Formalizing Verbal Theories

Rooij, Iris van; Blokpoel, Mark

doi:10.1027/1864-9335/a000428

Cited by 48 publications

(31 citation statements)

References 23 publications

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“…In order to be able to evaluate the similarities and differences between the hierarchical structure of language and action in a transparent way, we need a theory-neutral conceptual vocabulary to describe these structures. Ideally, this description should be accompanied by a formal analysis of the similarities and differences, as well as an evaluation of their implications (Guest & Martin, 2021;Martin, 2016Martin, , 2020O'Donnell, Hauser, & Fitch, 2005;Partee, ter Meulen, & Wall, 1993;van Rooij & Blokpoel, 2020). To this end, the following paragraphs will present a formal model in which we incorporate the properties of syntactic structure as defined in Section 2.1.…”

Section: Formalizing Linguistic Structurementioning

confidence: 99%

“…To this end, the aim of this paper is to characterize the similarities and differences between the hierarchical structures in language and action in both conceptual and formal terms (cf. Guest & Martin, 2021;Martin, 2020;van Rooij & Blokpoel, 2020). The paper is structured as follows: in Section 2, we discuss the type of data that shows that the syntax of natural language is organized hierarchically, after which we list the core properties of such hierarchical syntactic structure (Section 2.1).…”

Section: Introductionmentioning

confidence: 99%

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Hierarchical structure in language and action: A formal comparison

Coopmans¹,

Kaushik²,

Martin³

2021

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Since the cognitive revolution, language and action have been compared as cognitive systems, with cross-domain convergent views recently gaining renewed interest in biology, neuroscience, and cognitive science. Language and action are both combinatorial systems whose mode of combination has been argued to be hierarchical, combining elements into constituents of increasingly larger size. This structural similarity has led to the suggestion that they rely on shared cognitive and neural resources. In this paper, we compare the conceptual and formal properties of hierarchy in language and action using tools from category theory. We show that the strong compositionality of language requires a formalism that describes the mapping between sentences and their syntactic structures as an order-embedded Galois connection, while the weak compositionality of actions only requires a monotonic mapping between action sequences and their goals, which we model as a monotone Galois connection. We aim to capture the different system properties of language and action in terms of the distinction between hierarchical sets and hierarchical sequences, and discuss the implications for the way both systems are represented in the brain.

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Section: Formalizing Linguistic Structurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hierarchical structure in language and action: A formal comparison

Coopmans¹,

Kaushik²,

Martin³

2021

Preprint

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“…Statistics is a formal science whose methods follow from probability calculus to be valid, and this validity is established either by mathematical proofs or by simulation proofs before being advanced for the use of scientists. Formalization allows us to subject our verbal intuitions to scrutiny, revealing holes, inconsistencies, and undeclared assumptions and to make precise, transparent claims that hold under well-specified assumptions [ 19 ]. As such, by statistical rigor, we mean doing and showing the necessary formal work to establish how we know a methodological claim is valid, in a way that does not leave room for idle speculation.…”

Section: Introductionmentioning

confidence: 99%

The case for formal methodology in scientific reform

et al. 2021

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Current attempts at methodological reform in sciences come in response to an overall lack of rigor in methodological and scientific practices in experimental sciences. However, most methodological reform attempts suffer from similar mistakes and over-generalizations to the ones they aim to address. We argue that this can be attributed in part to lack of formalism and first principles. Considering the costs of allowing false claims to become canonized, we argue for formal statistical rigor and scientific nuance in methodological reform. To attain this rigor and nuance, we propose a five-step formal approach for solving methodological problems. To illustrate the use and benefits of such formalism, we present a formal statistical analysis of three popular claims in the metascientific literature: (i) that reproducibility is the cornerstone of science; (ii) that data must not be used twice in any analysis; and (iii) that exploratory projects imply poor statistical practice. We show how our formal approach can inform and shape debates about such methodological claims.

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Section: Introductionmentioning

confidence: 99%

The case for formal methodology in scientific reform

Devezer

Navarro

Vandekerckhove

et al. 2020

Preprint

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Current attempts at methodological reform in sciences come in response to an overall 9 lack of rigor in methodological and scientific practices in experimental sciences. However, some of 10 these reform attempts suffer from the same mistakes and over-generalizations they purport to 11 address. Considering the costs of allowing false claims to become canonized, we argue for more 12 rigor and nuance in methodological reform. By way of example, we present a formal analysis of 13 three common claims in the metascientific literature: (a) that reproducibility is the cornerstone of 14 science; (b) that data must not be used twice in any analysis; and (c) that exploratory projects are 15 characterized by poor statistical practice. We show that none of these three claims are correct in 16 general and we explore when they do and do not hold. 17 18 42 1 of 28 Manuscript submitted.an opportunity: reformers are in an opportune position to take criticism and self-correct before 43 allowing false claims to be canonized as methodological facts (Nissen et al., 2016). 44 In this paper we advocate for the necessity of statistically rigorous and scientifically nuanced 45 arguments to make proper methodological claims in the reform literature. Toward this aim, we 46 evaluate three examples of methodological claims that have been advanced and well-accepted (as 47 implied by the large number of citations) in the reform literature: 48 1. Reproducibility is the cornerstone of, or a demarcation criterion for, science. 49 2. Using data more than once invalidates statistical inference. 50 3. Exploratory research uses "wonky" statistics. 51 Each of these claims suffers from some of the problems outlined earlier and as a result, has 52 contributed to methodological half-truths (or untruths). We evaluate each claim using statistical 53 theory against a broad philosophical and scientific background. 54 While we focus on these three claims, we believe our call for rigor and nuance can reach 55 further with the following emphasis: Statistics is a formal science whose methodological claims 56 follow from probability calculus. Methodological claims are either proved mathematically or by 57 simulation before being advanced for the use of scientists. Most valid methodological advances 58 are incremental, and they rarely ever provide simple prescriptions to complex inference problems. 59 Norms issued on the basis of bold claims about new methods might be quickly adopted by empirical 60 scientists as heuristics and might alter scientific practices. However, advancing such reforms in the 61 absence of formal proofs is sacrificing rigor for boldness and can lead to unforeseeable scientific 62 consequences. We believe that hasty revolution may hold science back more than it helps move 63 it forward. We hope that our approach may facilitate scientific progress that stands on firm 64 ground-supported by theory or evidence. 65 Claim 1: Reproducibility is the cornerstone of, or a demarcation criterion 66 for, science. 67 A common asser...

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Formalizing Verbal Theories

Cited by 48 publications

References 23 publications

Hierarchical structure in language and action: A formal comparison

Hierarchical structure in language and action: A formal comparison

The case for formal methodology in scientific reform

The case for formal methodology in scientific reform

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