Expressions are synonymous if they have the same semantic content. Complex expressions are synonymously isomorphic in Alonzo Church’s sense if one is obtainable from the other by a sequence of alphabetic changes of bound variables or replacements of component expressions by syntactically simple synonyms. Synonymous isomorphism provides a very strict criterion for synonymy of sentences. Several eminent philosophers of language hold that synonymous isomorphism is not strict enough. These philosophers hold that ‘Greeks prefer Greeks’ and (...) ‘Greeks prefer Hellenes’ express different propositions even if they are synonymously isomorphic. They hold that the very recurrence (multiple occurrence) of ‘Greeks’ contributes to the proposition expressed something that indicates the very recurrence in question. Kit Fine argues that this thesis, which he labels semantic relationism calls for a radically new conception of semantics. I have argued that the relevant phenomenon is wholly pragmatic, entirely non-semantic. Here I supplement the case with a new argument. No cognition without recognition—or almost none. With this observation, standard Millianism has sufficient resources to confront Frege’s puzzle and related problems without injecting pragmatic phenomena where they do not belong. (shrink)

Alonzo Church famously provided three principal competing criteria for “strict synonymy,” i.e., sameness of semantic content. These are his Alternatives (0), (1), and (2)—numbered in order of increasing course-grainedness of content. On Alternative (2), expressions are deemed strictly synonymous iff they are logically equivalent. This criterion seems hopeless as an account of the objects of propositional attitude. On Alternative (1), expressions are deemed synonymous iff they are λ-convertible. Alternative (1) also evidently conflicts with discourse about the attitudes. On (...) Alternative (0), expressions are deemed strictly synonymous iff they are “synonymously isomorphic” in Church’s sense. On Alternative (0), semantic content is so fine-grained that not even “Romeo loves Juliet” and “Juliet is loved by Romeo” qualify as strictly synonymous. A fourth alternative, here called “Alternative (3),” deems expressions strictly synonymous iff they are co-intensional, i.e., they have the same semantic extension with respect to the same possible worlds. This criterion’s notion of content is even more course grained than that of Alternative (2). Several objections to Alternative (3) are considered. (This article is wholly contained within the author’s more definitive essay, “Singular Concepts”.). (shrink)

At the beginning of the 20th century, Gestalt psychologists put forward the concept of psychoneural isomorphism, which was meant to replace Fechner’s obscure notion of psychophysical parallelism and provide a heuristics that may facilitate the search for the neural correlates of the mind. However, the concept has generated much confusion in the debate, and today its role is still unclear. In this contribution, I will attempt a little conceptual spadework in clarifying the concept of psychoneural isomorphism, focusing exclusively (...) on conscious visual perceptual experience and its neural correlates. Firstly, I will outline the history of our concept, and its alleged metaphysical and epistemic roles. Then, I will clarify the nature of isomorphism and rule out its metaphysical role. Finally, I will review some epistemic roles of our concept, zooming in on the work of Jean Petitot, and suggest that it does not play a relevant heuristic role. I conclude suggesting that psychoneural isomorphism might be an indicator of robustness for certain mathematical descriptions of perceptual content. (shrink)

The isomorphism invariance criterion of logical nature has much to commend it. It can be philosophically motivated by the thought that logic is distinctively general or topic neutral. It is capable of precise set-theoretic formulation. And it delivers an extension of ‘logical constant’ which respects the intuitively clear cases. Despite its attractions, the criterion has recently come under attack. Critics such as Feferman, MacFarlane and Bonnay argue that the criterion overgenerates by incorrectly judging mathematical notions as logical. We consider (...) five possible precisifications of the overgeneration argument and find them all unconvincing. (shrink)

An isomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That isomorphism can be interpreted physically as the invariance between a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting another way for proving it, more concise and meaningful physically. Mathematically, the isomorphism means (...) the invariance to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”. (shrink)

A number of high-profile mislabeling incidents have led to many studies exploring the decision-making processes that firms make around performing illegal acts. However, it remains unclear why the proportion of firms conducting these acts constantly fluctuates and never disappears. Therefore, this study investigated this by carrying out a longitudinal analysis of food labeling in the Taiwanese rice industry. Drawing on the institutional isomorphism theory, it was found that the degree of mislabeling is negatively correlated with both the level of (...) control of inspection regulations and public attention toward food regulations, and positively correlated with the previous proportion of firms mislabeling their products. Thus, there is a feedback loop between regulatory control, public attention, and the amount of mislabeling, with the amount of mislabeling not only being affected by the former degree of regulatory control, public attention, and mislabeling, but also modifying the future status of each of these. These findings further our understanding of the causal effects of illegal actions in the institutional agricultural environment. (shrink)

In the course of his critique of the Buddhist doctrine of universal momentariness, Udayana argues for an isomorphism between our understandings of space and time, which is meant to undercut the Buddhists’ well-known “inference from existence.” The present paper examines these arguments from Udayana’s Ātmatattvaviveka, together with Ratnakīrti’s treatment of them in his Kṣaṇabhaṅgasiddhi Anvayātmikā. As an historical study, the paper aims to elucidate the connections between Udayana and Ratnakīrti, and the implications of those connections for the dependence of (...) the inference from existence upon various arguments which appear elsewhere in Ratnakīrti’s corpus. As a work of philosophical interpretation, the paper will clarify what is at stake in the local debate over the space–time isomorphism. Ratnakīrti’s position will best be understood as an account on which different simple causal properties are ascribed, or indexed, to an allegedly persisting entity at different times, while Udayana will prefer an account on which complex properties indexed to the place and/or time of the effect—for instance, “generating a sprout in this particular place” or “producing a visual awareness at a certain time”—will belong to a persisting thing throughout its entire existence. Furthermore, the acceptance or rejection of space and time as substantial entities in their own right, as distinct from the entities which are conventionally said to exist in space and time, will have important implications for the accounts of causality that each thinker can accept. (shrink)

We examine how degrees of computably enumerable equivalence relations under computable reduction break down into isomorphism classes. Two ceers are isomorphic if there is a computable permutation of ω which reduces one to the other. As a method of focusing on nontrivial differences in isomorphism classes, we give special attention to weakly precomplete ceers. For any degree, we consider the number of isomorphism types contained in the degree and the number of isomorphism types of weakly precomplete (...) ceers contained in the degree. We show that the number of isomorphism types must be 1 or ω, and it is 1 if and only if the ceer is self-full and has no computable classes. On the other hand, we show that the number of isomorphism types of weakly precomplete ceers contained in the degree can be any member of $[0,\omega ]$. In fact, for any $n \in [0,\omega ]$, there is a degree d and weakly precomplete ceers ${E_1}, \ldots,{E_n}$ in d so that any ceer R in d is isomorphic to ${E_i} \oplus D$ for some $i \le n$ and D a ceer with domain either finite or ω comprised of finitely many computable classes. Thus, up to a trivial equivalence, the degree d splits into exactly n classes.We conclude by answering some lingering open questions from the literature: Gao and Gerdes [11] define the collection of essentially FC ceers to be those which are reducible to a ceer all of whose classes are finite. They show that the index set of essentially FC ceers is ${\rm{\Pi }}_3^0$-hard, though the definition is ${\rm{\Sigma }}_4^0$. We close the gap by showing that the index set is ${\rm{\Sigma }}_4^0$-complete. They also use index sets to show that there is a ceer all of whose classes are computable, but which is not essentially FC, and they ask for an explicit construction, which we provide.Andrews and Sorbi [4] examined strong minimal covers of downwards-closed sets of degrees of ceers. We show that if $\left$ is a uniform c.e. sequence of non universal ceers, then $\left\{ {{ \oplus _{i \le j}}{E_i}|j \in \omega } \right\}$ has infinitely many incomparable strong minimal covers, which we use to answer some open questions from [4].Lastly, we show that there exists an infinite antichain of weakly precomplete ceers. (shrink)

This paper presents and defends a novel meta‐epistemological thesis, epistemic isomorphism, according to which our relations to others and to ourselves have the same pattern of relevance to our rationality. This means that correct epistemological theorizing will give formal parity to interpersonal and intrapersonal epistemic norms, such that what holds interpersonally also holds, mutatis mutandis, intrapersonally. In addition to arguing for epistemic isomorphism, the paper presents some epistemological case studies in which it is shown that the methodological and (...) argumentative strategies used by epistemologists in these case studies give expression to the idea of epistemic isomorphism as well as the argument presented here for its truth. Finally, the paper considers a possible counterexample to epistemic isomorphism based on an agent‐centered theory of justification, but it shows how to reconcile this theory with epistemic isomorphism. (shrink)

This paper discusses some engineering considerations that should be taken into account when building a knowledge based system, and recommends isomorphism, the well defined correspondence of the knowledge base to the source texts, as a basic principle of system construction in the legal domain. Isomorphism, as it has been used in the field of legal knowledge based systems, is characterised and the benefits which stem from its use are described. Some objections to and limitations of the approach are (...) discussed. The paper concludes with a case study giving a detailed example of the use of the isomorphic approach in a particular application. (shrink)

We give a formalism for approximate isomorphism in continuous logic simultaneously generalizing those of two papers by Ben Yaacov [2] and by Ben Yaacov, Doucha, Nies, and Tsankov [6], which are largely incompatible. With this we explicitly exhibit Scott sentences for the perturbation systems of the former paper, such as the Banach‐Mazur distance and the Lipschitz distance between metric spaces. Our formalism is simultaneously characterized syntactically by a mild generalization of perturbation systems and semantically by certain elementary classes of (...) two‐sorted structures that witness approximate isomorphism. As an application, we show that the theory of any ‐tree or ultrametric space of finite radius is stable, improving a result of Carlisle and Henson [8]. (shrink)

An interesting feature of some sets of representations is that their structure mirrors the structure of the items they represent. Founding an account of representational content on isomorphism, homomorphism or structural resemblance has proven elusive, however, largely because these relations are too liberal when the candidate structure over representational vehicles is unconstrained. Furthermore, in many cases where there is a clear isomorphism, it is not relied on in the way the representations are used. That points to a potential (...) resolution: that an isomorphism must be used, hence usable, if it is to be an ingredient in a theory of content. This paper argues that the class of exploitable isomorphisms can indeed play a content-constituting role. (shrink)

For the information theorist, the lawful generalizations that subsume instantiations of properties in the environment and instantiations of properties of perceptual representations determine the latter's content. Perceptual representations are also commonly thought to be isomorphic to what they represent, which presents the information theorist with a puzzle. What role could isomorphism play in perceptual representation when lawful generalizations determine content? I show that in order for the information that they carry to be available to cognition, perceptual representations must be (...) isomorphic with respect to the constituent structure of the properties that they represent. Isomorphism therefore plays an important role in the information theorist's account of perceptual representation, even though it plays no role in determining content. (shrink)

The ultraproduct construction is generalized to p‐ultramean constructions () by replacing ultrafilters with finitely additive measures. These constructions correspond to the linear fragments of continuous logic and are very close to the constructions in real analysis. A powermean variant of the Keisler‐Shelah isomorphism theorem is proved for. It is then proved that ‐sentences (and their approximations) are exactly those sentences of continuous logic which are preserved by such constructions. Some other applications are also given.

We consider the complexity of the isomorphism relation on countable first-order structures with transitive automorphism groups. We use the theory of Borel reducibility of equivalence relations to show that the isomorphism problem for vertex-transitive graphs is as complicated as the isomorphism problem for arbitrary graphs and determine for which first-order languages the isomorphism problem for transitive countable structures is as complicated as it is for arbitrary countable structures. We then use these results to characterize the complexity (...) of the isometry relation for certain classes of homogeneous and ultrahomogeneous metric spaces. (shrink)

We study the isomorphism relation on Borel classes of locally compact Polish metric structures. We prove that isomorphism on such classes is always classifiable by countable structures (equivalently: Borel reducible to graph isomorphism), which implies, in particular, that isometry of locally compact Polish metric spaces is Borel reducible to graph isomorphism. We show that potentially $\boldsymbol {\Pi }^{0}_{\alpha + 1}$ isomorphism relations are Borel reducible to equality on hereditarily countable sets of rank $\alpha $, $\alpha (...) \geq 2$. We also study approximations of the Hjorth-isomorphism game, and formulate a condition ruling out classifiability by countable structures. (shrink)

We compare the medieval projects of commentaries and disputations with the modern projects of formal ontology and of mathematics.

Synonymic Collocations in the Tipitaka: a study. M.G.Dhadphale. Bhandarkar Oriental Research Institute, Poona 1980. xiii + 267pp. Rs 50.

We study the Borel reducibility of isomorphism relations in the generalized Baire space. In the main result we show for inaccessible κ, that if T is a classifiable theory and is stable with the orthogonal chain property (OCP), then the isomorphism of models of T is Borel reducible to the isomorphism of models of.

The globalizations of capital markets in the last 20 years has led to a historic degree of financial integration in the world. It is clear, however, that globalization is not conducive to a complete homogeneity of financial markets and institutions. Among others, one element of diversity is the importance of the impact of corruption in emerging countries. Corruption decreases the credibility of financial institutions and markets. Scandals and unethical behavior in financial institutions erode confidence in such firms. Relying on neoinstitutional (...) literature, this article focuses on the link between corruption and organizational isomorphism in financial institutions in emerging countries. Therefore, our aim is to examine the institutional reasons for corruption in financial institutions in emerging countries. Our structural equation model is based on empirical research in financial institutions in emerging countries. A questionnaire was administrated to 70 top executives of financial institutions in 18 different emerging countries. (shrink)

Two cases are distinguished. In one case two predicates belong to distinct languages. A straight-forward argument is presented that the predicates might be synonymous without being coextensive. In the second case the predicates belong to the same language. Here the issue is more involved, but the same conclusion is reached.

A serious crisis is identified in theories of neurocomputation, marked by a persistent disparity between the phenomenological or experiential account of visual perception and the neurophysiological level of description of the visual system. In particular, conventional concepts of neural processing offer no explanation for the holistic global aspects of perception identified by Gestalt theory. The problem is paradigmatic and can be traced to contemporary concepts of the functional role of the neural cell, known as the Neuron Doctrine. In the absence (...) of an alternative neurophysiologically plausible model, I propose a perceptual modeling approach, to model the percept as experienced subjectively, rather than modeling the objective neurophysiological state of the visual system that supposedly subserves that experience. A Gestalt Bubble model is presented to demonstrate how the elusive Gestalt principles of emergence, reification, and invariance can be expressed in a quantitative model of the subjective experience of visual consciousness. That model in turn reveals a unique computational strategy underlying visual processing, which is unlike any algorithm devised by man, and certainly unlike the atomistic feed-forward model of neurocomputation offered by the Neuron Doctrine paradigm. The perceptual modeling approach reveals the primary function of perception as that of generating a fully spatial virtual-reality replica of the external world in an internal representation. The common objections to this picture-in-the-head concept of perceptual representation are shown to be ill founded. Key Words: brain-anchored; Cartesian theatre; consciousness; emergence; extrinsic constraints; filling-in; Gestalt; homunculus; indirect realism; intrinsic constraints; invariance; isomorphism; multistability; objective phenomenology; perceptual modeling; perspective; phenomenology; psychophysical parallelism; psychophysical postulate; qualia; reification; representationalism; structural coherence. (shrink)

Millikan’s theory of content purports to rely heavily on the existence of isomorphisms between a system of representations and the things in the world which they represent — “the mapping requirement for being intentional signs” (Millikan 2004, p. 106). This paper asks whether those isomorphisms are doing any substantive explanatory work. Millikan’s isomorphism requirement is deployed for two main purposes. First, she claims that the existence of an isomorphism is the basic representing relation, with teleology playing a subsidiary (...) role — to account for misrepresentation (the possibility of error). Second, Millikan relies on an isomorphism requirement in order to guarantee that a system of representations displays a kind of productivity. This seemingly strong reliance on isomorphism has prompted the objection that isomorphism is too liberal to be the basic representing relation: there are isomorphisms between any system of putative representations and any set, of the same cardinality, of items putatively represented. This paper argues that all the work in fixing content is in fact done by the teleology. Deploying Millikan’s teleology-based conditions to ascribe contents will ensure that there is an isomorphism between representations and the things they represent, but the isomorphism ‘requirement’ is playing no substantive explanatory role in Millikan’s account of content determination. So an objection to her theory based on the liberality of isomorphism is misplaced. The second role for isomorphism is to account for productivity. If some kind of productivity is indeed necessary for representation, then functional isomorphism will again be too liberal a constraint to account for that feature. The paper suggests an alternative way of specifying the relation between a system of representations and that which they represent which is capable of playing an explanatory role in accounting for Millikan’s type of productivity. In short, the liberality of isomorphism is no objection to Millikan’s teleosemantics, since the isomorphism ‘requirement’ need play no independent substantive role in Millikan’s account of representation. (shrink)

Based on neo-institutional literature, this article aims to show the influence of organizational isomorphism on corruption. The focus is institutional explanations of corruption. Our model is based on empirical research in Russia at the end of the 1990s. A face-to-face questionnaire was conducted with 552 top executives in private firms across various economic sectors. We used the structural equation model Partial Least Squares, PLS, technique to test our hypotheses. The developed model provides an integrated approach to the study of (...) the relationship between corruption and organizational isomorphism. Our empirical data from firms in Russia allowed us to test various theoretical hypotheses concerning the influence of organizational isomorphism on corruption. Our emphasis is on the influence of competitive and institutional isomorphism on corruption. (shrink)

Global policy transfer has become increasingly popular in recent years, and one recent example of such policy transfer is the England–China Teacher Exchange, which was initiated in 2014 with the explicit aim of raising attainment in maths in English primary schools by trialling concepts used in Shanghai schools, Shanghai rising to the top of the PISA rankings in 2009. However, as this paper will argue this is an overly simplistic attempt to transfer a policy between two wholly different contexts, the (...) lack of success of the policy seen in the very limited impact on student attainment in the participating schools. Whilst such policy transfer has increasingly taken place in the context of isomorphism and global pressures to adopt policy from high performing education systems, it is argued that policy needs to be explicitly reconsidered in terms of the local context it is being imported into if it is to be embedded in an effective manner, as well as rooted firmly in research. It is also argued that the England–China Teacher Exchange reflects a broader ideological focus in coalition government policy on the marketisation of education alongside the PISA rankings, rather any wider consideration of how this particular policy would drive up standards. (shrink)

We study the complexity of the isomorphism relation on classes of computable structures. We use the notion of FF-reducibility introduced in [9] to show completeness of the isomorphism relation on many familiar classes in the context of all ${\mathrm{\Sigma }}_{1}^{1}$ equivalence relations on hyperarithmetical subsets of ω.

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider only countable members. This paper explores such a notion for classes of computable structures by working out a sequence of examples. We follow recent work by Goncharov and Knight in using the degree of the isomorphism problem for a class to distinguish classifiable classes from non-classifiable. (...) In this paper, we calculate the degree of the isomorphism problem for Abelian p-groups of bounded Ulm length. The result is a sequence of classes whose isomorphism problems are cofinal in the hyperarithmetical hierarchy. In the process, new back-and-forth relations on such groups are calculated. (shrink)

This paper discusses the general problem of translation functions between logics, given in axiomatic form, and in particular, the problem of determining when two such logics are "synonymous" or "translationally equivalent." We discuss a proposed formal definition of translational equivalence, show why it is reasonable, and also discuss its relation to earlier definitions in the literature. We also give a simple criterion for showing that two modal logics are not translationally equivalent, and apply this to well-known examples. Some philosophical (...) morals are drawn concerning the possibility of having two logical systems that are "empirically distinct" but are both translationally equivalent to a common logic. (shrink)

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider only countable members. This paper explores such a notion for classes of computable structures by working out several examples. One motivation is to see whether some classes whose set of countable members is very complex become classifiable when we consider only computable members. We follow recent work (...) by Goncharov and Knight in using the degree of the isomorphism problem for a class to distinguish classifiable classes from non-classifiable. For real closed fields we show that the isomorphism problem is Δ1 1 complete (the maximum possible), and for others we show that it is of relatively low complexity. We show that the isomorphism problem for algebraically closed fields, Archimedean real closed fields, or vector spaces is Π0 3 complete. (shrink)

The relevance of Wolfgang K hler's psychoneural isomorphism principle to contemporary cognitive neuroscience is explored. K hler's approach to the mind—body problem is interpreted as a response to the foundational crisis of psychology at the beginning of the twentieth century. Some aspects of his isomorphism doctrine are discussed, with a view to reaching an interpretation that is both historically accurate and pertinent to issues currently debated in the philosophy of psychology. The principle was meant to be empirically verifiable. (...) Accordingly, some similarities between K hler's approach and current neural network modeling are pointed out, and it is shown that some recent trends in the neurosciences are broadly compatible with K hler's views on cortical functioning. Isomorphism is interpreted as a form of neuroreductionism constrained by bridging laws relating mental phenomena to macrosocopic parameters of neural function. While isomorphism is probably valid for perceptual phenomena, its applicability to higher mental processes remains doubtful. (shrink)

This paper answers some questions of D. Ross in [R]. In § 1, we show that some consequences of the ℵ0- or ℵ1-special model axiom in [R] cannot be proved by the κ-isomorphism property for any cardinal κ. In § 2, we show that with one exception, the ℵ0-isomorphism property does imply the remaining consequences of the special model axiom in [R]. In § 3, we improve a result in [R] by showing that the κ-special model axiom is (...) equivalent to the ℵ0-special model axiom plus κ-saturation. (shrink)

In the present paper we discuss a recent suggestion of Schroeder-Heister concerning the possibility of defining an intensional notion of harmony using isomorphism in second-order propositional logic. The latter is not an absolute notion, but its definition is relative to the choice of criteria for identity of proofs. In the paper, it is argued that in order to attain a satisfactory account of harmony, one has to consider a notion of identity stronger than the usual one (based on β- (...) and η-conversions) that the authors have investigated in recent work. (shrink)

We prove a strengthened version of Shavrukov’s result on the non-isomorphism of diagonalizable algebras of two $\Sigma _1$ -sound theories, based on the improvements previously found by Adamsson. We then obtain several corollaries to the strengthened result by applying it to various pairs of theories and obtain new non-isomorphism examples. In particular, we show that there are no surjective homomorphisms from the algebra $(\mathfrak {L}_T, \Box _T\Box _T)$ onto the algebra $(\mathfrak {L}_T, \Box _T)$. The case of bimodal (...) diagonalizable algebras is also considered. We give several examples of pairs of theories with isomorphic diagonalizable algebras but non-isomorphic bimodal diagonalizable algebras. (shrink)

Under the influence of groundbreaking work by John Meyer and Brian Rowen, as well as Paul DiMaggio and Walter Powell, over the last 30 years research in the new sociological institutionalism has focused on processes of isomorphism. I argue that this is a one-sided focus that leaves out many insights from other institutional and macrosociological approaches and does not do justice to actual social change because it overlooks the role played by divergent institutional development. While the suggestion of divergent (...) trends is not new, there have been few attempts to integrate divergence into the theoretical premises of the new sociological institutionalism. Based on the typology proposed by DiMaggio and Powell, I show that the mechanisms identified by them as sources of isomorphic change can support processes of divergent change as well. The theoretical challenge is to identify conditions under which these mechanisms push institutional change toward homogenization or divergence. (shrink)

Pessoa, Thompson & Noë present compelling evidence in support of their central claims about the diversity of filling-in, but they embed those claims within a larger framework that rejects analytical isomorphism and uses the personal/subpersonal distinction to challenge the explanatory importance of filling-in. The latter views seem more problematic.

We give the first systematic study of strong isomorphism reductions, a notion of reduction more appropriate than polynomial time reduction when, for example, comparing the computational complexity of the isomorphim problem for different classes of structures. We show that the partial ordering of its degrees is quite rich. We analyze its relationship to a further type of reduction between classes of structures based on purely comparing for every n the number of nonisomorphic structures of cardinality at most n in (...) both classes. Furthermore, in a more general setting we address the question of the existence of a maximal element in the partial ordering of the degrees. (shrink)

We show that every countable ideal of degrees that are low for isomorphism is contained in a principal ideal of degrees that are low for isomorphism by adapting an exact pair construction. We further show that within the hyperimmune free degrees, lowness for isomorphism is entirely independent of computable traceability.

I argue against theories that attempt to reduce scientific representation to similarity or isomorphism. These reductive theories aim to radically naturalize the notion of representation, since they treat scientist's purposes and intentions as non-essential to representation. I distinguish between the means and the constituents of representation, and I argue that similarity and isomorphism are common but not universal means of representation. I then present four other arguments to show that similarity and isomorphism are not the constituents of (...) scientific representation. I finish by looking at the prospects for weakened versions of these theories, and I argue that only those that abandon the aim to radically naturalize scientific representation are likely to be successful. (shrink)

The Gestalt principle of isomorphism reveals the primacy of subjective experience as a valid source of evidence for the information encoded neurophysiologically. This theory invalidates the abstractionist view that the neurophysiological representation can be of lower dimensionality than the percept to which it gives rise.

A cofinitary group is a subgroup of Sym(ℕ) where all nonidentity elements have finitely many fixed points. A maximal cofinitary group is a cofinitary group, maximal with respect to inclusion. We show that a maximal cofinitary group cannot have infinitely many orbits. We also show, using Martin's Axiom, that no further restrictions on the number of orbits can be obtained. We show that Martin's Axiom implies there exist locally finite maximal cofinitary groups. Finally we show that there exists a uniformly (...) computable sequence of permutations generating a cofinitary group whose isomorphism type is not computable. (shrink)

The suggestion that analytic isomorphism should be rejected applies especially to the domain of speech perception because (1) the guiding assumption that solving the lack of invariance problem is the key to explaining speech perception is a form of analytic isomorphism, and (2) after nearly half a century of research there is virtually no empirical evidence of isomorphism between perceptual experience and lower-level processing units.