Emiliano Ippoliti

In this paper I discuss the epistemic value of a quote and the effect of technological innovations on this value and on market design. The epistemic value of a quote is the agent’s belief about the correct price of an asset. Time, even milliseconds, is an essential feature of this epistemic value: in these milliseconds you can access certain information, and get to know how the markets is moving, and adjust your order to it consequently, so they produce an advantage that can be used to profit, or to avoid losses, from price changes that happen very quickly. The epistemic value of a financial millisecond is the advantage that can be gained by being able to trade in a millisecond faster than your competitors.‘Micro-quotes’ are the result of financial technology innovations. Micro-quotes are quotes with a theoretical expiration date measured in milliseconds since they can be placed and then canceled at any time. I discuss how they produce ‘ghost liquidity’ and a loss of epistemic values, and how a solution is a different market design. In this case a solution is the introduction of speed bumps, which try to level the playing field for traders who do not have the fastest technology by delaying the execution of orders for a short period of time, which gives slower traders a chance to react to price changes. I examine three distinct speed bump worlds (World 1: Takers-priority, World 2: Makers-priority, World 3: No-priority) and their epistemic and moral features, and I discuss how they can be purposely designed based on predetermined objectives. This process falls under the realm of ‘reverse finance’, wherein we begin with specific financial market goals and then create a system that can achieve those objectives more effectively.Finally, I examine how the choice of the target and time threshold of speed bumps is not a value-neutral or technical decision. It has a significant impact on the structure and agents of financial markets, and it is epistemically and morally loaded: it determines who has access to information and who is able to profit from market movements, and also how efficient and stable financial markets are.

This volume presents ten thought-provoking essays exploring issues in the philosophy of finance that are crucial for the economy and society. They also show the mutual relations and benefits between finance and philosophy. These issues include the link between financial systems and climate change, the ontologies of finance that are essential for market design, the role and effect of AI in the financial systems, the nature and prospects of money and their digital version, methodological problems in the use of models and mathematics in the financial world, and critical discussions of some of the main theories on financial systems, like the efficient market hypothesis. As this volume covers a wide array of topics whilst still forming a coherent whole, it is of interest to philosophers of finance, philosophers of science, epistemologists, and philosophers of economics, as well as to scientists and practitioners interested in the debates over methodological, ontological, epistemological as well as ethical issues in finance.

This paper briefly outlines key elements of the heuristic view, which primarily seeks to rationally explain how knowledge is acquired. Central to this view is the concept of discovery, linking the heuristic view to the historical search for a logic of discovery that has been a focal point of philosophy from its early stages through the late nineteenth century. The discussion then centers on comparing Lakatos’ and Cellucci’s versions of the heuristic view, highlighting both shared elements and distinguishing features between the two. Finally, an overview of the trends and future prospects of the heuristic view that emerge by the contributions to this volume is presented.

The heuristic view has evolved over the past few decades to provide a better understanding of how problems are posed and solved. It has become a robust perspective that accounts for the core of cognitive enterprise in a rational and logical way, specifically hypothesis generation. The heuristic view focuses on the process of generating and evaluating hypotheses, not just after the fact (ex post), but also before the fact (ex ante) and in the process of doing so (in fieri). I use these tools to shed light on one of the most influential and controversial hypotheses in finance, the efficient market hypothesis (EMH).I consider the EM’s generation from an historical perspective and argue that several features of the EMH stem from the specific way it was formulated and the heuristic procedures that were employed. A heuristic approach can reveal the EMH’s main features and weaknesses, which could have been identified during its formulation. These weaknesses are primarily the result of the inaccurate application of several heuristic procedures, such as inversion heuristics, datasets with suppressed evidence, and the absence of hypothesis refutation. This has greatly inflated the EMH’s plausibility and scope, extending its degenerative phase.

This volume offers a series of thought-provoking analyses that explore non-mainstream perspectives on knowledge acquisition and scientific discovery. A central theme across many of the contributions is the heuristic conception of method, a view that finds its philosophical roots in Imre Lakatos’s work in the philosophy of mathematics and, more distantly, in Platonic notions of philosophical inquiry. Knowledge acquisition is frequently conceptualized as a form of problem-solving, and problem-solving is typically regarded as a rational endeavor. However, the dominant view in the philosophy of science has long held that scientific discovery resists systematic explanation in terms of logic and rationality. If an alternative account of discovery grounded in these terms can be developed, it would represent a significant theoretical advancement. The essays collected in this book critically assess the promise and limitations of such non-standard accounts, and they investigate the possibility of framing scientific discovery within a logical and rational framework. This volume will be of particular interest to scholars in the philosophy of science, epistemology, philosophy of mathematics, and philosophy of logic, as well as to scientists engaged in theoretical inquiry and graduate students working in these or related areas.

The study of knowledge acquisition and scientific discovery has evolved into its own field thanks to the development of the heuristic perspective. This approach suggests that these processes can be understood through logic, rationality, and problem-solving techniques. Unlike traditional views, which conceive the justification of knowledge logic and rational, the heuristic perspective conceives problem-solving as a means to generate new knowledge in a logical and rational way.Recent advancements in this view have improved our understanding of problem-solving, proposing new methods and even algorithms that could potentially automate these processes. This perspective builds on ideas from philosophers like Plato, Aristotle and Lakatos and has been further developed by scholars such as Popper, Simon, Cellucci, and Magnani. The paper examines the heuristic view, its fresh conceptualization of problem-solving and discovery, and its implications for fields like Big Data and machine learning.

The view from outside on finance maintains that we can make sense of, and profit from, stock markets’ behavior, or at least few crucial properties of it, by crunching numbers and looking for patterns and regularities in certain sets of data. The basic idea is that there are general properties and behavior of stock markets that can be detected and studied through mathematical lens, and they do not depend so much on contextual or domain-specific factors. In this sense the financial systems can be studied and approached at different scales, since it is virtually impossible to produce all the equations describing at a micro level all the objects of the system and their relations. The typical view of the externalist approach is the one provided, for instance, by the application of statistical physics. By focusing on collective behaviors, statistical physics neglects all the conceptual and mathematical intricacies deriving from a detailed account of the inner, individual, and at micro level functions of a system. This chapter examines how the view from outside deals with critical issues such as the mathematical modeling (Sect. 2), the construction and interpretation of data (Sect. 3), and the problem of prediction and performativity (Sect. 4).

This paper sets out to show how mathematical modelling can serve as a way of ampliating knowledge. To this end, I discuss the mathematical modelling of time in theoretical physics. In particular I examine the construction of the formal treatment of time in classical physics, based on Barrow’s analogy between time and the real number line, and the modelling of time resulting from the Wheeler-DeWitt equation. I will show how mathematics shapes physical concepts, like time, acting as a heuristic means—a discovery tool—, which enables us to construct hypotheses on certain problems that would be hard, and in some cases impossible, to understand otherwise.

This book discusses how scientific and other types of cognition make use of models, abduction, and explanatory reasoning in order to produce important, innovative, and possibly creative changes in theories and concepts. Gathering revised contributions presented at the international conference on Model-Based Reasoning (MBR023), held on June 7–9, 2023 in Rome, Italy, the book addresses various intertwined topics ranging from the epistemology and applications of models also concerning the problem of knowledge production and scientific methodology (information visualization, experimental methods, and design) to the analysis of their role in cognition, decision-making, also with respect to social implications. The problem of model-based cognition is also illustrated taking advantage of recent results regarding problem-solving, abduction, and logic, paying attention to a critique of the dominant and received approaches, to the aim of fostering new discussions and stimulate new ideas. All in all, the book provides researchers and graduate students in the fields of applied philosophy, epistemology, cognitive science, and artificial intelligence alike with an authoritative snapshot of the latest theories and applications of model-based reasoning.

Predicting stock markets is a problem that has generated many answers. According to one group of responses, the divergence thesis, it is impossible to accomplish this since the prediction has a ‘bending effect’ that would cause the market to behave in a way that would permanently depart from what was predicted, i.e. the prediction would falsify itself. There are at least three types of impossibility: logical, theoretical and empirical. A second class of responses argues that despite the ‘bending effect’ of predictions, it is still feasible to predicting stock markets. These responses, the convergence thesis, contend that we can achieve it by demonstrating that there are fixed points or that the prediction and market behavior will eventually converge. I expand this line of reasoning by showing that the performativity makes it possible certain predictions by an alignment between the ‘ontic’ and the ‘epistemic’ state of the markets. In addition, I show that performativity enables us to explain how a prediction is produced, why it works initially and then why it fails (i.e. why its predictive power is destroyed).

The ampliativity of deduction has been defended in several ways—such as the semi-decidability of the theories, the surprise of unexpected consequences, the need of new individuals in deduction, or ampliative inference as deduction with suppressed premises (Dummett, Frege. Philosophy of mathematics. Duckworth, London, 1991; Hintikka, Logic, language-games and information. Oxford University Press, Oxford, 1973; Musgrave, Imre Lakatos and theories of scientific change. Kluwer, Boston, 1989; Rota, Indiscrete thoughts. Birkhäuser, Boston, 1997). These lines of defensive arguments fail if we characterize ampliativity in a strong way, that is, in terms of ‘novelty’ stricto sensu, as an inferential process producing genuinely new pieces of information in the conclusion of a reasoning (Cellucci, Rethinking logic. Springer, Dordrecht, 2013; Ippoliti, Heuristic reasoning. Springer, Basel, 2015). Nevertheless, it is possible to defend a weaker stance of the ampliativity of deduction and its usefulness. This requires interpreting novelty more loosely, that is, as the inferential production of new relations among known entities. This stance maintains that, in this sense, deduction can provide us with new knowledge. Thus, a typical deductive activity, as re-proving theorems, can be thought as heuristic and ampliative because it establishes new relations between known elements (e.g. between given axioms or properties and the statement of the theorem). I argue that also this line of defence is defective for it does not account for the necessity and usefulness of reproving theorems. In particular, a foundationalist, axiomatic-deductive viewpoint does not fully account for the usefulness and the weak ampliative power of deduction.

What is a financial crash, and why does it happen? The answers to these fundamental questions require an investigation of the ontological and epistemic state of the financial markets which will identify the causes of a financial crash, the entities involved, and the relations between them.To this end, I examine several theories on financial systems which have conceptualized financial crashes. I analyze how these theories: a) identify different causes of a crash; b) deal with the basic entities and units of analysis; c) define what we can know about those causes and entities, and what they can reveal about an impending crash. On this basis, I outline some ontological and epistemic preconditions that are necessary for a financial crash to occur. I also examine an example of a price drop on the stock market and the role played by the epistemic and ontic states of the market in that event.

How do we get new knowledge? Following the maverick tradition in the philosophy of science, Carlo Cellucci gradually came to the conclusion that logic can only fulfill its role in mathematics, science and philosophy if it helps us to answer this question. He argues that mathematical logic is inadequate and that we need a new logic, framed in a naturalistic conception of knowledge and philosophy - the heuristic conception. This path from logic to a naturalistic conception of knowledge and philosophy explains the title, From a Heuristic Point of View, which recalls the celebrated collection of essays, From a Logical Point of View, by Willard Van Orman Quine, the father of modern naturalized epistemology. The word 'heuristic' points to Cellucci's favorite theme and the main difference between him and Quine: the emphasis on discovery and building a 'logic' for generating new knowledge. This book is a collection of essays from leading figures in this field who discuss, criticize, or expand on the main topics in Cellucci's work, dealing with some of the most challenging questions in logic, science and philosophy.

I argue that mathematical representations can have heuristic power since their construction can be ampliative. To this end, I examine how a representation introduces elements and properties into the represented object that it does not contain at the beginning of its construction, and how it guides the manipulations of the represented object in ways that restructure its components by gradually adding new pieces of information to produce a hypothesis in order to solve a problem.In addition, I defend an ‘inferential’ approach to the heuristic power of representations by arguing that these representations draw on ampliative inferences such as analogies and inductions. In effect, in order to construct a representation, we have to ‘assimilate’ diverse things, and this requires identifying similarities between them. These similarities form the basis for ampliative inferences that gradually build hypotheses to solve a problem.To support my thesis, I analyse two examples. The first one is intra-field, that is, the construction of an algebraic representation of 3-manifolds; the second is inter-fields, that is, the construction of a topological representation of DNA supercoiling.

As the world economy has for better or worse become more and more dependent on the financial markets, a rethinking of the role of finance in both theory and practice is necessary. I argue that such a rethinking requires a new look at the theories of finance that is philosophical in kind. In effect, as Martha Nussbaum claims, if the absence of philosophy in economics is arguably one of the main reasons for the flaws in certain economic theories, the absence of philosophy in finance is one the main reasons for the flaws in our theories on financial systems. In this paper I discuss the mutual relations and benefits between finance and philosophy. First, I examine the contribution that philosophy can offer to finance by analyzing a few critical issues in financial ontology, financial methodology and financial mathematics. I argue that philosophy is essential to enabling finance to achieve the goals for which it was designed, not only because it is a valuable external addition, but also internally, since philosophy is the proper tool for bringing about new theories and approaches. Then, I examine the contribution that finance can offer to philosophy by analyzing the relationship between theory and practice, data and hypothesis, and prediction, description and control in the context of financial systems. I argue that finance can help us to rethink some philosophical tenets on these issues.

The results of Cubitt et al. on the spectral gap problem add a new chapter to the issue of undecidability in physics, as they show that it is impossible to decide whether the Hamiltonian of a quantum many-body system is gapped or gapless. This implies, amongst other things, that a reductionist viewpoint would be untenable. In this paper, we examine their proof and a few philosophical implications, in particular ones regarding models and limitative results. In more detail, we examine the way these theorems model many-body quantum systems, and we question what, if anything, is the physical counterpart of the models used by Cubitt et al. We argue that these models are non-representational and that, even if they are so artificial that it is hard to imagine a physical system arising from them, they nonetheless offer an opportunity to learn about the world and the relation between mathematics and reality. On this basis, we draw the conclusion that their results do not undermine the reductionist viewpoint in a strong sense but leave the question open in a weak sense.

This paper sets out to show how mathematical modelling can serve as a way of ampliating knowledge. To this end, I discuss the mathematical modelling of time in theoretical physics. In particular I examine the construction of the formal treatment of time in classical physics, based on Barrow’s analogy between time and the real number line, and the modelling of time resulting from the Wheeler-DeWitt equation. I will show how mathematics shapes physical concepts, like time, acting as a heuristic means—a discovery tool—, which enables us to construct hypotheses on certain problems that would be hard, and in some cases impossible, to understand otherwise.

I examine the role that mathematics plays in understanding and modelling finance, especially stock markets, and how philosophy affects it. To this end, I explore how mathematics penetrates finance via physics, constructing a ‘financial physics’, and I outline the philosophical backgrounds of this process, in particular the ‘philosophy of equilibrium’ and that of critical points or ‘out-of-equilibrium’. I discuss the main characteristics and a few weaknesses of these mathematizations of financial systems, notably econometrics and econophysics, and I compare the two ways, top-down and bottom-up, of building mathematical approaches to finance. The top-down approach is the most used and the most conservative. I argue that it guarantees a mathematical account, but it is less effective than the more difficult bottom-up approach, which is more appropriate and which may end up without a mathematical account of financial phenomena. I then consider two important issues raised by a mathematical approach to finance, that is, the performative and the reversing side of mathematics, and an ethics of mathematics. In the first case I argue that mathematics not only can be a performative device, but it also enables ‘reversing’ dynamics, that is, a mathematical model may become not a representational tool, but a device of social engineering—a mathematical way of investigating what are the initial conditions and processes needed to obtain an intended result. In the second case I argue that this specific relation between mathematical modelling and prediction raises an ethical question in finance, namely, a responsible construction and use of the mathematical models provided by a financial physics.

In my paper, I examine the role that models play, and the relation between models and data, in financial systems, in particular in stock markets. I discuss several dangerous liaisons between models and data both from a theoretical and a practical viewpoint, and I consider their effects on the behaviour of the financial systems and their actors.I will examine two issues in particular.First, these liaisons defy the way traditional philosophy of science accounts for models and the relation between models and data, as stock markets exhibit several dynamics and features that do not fit them. For instance, they challenge the ontological issue about models (the debate about the fictional character of models), or the way models and phenomena are connected, and consequently undermine classical taxonomies as ‘models of data’, ‘models of phenomena’, ‘models of theory’.Second, these relations and liaisons open the way to possible exploitations and manipulation of stock market’s dynamics by means of appropriate use of models and data, including ‘reverse finance’, which should be closely analysed in order to contribute to better functioning and serving of the financial systems.

The nature of the data of financial systems raises several theoretical and methodological issues, which not only impact finance, but have also philosophical and methodological implications, viz. on the very notion of data. In this paper I will examine several features of financial data, especially stock markets data: these features pose serious challenges to the interpretation and employment of stock markets data, weakening the ‘myth of data’. In particular I will focus on two issues: (1) the way data are produced and shared, and (2) the way data are processed. The first raises an internal issue, while the second an external one. I will argue that the process of construction and employment of the stock markets data exemplifies how data are theoretical objects and that ‘raw data’ do not exist. Data are not light and ready-to-use objects, but have to be handled conceptually and technically very carefully and they are a kind of ‘dark matter’. Dark data, for the note.

The view from inside maintains that not only to study and understand, but also to profit from financial markets, it is necessary to get as much knowledge as possible about their internal ‘structure’ and machinery. This view maintains that in order to solve the problems posed by finance, or at least a large part of them, we need first of all a qualitative analysis. Rules, laws, institutions, regulators, the behavior and the psychology of traders and investors are the key elements to the understanding of finance, and stock markets in particular. Accordingly, data and their mathematical analysis are not the crucial elements, since data are the output of a certain underlying structure of markets and their actors. The underlying structure is the ultimate object of the inquiry. This chapter examines how the view from inside raises, and deals with, critical issues such as markets failure, information disclosure, and regulation, the notion of data, performativity, and the study of micro-structures.

The examination of the construction of several approaches put forward to solve problems in topology and knot theory will enable us to shed light on the rational ways of advancing knowledge. In particular I will consider two problems: the classification of knots and the classification of 3-manifolds. The first attempts to tell mathematical knots apart, searching for a complete invariant for them. In particular I will examine the approaches based respectively on colors, graphs, numbers, and braids, and the heuristic moves employed in them. The second attempts to tell 3-manifolds apart, again searching for a complete invariant for them. I will focus on a specific solution to it, namely the algebraic approach and the construction of the fundamental group, and the heuristic moves used in it. This examination will lead us to specify some key features of the ampliation of knowledge, such as the role of representation, theorem-proving and analogy, and will clear up some aspects of the very nature of mathematical objects.