The notion of computation seems to have acquired a certain importance in different scientific domains. Although it entered the terminology of each particular discipline its epistemic status is not always clear concerning the results it produces as a tool for analysis or the ontology of the object as studied for itself. It seems therefore important to raise the question of what a computation is, assuming the multidisciplinary perspective that it integrates.
Therefore the goal of this conference is to ask future scholars of different disciplines, all variously involved with the notion of computation, to engage a discussion focusing on the relevant cases at stake in their domain of study from the point of view of their individual practice. Before asking the hard question of knowing what a computation is or what it means to compute, this conference aims at gathering paradigmatic examples that could stand for the way computations are studied or used in a particular field of research, and thus can serve as indicators towards a conceptual clarification of the notion of computation.
This paper provides a compelling argument about why we should think of computational implementation as a three-place relation. The argument's structure takes four steps: First (1), I introduce the Bridging Problem (a well-known problem from the philosophy of applied mathematics). Next (2), I introduce the Problem of Implementation (a central issue in the physical computation discourse) and argue that it is a species of the Bridging Problem. By subsequently (3) scouting the contemporary solutions to the Bridging Problem, I find that the math-world relation depends on our descriptive practices and does not hold on its own. As a result (4), implementation should also be understood as a three-place relation, where the relata are computational formalisms, physical systems, and epistemic agents. I close by discussing the wider ramifications of this view and suggest some avenues for future research on physical computation.
We often present complexity as being computability in practice : what problem can we solve effectively ? However it is possible to define classes of complexity computing with real numbers in the same way as over the boolean eventhough we can't represent real numbers in computers. How should we understand tractability from an algebraic point of view ?
In the context of traditional computational systems, the notion of computational error has been the object of numerous inquiries. In particular, one of the most fine-grained accounts is based on the Ontology of the Levels of Abstraction (LoAs), according to which traditional computational artefacts are objects existing at many different levels of abstraction whose function is normatively fixed by a formal specification of their behaviour.
I suggest that machine learning systems imply a very different ontology of errors. In fact, a system of this kind is better interpreted as constituted of, not one, but three distinct artefacts: one data artifact (the Training Sample) and two computational artifacts in the traditional sense (Training Engine and Machine Learning Model). Thus, the function of a machine learning artifact is shaped by the functional integration of these three components. Building on this new ontology, I revise the traditional taxonomy of miscomputation, proposing a restructured and expanded classification.
In order to connect information-processing with representations, computational theories of mind (CTM) usually appeal to three ingredients: contents, vehicles and formats. The last has been so far the least explored theoretically, but remains a key explanatory concept in computational neuroscience, esp. in recent debates on the nature of neural representations (Heinen 2024; Pacheco-Estefan 2024). Additionally, the received view on formats in philosophy mainly draws from intuitions about everyday, public representations such as maps, pictures and language-like symbols (e.g. Imagery Debate; Tye 1991), which do not seem well-suited for explanations for computations in the brain.
Recently Coelho Mollo & Vernazzani (2023) convincingly claimed that formats should then rather be understood ‘as computational profiles’ – sets of internal and external constraints that govern the possible transitions within a system (i.e. computations that are relevant to the task at hand). However, I argue that formats are mobilized for explanations in cognitive science practice primarily to detect information that is actually exploited downstream. Literature on neural decodability (‘decoders dilemma’; Ritchie et al. 2019) and behavioural evidence from psychology (Yousif 2022) suggests that information does not simply has to be ‘present’ or ‘stored’ within a certain representational scheme, but also has to be formatted adequately to be available for readout and usage down the drain. Hence, I posit that descriptions simply in terms of possible transformations cannot be sufficient for uncovering the true informational content. Correct formatting to be genuinely informative has to rely on causal and pragmatic relations, too. To ameliorate that, I suggest bolstering computational profiles view with additional conditions, such as Kulvicki’s (2009) ‘immediate availability’ and ‘extractable form’.
Since their appearance in the 1950s, computational models capable of performing probabilistic choices have received wide attention and are nowadays pervasive in almost every area of computer science. Their development was also inextricably linked with inquiries about computational power and resource issues. Although most crucial notions in this field are (considered) well-known, the related terminology is sometimes imprecise or misleading. This talk aims to clarify the core features and main differences between machines and classes developed in relation to randomized computation. To do so, I will compare the modern definitions with original ones, recalling the context in which they first appeared, and investigate the relations linking probabilistic and counting models.
Machine models of computation are based on mechanistic properties attributed to computing, differentiating them from the functional models of computation based on arithmetic properties. The former models are largely inspired by the Turing machine where the description of such a symbolic procedure originally set a bound on the change that the human computer could perform in one step. This characterization of an atomic action was latter depicted by commentators as the condition of locality. It seems essential for describing any discrete computing system and is mentioned in different accounts formalizing it as a restriction set on the transition function. The goal of this talk is to retrace the justifications of such a condition of locality and compare different attempts at giving a mathematical meaning to a mechanistic characteristic, questioning in the meantime its status as an axiom for computation.
The word "algorithm" has entered our everyday life for some time now. However, while it is a common word that can be used to talk about some nebulous object (i.e. a social media algorithm), how do logicians/computer scientists define it ? Turns out while it is a subject that has been and is discussed, there still isn't an commonly accepted definition.
The goal is to first present some historical context : how were algorithm first formalized and why those definition are lacking. Then we will present the characteristics that are commonly seen as useful in a definition of algorithm : mainly, the choice of the context around which the algorithm is defined and the constraint on how we describe said algorithm. Finally, 3 different tentatives to formalize this notion will be presented : 1 from Yuri Gurevich : the ASMs, 1 from Yiannis Moschovakis : the Recursive Programs and 1 from Thomas Seiller : the AMCs and their graphings.
In this talk, I will discuss computing practices, and its relation to practices of proofs, in both mathematics and the historiography of mathematics. To do so, I will focus on a group of equations mathematician Magnus R. Hestenes (1906–1991) wrote in 1950. Initially, Hestenes used these equations as intermediate steps in a series of computations, aimed at deriving a theorem describing the optimal flight of an aircraft. However, in 1961, mathematician Leonard D. Berkovitz (1924–2009) compared the equations to a result just obtained by Soviet mathematicians – namely, Pontryagin's maximum principle. I will show that this comparison relies on a selective reading of Hestenes' work, one that casts shadow on its computational aspects and emphasises so-called results and proofs. Moreover, I will discuss how this reading shaped a memory of Hestenes' work, and how it subsequently shaped the historiography on Pontryagin's maximum principle
Usually in computer science, we tend to study finite structures, as the memory of computers is. The actual cost of computing with them is well-defined and related to their (finite) size. But what if we want to do computations with real numbers, which may have infinitely many digits?
The first "computers", machines doing some computations, were actually working over the reals. In the presentation, we will see several examples of analogue models of computation and how we can redefine the notion of cost in this framework.
Computing can be understood as the formal definition of abstract logical operations. As such, computing can be entierly disconnected from its practical implementation(s), content with only a theoretical way to read and write on an infinite (therefore inexistant) linear medium. Nonetheless, effective computing takes place in specific implementations, in specific contexts. This contribution aims at framing computing through the lens of its power, understood as its potentiality to affect concrete situations.
We intend to look at computing power through three different, yet connected, approaches. First, we will consider computing power as a way to solve problems, by looking at the computational turn of the scientific research. The application of computational methods to non-computational fields, such as social sciences and the humanities, will allow us to investigate the compelling aspects of such a methodological approach (Galloway, 2014; Berry, 2019), focusing on the speed and the scaling of information management. Second, we turn to computing as a actor in Machtpolitik, a political theory of state relation, to analyze how computation is used in practical ways to manage political information (Tufekci, 2014), and depends on a wide range of resources (Bratton, 2016). Finally, we will consider computing as an autotelic process: by managing information, computing information creates more information which must subsequently be managed. By drawing on the work of Jacques Ellul (1964), we will conclude on how the external effects which computing results from an internal drive towards efficiency, and away from complexity.
The recent use of computer programs to apply the law often raises the question of whether law is computable or, more precisely, whether legal reasoning can be reduced to a form of computation. Possible answers can be found by examining the research field of legal logic. Indeed, through time, a number of researchers have proposed formalizations of legal reasoning in the form of logical systems. These proposals are diverse and have been the subject of some criticism. An analysis of these conceptions of legal logic, and of the criticisms that can be levelled at them, can open up new avenues of reflection to determine the extent to which law can be said to be computable.
The negative response to the Entscheidungsproblem in the 1930s established the irreducibility of mathematical reasoning to computation. At the same time several mathematicians and logicians began to think about the possible relationships between logical systems and computational models. Their works led to the so-called Curry-Howard correspondence and their results enabled to develop new tools for doing mathematics known today as interactive theorem provers (ITPs). More or less informal mathematical proofs can be formalised in the language(s) of an ITP in order to be checked by it. In this environment a proof is a program and the correctness with respect to its specification of the latter implies the validity of the former. ITP not only provides a practical tool for mathematicians and computer scientists but also a theoretical tool for philosophers to explore the interactions between the reasoning parts and the computational components of mathematical proofs. In this talk we will try to show, using examples, how ITP can help to identify and articulate these elements.
