy which became the guiding principle of all analytical philosophy (Dummett, 2014) and he opposed Hegel’s unity of concept and object of knowledge. Charles Peirce took a middle position, a position that is expressed in his so-called Pragmatic Maxim (Peirce, CP 5.3). Taken together we might say that a universal principle of complementarity of meaning and reference, or of meaning and information (in the sense of Shannon) finds its origin in Post-Kantian philosophy. We encounter here the very same approach of principled thinking endorsed by Einstein in physics (special theory of relativity) or by the formal axiomatic approach in mathematics (Hilbert)! Key Words: Bolzano, Hegel, Peirce; Complementarity of sense and reference; Geometry from Euclid to Einstein; Hilbert.

Sense and Reference of Pictures

John Hyman insists that Frege-style cases for depiction show that any sound theory of depiction must distinguish between the ‘sense’ and the ‘reference’ of a picture. I argue that this rests on a mistake. Making sense of the cases does not require the distinction.

WHY SHOULD WE SPEAK ABOUT A COMPLEMENTARITY OF SENSE AND REFERENCE?

Until around 1800, Western philosophy believed that there were two types of conception in the world: the mental and the physical. Hence the extensive discussions about the analytical and synthetic knowledge that dominated the philosophy of Kant, the greatest Enlightenment philosopher. However, from the Peircean studies, the discussion about the conceptions has expanded, giving rise to the complementarity, which currently addresses the conceptions of extension and intensionof logic and philosophy. In the educational context it is often claimed that mathematics is a language, since it provides both a means of communication and a substantiation of our thoughts. As a result, mathematical fluidity is now considered the most important. From this perspective, the pedagogical principles underlying mathematics teaching become similar to those used in language teaching. But mathematics is not mere language. Language is a wonderful instrument of the human spirit, yet it serves logic, poetics, and rhetoric far better than mathematics. Thus, this article aims to show that the approach of elementary mathematics education must consist in teaching to read a term beyond its correspondence between letters and sounds, and also to permit the understanding how a skill set can be worked completely in abstract in relation to content. The semiotic methodology is utilized as input to analyze what is really the mathematics.

Solving the Identity Problems

I return to the problems concerning identity that plagued Frege’s Begriffsschrift and eventually led to the theory of sense and reference. I claim that within a flexible theory of the truth conditions, what I call the “reflexive-referential” theory, there is a common sense solution.

Sense and Denotation: The Theory

I describe Frege’s theory of sense and denotation. (I use ‘denotation’ as a translation for ‘Bedeutung’ in discussing this theory.) I consider motivations and problems, especially for his treatment of the sense and reference of concept expressions, and whether a regress is involved in senses for names. I consider the relation of the new scheme to the scheme of the Begriiffsschrift.

Frege's Detour

I argue that Frege’s treatment of propositional attitudes in “On Sense and Reference” put the philosophy of language on a detour. His doctrine of “indirect reference” reflected and reinforced the view that beliefs, desires, etc. consist in having relations to propositions. According to this doctrine expressions in embedded sentences in indirect discourse and propositional attitude reports do refer as they do when unembedded, but instead refer to their ordinary senses, so sentences refer to Thoughts, Frege’s version of what are now callled general or qualitative propositions. Davidson call this move abandoning “semantic innocence” which is the view that such embedded sentences work as they usually do. I agree with Davidson, that semantic innocence should not be abandonned. I argue that such cognitive states have truth-conditions in virtue of their causal and informational roles, which can be encoded in a variety of ways for different purposes, and provide a better explanation of the considerations that drove Frege to abandon innocence. I trace the problems I see to Frege’s abandonment of the framework of his early work, the Begriffsschrift. I argue that by adding the levels of senses and Thoughts to his Begriffsschriftframework, and retaining “circumstances” as the referents of sentences containing singular terms, Frege could have avoided the doctrine of indirect reference, and philosophy could have taken a different path.