This special issue on general proof theory collects papers resulting from the conference on general proof theory held in November 2015 in Tübingen.

This paper develops a proof theory for logical forms of proofs in the case of monadic languages. Among the consequences are different kinds of generalization of proofs in various schematic proof systems. The results use suitable relations between logical properties of partial proof data and algebraic properties of corresponding sets of linear diophantine equations.

I see the question what it is that makes an inference valid and thereby gives a proof its epistemic power as the most fundamental problem of general proof theory. It has been surprisingly neglected in logic and philosophy of mathematics with two exceptions: Gentzen’s remarks about what justifies the rules of his system of natural deduction and proposals in the intuitionistic tradition about what a proof is. They are reviewed in the paper and I discuss to (...) what extent they succeed in answering what a proof is. Gentzen’s ideas are shown to give rise to a new notion of valid argument. At the end of the paper I summarize and briefly discuss an approach to the problem that I have proposed earlier. (shrink)

In this paper we introduce hypersequent-based frameworks for the modelling of defeasible reasoning by means of logic-based argumentation and the induced entailment relations. These structures are an extension of sequent-based argumentation frameworks, in which arguments and the attack relations among them are expressed not only by Gentzen-style sequents, but by more general expressions, called hypersequents. This generalization allows us to overcome some of the known weaknesses of logical argumentation frameworks and to prove several desirable properties of the entailments that (...) are induced by the extended frameworks. It also allows us to incorporate as the deductive base of our formalism some well-known logics, which lack cut-free sequent calculi, and so are not adequate for standard sequent-based argumentation. We show that hypersequent-based argumentation yields robust defeasible variants of these logics, with many desirable properties. (shrink)

Prawitz conjectured that the proof-theoretically valid logic is intuitionistic logic. Recent work on proof-theoretic validity has disproven this. In fact, it has been shown that proof-theoretic validity is not even closed under substitution. In this paper, we make a minor modification to the definition of proof-theoretic validity found in Prawitz’s 1973paper ‘Towards a foundation of a general proof theory’ and refined by Schroeder-Heister in ‘Validity concepts in proof-theoretic semantics’ (2006). We will call the (...) new notion generalized proof-theoretic validity and show that the logic of generalized proof-theoretic validity is intuitionistic logic. (shrink)

In this paper it is suggested to generalize our understanding of general (structural) proof theory and to consider it as a general theory of two kinds of derivations, namely proofs and dual proofs. The proposal is substantiated by (i) considerations on assertion, denial, and bi-lateralism, (ii) remarks on compositionality in proof-theoretic semantics, and (iii) comments on falsification and co-implication. The main formal result of the paper is a normal form theorem for the natural deduction proof (...) system N2Int of the bi-intuitionistic logic 2Int. The proof makes use of the faithful embedding of 2Int into intuitionistic logic with respect to validity and shows that conversions of dual proofs can be sidestepped. (shrink)

Bilateral proof systems, which provide rules for both affirming and denying sentences, have been prominent in the development of proof-theoretic semantics for classical logic in recent years. However, such systems provide a substantial amount of freedom in the formulation of the rules, and, as a result, a number of different sets of rules have been put forward as definitive of the meanings of the classical connectives. In this paper, I argue that a single general schema for bilateral (...) proof rules has a reasonable claim to inferentially articulating the core meaning of all of the classical connectives. I propose this schema in the context of a bilateral sequent calculus in which each connective is given exactly two rules: a rule for affirmation and a rule for denial. Positive and negative rules for all of the classical connectives are given by a single rule schema, harmony between these positive and negative rules is established at the schematic level by a pair of elimination theorems, and the truth-conditions for all of the classical connectives are read off at once from the schema itself. (shrink)

-/- !! For the latest and further elaborated Version of that Work, please see the more recent Trilogy"The Infinite Choice Barrier" (I-III) -/- This paper presents a formal critique of algorithmic cognition and develops what I call the Infinite Choice Barrier (ICB): a mathematically demonstrable boundary that no algorithmic system can cross. The argument is not empirical, it does not rest on engineering limitations or compute constraints. It rests on the symbolic closure of algorithmic systems. A finite symbol set Σ (...) and inference rule set R cannot generate novel primitives outside Σ,R. Accordingly, AGI — defined as an autonomous, algorithmic system capable of human-level general problem solving — is formally impossible. The proof does not deny the power of algorithms, but clarifies their boundary. Within that boundary, extraordinary advances are possible. Beyond it, they are not. (shrink)

The generality of a derivation is an equivalence relation on the set of occurrences of variables in its premises and conclusion such that two occurrences of the same variable are in this relation if and only if they must remain occurrences of the same variable in every generalization of the derivation. The variables in question are propositional or of another type. A generalization of the derivation consists in diversifying variables without changing the rules of inference. This paper examines in the (...) setting of categorial proof theory the conjecture that two derivations with the same premises and conclusions stand for the same proof if and only if they have the same generality. For that purpose generality is defined within a category whose arrows are equivalence relations on finite ordinals, where composition is rather complicated. Several examples are given of deductive systems of derivations covering fragments of logic, with the associated map into the category of equivalence relations of generality. This category is isomorphically represented in the category whose arrows are binary relations between finite ordinals, where composition is the usual simple composition of relations. This representation is related to a classical representation result of Richard Brauer. (shrink)

This paper is a mathematical consolidation of my papers on the impossibility of AGI. It presents a triangulated impossibility proof for Artificial General Intelligence (AGI), defined as an algorithmic system capable of solving a sufficiently broad class of human problems at human-level competence. Three formally independent but converging mathemati- cal arguments-based in computability theory, information theory, and algorithmic complexity- jointly demonstrate that AGI, as such, cannot exist. -/- This boundary, named the Infinite Choice Barrier (ICB), is neither technical (...) nor architectural. It is structural by its nature. It marks a categorical limitation on algorithmic cognition. -/- Philosophical groundwork and contextual development of the formal proof are explored in: Part I: AGI is Impossible - Here is The Proof Part II: AGI is Mathematically Impossible 2: When Entropy Returns (Both papers available on Philpapers) A third part is still to be finalized and will be uploaded, the formal part is already in this paper. (shrink)

The topic of identity of proofs was put on the agenda of general (or structural) proof theory at an early stage. The relevant question is: When are the differences between two distinct proofs (understood as linguistic entities, proof figures) of one and the same formula so inessential that it is justified to identify the two proofs? The paper addresses another question: When are the differences between two distinct formulas so inessential that these formulas admit of identical proofs? (...) The question appears to be especially natural if the idea of working with more than one kind of derivations is taken seriously. If a distinction is drawn between proofs and disproofs (or refutations) as primitive entities, it is quite conceivable that a proof of one formula amounts to a disproof of another formula, and vice versa. A notion of inherited identity of derivations is introduced for derivations in a cut-free sequent system for Almukdad and Nelson’s constructive paraconsistent logic N4 with strong negation. The notion is obtained by identifying sequent rules the application of which has no effect on the identity of derivations. Then the notion of inherited identity is used to define a bilateralist notion of synonymy between formulas, which is a relation drawing more fine-grained distinctions between formulas than strong equivalence. (shrink)

We further develop a recent new proof (by Greenberger, Horne, and Zeilinger—GHZ) that local deterministic hidden-variable theories are inconsistent with certain strict correlations predicted by quantum mechanics. First, we generalize GHZ's proof so that it applies to factorable stochastic theories, theories in which apparatus hidden variables are causally relevant to measurement results, and theories in which the hidden variables evolve indeterministically prior to the particle-apparatus interactions. Then we adopt a more general measure-theoretic approach which requires that GHZ's (...) argument be modified in order to produce a valid proof. Finally, we motivate our more general proof's assumptions in a somewhat different way from previous authors in order to strengthen the implications of our proof as much as possible. After developing GHZ's proof along these lines, we then consider the analogue, for our proof, of Bohr's reply to the EPR argument, and conclude (pace GHZ) that in at least one respect (viz. that of most concern to Bohr) the proof is no more powerful than Bell's. Nevertheless, we point out some new advantages of our proof over Bell's, and over other algebraic proofs of nonlocality. And we conclude by giving a modified version of our proof that, like Bell's, does not rely on experimentally unrealizable strict correlations, but still leads to a testable “quasi-algebraic” locality inequality.“... to admit things not visible to the gross creatures that we are is, in my opinion, to show a decent humility, and not just a lamentable addiction to metaphysics.”J. S. Bell. (shrink)

This paper studies the notions of conceptual grounding and conceptual explanation (which includes the notion of mathematical explanation), with an aim of clarifying the links between them. On the one hand, it analyses complex examples of these two notions that bring to the fore features that are easily overlooked otherwise. On the other hand, it provides a formal framework for modeling both conceptual grounding and conceptual explanation, based on the concept of proof. Inspiration and analogies are drawn with the (...) recent research in metaphysics on the pair metaphysical grounding–metaphysical explanation, and especially with the literature in philosophy of science on the pair causality-causal explanation. (shrink)

This is a tripartite work. The first part is a brief discussion of what it is to be a logical constant, rejecting a view that allows a particular self-referential “constant” $$\bullet $$ ∙ to be such a thing in favour of a view that leads to strong normalisation results. The second part is a commentary on the flattened version of Modus Ponens, and its relationship with rules of type theory. The third part is a commentary on work (joint with Nissim (...) Francez) on “general elimination rules” and harmony, with a retraction of one of the main ideas of that work, i.e. the use of “flattened” general elimination rules for situations with discharge of assumptions. We begin with some general background on general elimination rules. (shrink)

We prove an institutional version of A. Robinson ’s Consistency Theorem. This result is then appliedto the institution of many-sorted first-order predicate logic and to two of its variations, infinitary and partial, obtaining very general syntactic criteria sufficient for a signature square in order to satisfy the Robinson consistency and Craig interpolation properties.

Social Announcement Logic (SAL) is a framework for reasoning about belief diffusion in social networks, where information propagates locally based on an underlying follower structure. A key challenge in this area is to logically characterize what agents can achieve through communication, a problem often addressed using powerful but complex arbitrary announcement operators. Previous work on SAL with such operators resulted in infinitary axiomatizations, leaving the question of a finitary system open. This paper solves this open problem by presenting the first (...) finitary, sound, and weakly complete axiomatization for a Social Announcement Logic with an arbitrary sincere announcement operator. Our central technical innovation is a novel, two-stage model transformation technique used to prove the soundness of the crucial discharge rule for arbitrary announcements. This method avoids the complex necessity-form techniques common in the literature on Arbitrary Public Announcement Logic, resulting in a more direct, Henkin-style completeness proof. Overall, the work establishes a robust and computable proof-theoretic foundation for reasoning about belief dynamics in social networks. (shrink)

The paper is a continuation of another paper published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. The (...) relevant mathematical structure is Hilbert arithmetic in a wide sense, in the framework of which Hilbert arithmetic in a narrow sense and the qubit Hilbert space are dual to each other. A few cases involving set theory are possible: (1) only within the case “n=3” and implicitly, within any next level of “n” in Fermat’s equation; (2) the identification of the case “n=3” and the general case utilizing the axiom of choice rather than the axiom of induction. If the former is the case, the application of set theory and arithmetic can remain disjunctively divided: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. If the latter is the case, the proof is thoroughly within set theory. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided in both cases. The idea of “arithmetic mechanics” is sketched: it might deduce the basic physical dimensions of mechanics (mass, time, distance) from the axioms of arithmetic after a relevant generalization, Furthermore, a future Part III of the paper is suggested: FLT by mediation of Hilbert arithmetic in a wide sense can be considered as another expression of Gleason’s theorem in quantum mechanics: the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information. The availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent to the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem. (shrink)

This paper re-evaluates the formative year of quantum mechanics—from Heisenberg’s first paper on matrix mechanics to Schrödinger’s equivalence proof—by focusing on the role of radiation in the emerging theory. We argue that the radiation problem played a key role in early quantum mechanics, a role that has not been taken into account in the standard histories. Radiation was perceived by the main protagonists of matrix and wave mechanics as a central lacuna in these emerging theories and continued to contribute (...) to the theoretical development and conceptual clarification of quantum mechanics. Studying the interplay between quantum mechanics and radiation, the paper provides an account of (a) how quantum mechanics was able to connect to its empirical basis in spectroscopy and (b) how Schrödinger’s equivalence proof emerged from his explorative calculations on the emission of radiation. (shrink)

Midway through How to Do Things With Words, J.L. Austin’s announces a “fresh start” in his efforts to characterize the ways in which speech is action, and introduces a new conceptual framework from the one he has been using up to that point. Against a common reading that portrays this move as simply abandoning the framework so far developed, Marina Sbisà contends that the text takes the argumentative form of a proof by contradiction, such that the initial framework plays (...) an instrumental role as part of a proof in favour of the subsequent one. Despite agreeing with Sbisà’s broad instrumentalist approach, we argue that her regimentation of Austin’s narrative into a proof by contradiction ultimately fails - both as a proof and as an interpretation of Austin. Instead, we suggest that a better way of interpreting the peculiar structure of How to Do Things With Words is as a pedagogical exercise whose point is to bring a concealed alternative into view in a manner that also explains its initial concealment, and that this approach provides richer resources for supporting Sbisà’s own conventionalist understanding of illocution than that afforded by reading the text as a proof by contradiction. (shrink)

Mathematical structuralism is deeply connected with Hilbert and Bernays’s proof theory and its programmatic aim to ensure the consistency of all of mathematics. That aim was to be reached on the basis of finitist mathematics. Gödel’s second incompleteness theorem forced a step from _absolute finitist_ to _relative constructivist_ proof-theoretic reductions. This mathematical step was accompanied by philosophical arguments for the special nature of the grounding constructivist frameworks. Against that background, this chapter examines Bernays’s reflections on proof-theoretic reductions (...) of _mathematical structures_ to _methodological frames_ via _projections_. However, these reflections are focused on narrowly arithmetic features of frames. Drawing on broadened meta-mathematical experience, this chapter proposes a more general characterization of frames that has ontological and epistemological significance. The characterization is given in terms of _accessibility_: domains of objects are accessible if their elements are inductively generated, and principles for such domains are accessible if they are grounded in our understanding of the generating processes. (shrink)

This paper systematically outlines Wittgenstein's ab-notation. The purpose of this notation is to provide a proof procedure in which ordinary logical formulas are converted into ideal symbols that identify the logical properties of the initial formulas. The general ideas underlying this procedure are in opposition to a traditional conception of axiomatic proof and are related to Peirce's iconic logic. Based on Wittgenstein's scanty remarks concerning his ab-notation, which almost all apply to propositional logic, this paper explains how (...) to extend his method to a subset of first-order formulas, namely, formulas that do not contain dyadic sentential connectives within the scope of any quantifier. (shrink)

In this paper we introduce a Gentzen calculus for (a functionally complete variant of) Belnap's logic in which establishing the provability of a sequent in general requires \emph{two} proof trees, one establishing that whenever all premises are true some conclusion is true and one that guarantees the falsity of at least one premise if all conclusions are false. The calculus can also be put to use in proving that one statement \emph{necessarily approximates} another, where necessary approximation is a (...) natural dual of entailment. The calculus, and its tableau variant, not only capture the classical connectives, but also the `information' connectives of four-valued Belnap logics. This answers a question by Avron. (shrink)

Some thirty years ago, two proposals were made concerning criteria for identity of proofs. Prawitz proposed to analyze identity of proofs in terms of the equivalence relation based on reduction to normal form in natural deduction. Lambek worked on a normalization proposal analogous to Prawitz's, based on reduction to cut-free form in sequent systems, but he also suggested understanding identity of proofs in terms of an equivalence relation based on generality, two derivations having the same generality if after generalizing maximally (...) the rules involved in them they yield the same premises and conclusions up to a renaming of variables. These two proposals proved to be extensionally equivalent only for limited fragments of logic. The normalization proposal stands behind very successful applications of the typed lambda calculus and of category theory in the proof theory of intuitionistic logic. In classical logic, however, it did not fare well. The generality proposal was rather neglected in logic, though related matters were much studied in pure category theory in connection with coherence problems, and there are also links to low-dimensional topology and linear algebra. This proposal seems more promising than the other one for the general proof theory of classical logic. (shrink)

Nathan Salmon, in his paper Trans-World Identification and Stipulation (1996) purports to give a proof for the claim that facts concerning trans-world identity cannot be conceptually reduced to general facts. He calls this claim ‘Extreme Haecceitism.’ I argue that his proof is fallacious. However, I also contend that the analysis and ultimate rejection of his proof clarifies the fundamental issues that are at stake in the debate between the reductionist and haecceitist solutions to the problem of (...) trans-world identity. These issues hinge on the ability of modal logic and possible worlds semantics to draw a hard and fast distinction between the logic and the metaphysics of modal logic. I shall claim that the considerations in this paper call into question the viability of such a distinction. (shrink)

The increased use of information technology in every day health care creates vast amounts of stored health data that can be used for research. The secondary research use of routinely collected data raises questions about appropriate consent mechanisms for such use. One option is meta consent where individuals state their own consent preferences in relation to future use of their data, e.g. whether they want the data to be accessible to researchers under conditions of specific consent, broad consent, blanket consent (...) or not at all. This study investigates whether meta consent preferences can be successfully elicited by a smartphone application in the adult Danish population. A smartphone app was developed for the elicitation of meta consent preferences. An invitation to use the app was distributed to a stratified, representative sample of the Danish adult population. The meta consent choices, the use of the app, user experience data, and demographic data were logged and analysed statistically using IBM SPSS version 20. Of 1000 potential respondents 221 used the app. One hundred eighty-eight of the respondents were female and 103 male. The age range was 19 to 79 years with an average of 51 years. Most users indicate 1) that they find the choices they are asked to make easy to understand, 2) that the application is easy to use, and 3) that this kind of choice should be offered to people. It is possible to collect meta consent preferences in the general, adult population using a smartphone app. (shrink)

Philosophers who regard some mathematical proofs as explaining why theorems hold, and others as merely proving that they do hold, disagree sharply about the explanatory value of proofs by mathematical induction. I offer an argument that aims to resolve this conflict of intuitions without making any controversial presuppositions about what mathematical explanations would be.

This paper examines the ultrafilter interpretation of Kurt Gödel’s ontological argument and explores its philosophical and mathematical consequences. After reviewing the formulations of Anselm of Canterbury, Gottfried Wilhelm Leibniz, and Gödel, we show how Gödel’s positivity axioms can be understood extensionally as defining an ultrafilter over the domain of individuals. We argue that this perspective sheds new light on the modal collapse, suggesting that it reflects not merely features of the modal framework, but deeper structural properties of the underlying ultrafilter. (...) We then relate this interpretation to the work of Harvey Friedman, where non-principal ultrafilters and divine objects are used to obtain relative consistency results in set theory. (shrink)

This chapter argues against the shift in paradigm in favor of scientific evidence in tort law cases. Recent proposals, seeking to require more demanding scientific evidence in toxic tort (and other) suits, are mistaken because these seem to impose a universal standard of evidence for quite different institutions—with the risk of distorting existing reasonable tort law relationships, and erring on the side of exclusion rather than admission of evidence. Since the plaintiff bears the burden of production, requiring that this be (...) met by proof equivalent to the criminal law's “beyond a reasonable doubt,” requirement, as some have argued, this substantially distorts the balance of interests between plaintiff and defendant. The appropriate paradigm is not that for scientific practice but the traditional tort law standard of evidence articulated in _Ferebee v. Chevron Chemical Co._, which said that the appropriate standard is not scientific certainty but “legal sufficiency.” The paradigm of choice in torts is in a sense inclined to retain much of the status quo. (shrink)

We critically examine Vickers’ project of future-proof science, which aims to identify scientific facts based upon a solid international scientific consensus. Vickers claims that second-order evidence—specifically a 95% consensus among a diverse, international scientific community—provides a principled criterion for identifying future-proof science. We challenge both the motivation behind this project and Vickers’ account of scientific consensus. Our analysis raises concerns about the methodological validity of the 30 alleged examples of future-proof science, questioning the selection, isolation, and interpretation (...) of such scientific claims. We argue that the dissimilarities among these examples expose potential flaws, such as lack of simplicity and semantic opacity, which undermine their effectiveness in supporting the project. Furthermore, we criticize the assumption that a solid international scientific consensus is a reliable indicator of future-proof science. Given that consensus in science is multifactorial, we contend that second-order evidence is insufficient to support any scientific claim as an instance of future-proof science. We also object that scientific consensus cannot be correlated to future-proof science, provided its mechanism is driven by social factors that are not necessarily aligned with the reliability required for claims about established scientific facts. Our analysis thus reveals that Vickers fails to tackle the so-called threshold problem afflicting his proposed criterion for future-proof science. (shrink)

We show that if the weak compactness of a cardinal is made indestructible by means of any preparatory forcing of a certain general type, including any forcing naively resembling the Laver preparation, then the cardinal was originally supercompact. We then apply this theorem to show that the hypothesis of supercompactness is necessary for certain proof schemata.

In this paper, we provide a general setting under which results of normalization of proof trees such as, for instance, the logicality result in equational reasoning and the cut-elimination property in sequent or natural deduction calculi, can be unified and generalized. This is achieved by giving simple conditions which are sufficient to ensure that such normalization results hold, and which can be automatically checked since they are syntactical. These conditions are based on basic properties of elementary combinations of (...) inference rules which ensure that the induced global proof tree transformation processes do terminate. (shrink)

A new version of the ontological argument for the existence of God is outlined and examined. After giving a brief account of some traditional ontological arguments for the existence of God, where their defects are identified, it is explained how this new argument is built upon their foundations and surmounts their defects. In particular, this version uses the resources of impossible worlds to plug the common escape route from standard modal versions of the ontological argument. After outlining the nature of (...) impossible worlds, and motivating the need for positing them, the new argument is delineated and its premises justified. It is taken for granted that the argument cannot be sound, since it would prove too much. However, its premises are all plausible, and their denial promises to have significant ramifications. Several intuitive lines of objections are then explored in order to illuminate their shortcomings. The puzzle that the argument poses is therefore not whether the argument is sound, for it clearly cannot be. Rather, it is to place pressure on its plausible premises, so some plausible account of how the argument fails can be identified, and that the devising of such an account promises to be insightful. In the process, we should gain an improved understanding of how such ontological arguments work. (shrink)

We develop a semantics for independence logic with respect to what we will call general models. We then introduce a simpler entailment semantics for the same logic, and we reduce the validity problem in the former to the validity problem in the latter. Then we build a proof system for independence logic and prove its soundness and completeness with respect to entailment semantics.

By generalizing Kreisel’s proof of the Second Incompleteness Theorem of G¨odel I extract a general principle which can also be used for otherpurely model-theoretical proofs of that theorem.

A common view about Moore’s Proof of an External World is that the argument fails because anyone who had doubts about its conclusion could not use the argument to rationally overcome those doubts. I agree that Moore’s Proof is—in that sense—dialectically ineffective at convincing an opponent or a doubter, but I defend that the argument (even when individuated taking into consideration the purpose of Moore’s arguing and, consequently, the preferred addressee of the Proof) does not fail. The (...) key to my defence is to conceive the Proof as addressed to subjects with a different epistemic condition. To sustain this view I formulate some hypothesis about the common general purpose of arguing and I defend that it can be fulfilled even when the addressee of an argument is not someone who disbelieves or doubts its conclusion. (shrink)

Kosta Došen argued in his papers Inferential Semantics (in Wansing, H. (ed.) Dag Prawitz on Proofs and Meaning, pp. 147–162. Springer, Berlin 2015) and On the Paths of Categories (in Piecha, T., Schroeder-Heister, P. (eds.) Advances in Proof-Theoretic Semantics, pp. 65–77. Springer, Cham 2016) that the propositions-as-types paradigm is less suited for general proof theory because—unlike proof theory based on category theory—it emphasizes categorical proofs over hypothetical inferences. One specific instance of this, Došen points out, is (...) that the Curry–Howard isomorphism makes the associativity of deduction composition invisible. We will show that this is not necessarily the case. (shrink)

The possibility of spectrum inversion has been debated since it was raised by Locke and is still discussed because of its implications for functionalist theories of conscious experience . This paper provides a mathematical formulation of the question of spectrum inversion and proves that such inversions, and indeed bijective scramblings of color in general, are logically possible. Symmetries in the structure of color space are, for purposes of the proof, irrelevant. The proof entails that conscious experiences are (...) not identical with functional relations. It leaves open the empirical possibility that functional relations might, at least in part, be causally responsible for generating conscious experiences. Functionalists can propose causal accounts that meet the normal standards for scientific theories, including numerical precision and novel prediction; they cannot, however, claim that, because functional relationships and conscious experiences are identical, any attempt to construct such causal theories entails a category error. (shrink)

There has been a recent upsurge in interest in the odd structure of J. L. Austin’s _How to Do Things with Words _(1975). The first several chapters of this book are concerned with a distinction between performative utterances (through which the speaker _does _something) and constative utterances (through which the speaker _says _something about the world). Austin then finds this distinction unsatisfactory and so sets off on a path towards a more unified theory of speech acts. Marina Sbisà (2007; 2024) (...) has explained this structure by interpreting Austin as offering a proof by contradiction for the claim that all speech is action. Wanderer and Townsend (2024) have disputed this interpretation, arguing that it leads to an uncharitable reading of Austin that fails to fully accord with the text. I defend Sbisà’s proof against Wanderer and Townsend’s criticisms, while adapting and reinterpreting certain aspects of it so as to improve it both as an interpretation of Austin and as an argument in its own right. I also supplement Sbisà’s account, by arguing that Austin chose to argue in a way that centres the performative/constative distinction because something like this distinction was popular amongst his contemporaries. Indeed, I claim that he explicitly alludes to certain strains of thought amongst these contemporaries that makes use of this distinction. (shrink)

The argument from ignorance is an informal fallacy that holds either that a statement not known to be true or proven true is false, or a statement not known to be false or proven false is true. For example, some creationists hold that since the theory of evolution has not been proven to be true, it is false. There is, however, a subtlety to this fallacy that is exploited in Richard H. Gaskins's far-ranging study of rhetoric and persuasion in modern (...) legal, philosophical, and scientific communities. The argument can assert that no evidence to support a claim entails that the claim is false if all the relevant supporting or refuting evidence has been collected. Thus, if a creationist claims that the earth was created some five thousand years ago, a critic could reply that abundant evidence refutes the claim. This additional claim in the argument, however, involves controversies about appropriate and adequate evidence, as well as questions of what Gaskins calls "finality and legitimacy." How long should one proceed with the search for evidence and how should one justify the procedures? (shrink)

Hume, in the Enquiry, remarks in a footnote as follows.