These comments are reflections on Gila Sher’s talk in the Reimagining Carnap series held on 18th of Feb. The talk aimed at identifying similarities, differences in Carnap and Quine’s epistemologies and put them in context of contemporary meta-philosophy, philo. of maths. and, epistemology. Sher framed the epistemological concerns in context of the “two requirements for knowledge”: freedom requirements and constrains. Constrains on knowledge comes from how the world is and also from biological, psychological and perhaps even social constrains. While freedom and choices in having knowledge both in Carnap and Quine comes from their versions of pragmatisms about choices of frameworks, languages etc. The freedom requirement seems more like a human specific requirement as it is not clear whether any non-human animal choose their frameworks etc. – in other words, this freedom requirement is a requirement for constructed knowledge systems contra. Intuitive or common sense sort of understanding of the world possessed by all animals and insects1.
The discussion then turned to Carnap’s science, meta-science distinction was made as the former containing both the analytic parts and synthetics elements and in which there is no room for talk of true or false analytic systems, which are decided only on pragmatic grounds. The claim that Sher wishes to make here regarding the formal systems is that “the world has formal features” and therefore which formal systems our theories and languages have cannot be merely pragmatic but a question of true or false. And if I remember correctly, Sher also mentioned that given this is the case, what mathematicians and logicians study are true systems, or they try to find true systems. But leaving aside this later claim about what mathematician study and a related interesting question from history of mathematics between relation of physical questions and mathematical innovations, here I will only focus on whether it is correct to say that for Carnap the “world has no formal features”. But first, to make the question clearer I will only focus on specific aspects of the world that particular sciences study, rather than a meta-claim about the whole world.
Does space itself have features of formal geometry, and therefore is there a matter of fact about whether it is T/F that the space is non-Euclidean or Euclidean? Carnap in his Introductory Remarks for the English edition of Reichenbach’s The Philosophy of Space & Time distinguishes between “pure geometry” and “physical geometry” and says that
The statements of pure geometry hold logically, but they deal only with abstract structures and say nothing about physical space. Physical geometry describes the structure of physical space; it is a part of physics. The validity of its statements is to be established empirically—as it has to be in any other part of physics—after rules for measuring the magnitudes involved, especially length, have been stated.
The contrast here is between statements dealing with structures that are either logical or are empirical. For Carnap, that is a contrast between L-Truths (sentences which are true in all models given the L-rules and axioms of the system) and empirical or factual F-True sentences (true in some models and which require correspondence C-rules for empirical interpretation). Physical formal structures, in this case physical geometry, are not “logical” but “empirical” in this sense, as emphasized by the importance of “rules for measuring the magnitudes involved, especially length”. And when one accepts an empirical theory or scientific language (something done pragmatically, in broad sense, and not semantically where the notion or logical/empirical are relevant) we accept the theory as a whole. Therefore, we do accept that the “formal structure” or geometry as an empirically accepted matter. The confusion that Carnap does not accept “formal features” of this world (or at least clearly defined aspects of it) probably emerges by appreciating that the analytic/synthetic distinction for him is a semantic distinction and not an epistemic one – i.e. it not regarding how theories and languages actually interact with the world in its use – including how they are accepted, which is done holistically2. In this sense then it is perhaps impossible to talk of “formal feature of world” but only “features of world expressed mathematically” or something along those lines.
During the Q&A, in response to my question Sher also made some remarks about philosophical language being akin to scientific language, and hence in such philosophical language one can talk about general issues like of “the world”. This made me think about the distinct kinds of outlook about science and philosophy continuum Carnap and Quine held, Quine for example believed philosophy to deal with distinct kind of questions than from science – distinct by the level of generality, if not by content. He gave the study of “causation” and “relations” as examples of philosophical inquiry that contributes to science. While for Carnap philosophy does not have its own domain of questions, even by level of abstraction (at least not in Quine’s sense). For Carnap, philosophy also participates in explication and also in clarification and analysis of particular theories and languages and not language independent inquiries even about “causations” or “relations” – either in formal or in empirical domain.
Another participant in the talk asked about the possibility of pseudo-questions in Quine. That made me recall Quine calling the questions “why the universe started” as being a pseudo-question in his BBC interview. The reason for calling it a pseudo-question was that there are no conceivable answers to the problem. This is different from the kind of pseudo-question that emerge from language external questions – questions about “realism” for example. Noam also used Quine like reason for calling questions like “what is it like to be a bat” nonsensical. It would be interesting to investigate whether these actually are identical reasons of calling something a pseudo-question framed differently, or if not, then what other criteria are there are.
1. Povinelli, Daniel, Folk Physics for Apes: The Chimpanzee’s theory of how the world works (Oxford, 2003; online edn, Oxford Academic, 1 Apr. 2010), https://doi.org/10.1093/acprof:oso/9780198572190.001.0001, accessed 12 Feb. 2026.
2. Section 6.6 of Bentley J, Uebel T. On Quine’s Epistemological Objection to Carnap’s Analyticity. In: Richardson A, Tuboly AT, eds. Interpreting Carnap: Critical Essays. Cambridge University Press; 2024:106-126.
