Ataraxia

Introduction

The description of how the scientific knowledge is justified, organized and changes with time is one of the intentions of the philosophy. One of its central questions is the issue of the empirical evidence in favor of the theoretical hypotheses.

There has been a long-standing debate among philosophers on whether science is based on critical falsification as suggested by Karl Popper, or on inductive generalizations. Although both models have had a significant impact on the field of science, none of them offers a completely satisfactory explanation of the way modern scientific reasoning works in practice.

Indeed, inductivism and falsificationism have severe flaws. The problem of induction is that there is no a circular way to justify inductive inferences (Hume's problem) and falsificationism cannot describe the empirical dynamics of confirmation in modern science, which does not usually rely on a single decisive experiment.

It is against this context that Bayesianism has come out as a strong alternative. It offers a quantitative and flexible model to allow scientists to rationally modify their confidence in hypotheses as new data is obtained by interpreting reasoning as a process of probabilistic belief updating on the basis of the Bayes theorem.

The following essay discusses Bayesianism as a scientific confirmation theory, with a case study of the discovery of the Higgs boson in CERN in 2012. It states that Bayesianism is an effective way to model the rational dynamics of belief change when new evidence is presented, and also admits that it has its own weaknesses when it comes to theory change and paradigm shifts.

The Problem of Induction

According to the problem of induction that was argued by David Hume, past observation cannot logically ensure that the future will follow the same pattern. Inductive reasoning makes use of a finite number of observations to formulate a general statement.

Hume said that reasoning alone cannot be used to justify inductive, without falling into circularity: we would have to have assumed the homogeneity of nature, that the future will resemble the past, to justify induction.

Efforts to improve induction through a probabilistic reformulation, asserts that most general laws are probably true if there is a sufficient amount of evidences. But this fails mathematically too, because the probability with finite evidence that a statement of general laws is true is near to zero.

It is out of this crisis that scientists followed an alternative model that can explain rational belief revision by not involving certainty, but rather embraces uncertainty as a fundamental part of scientific method.

The Problem of Falsificationism

Falsificationism by Popper replaced the concept of inductive confirmation with the concept of conjecture and refutation: scientific theories cannot be proven true, but falsified by counter-evidence. A scientific theory should be falsifiable which means that it has possible observations that can make it wrong.

However, this model has its problems, too. First, there are auxiliary assumptions, background conditions, measurement models and instrumentation hypotheses, which are always involved in testing a theory as demonstrated by the Duhem-Quine thesis and the research programmes of Imre Lakatos. When an experiment goes against a prediction, it is not always clear which assumption is to fault.

For instance, science does not give up about a theory once it is proven to be wrong. Scientists, as Thomas Kuhn and Lakatos suggested, usually work within paradigms or research programmes that allow to have discrepancies until a superior alternative is found.

Falsificationism therefore does not reflect the incremental and probabilistic aspect of confirmation in actual science. A more realistic description is provided by a probabilistic model such as Bayesianism, which does not falsify a hypothesis but rather raises or lowers the level of belief in the hypothesis.

Bayesianism

Bayesian reasoning is described mathematically by Bayes' theorem, which was formulated by Thomas Bayes:

$$P(H|E) = \frac{P(E|H),P(H)}{P(E)}$$

where:

• $P(H)$: prior probability of hypothesis $H$;
• $P(E|H)$: likelihood of observing evidence $E$ if $H$ is true;
• $P(E)$: overall probability of observing $E$;
• $P(H|E)$: posterior probability, the updated degree of belief in $H$ after observing $E$.

This model implicates that in case of new evidence there is no a certain conclusion, instead, the weight of the probabilities of hypotheses is changed. When $P(E|H)$ is high, then we will have a high confirmation of H.

A logic of scientific justification is then demonstrated by Bayesianism to a problem of updating of beliefs. Scientific reasoning turns into a learning process without end and every bit of evidence contributes to a progressive modification of credence.

Bayesianism has two main interpretations:

• Objective Bayesianism: we have to give probabilities in the basis of objective principles, like the Principle of Indifference. We give them equal chances when we do not know that any particular hypothesis is better than another;
• Subjective Bayesianism: probabilities are degrees of belief which in fact are held by individual scientists. Every scientist initially makes his own priors in terms of the background knowledge and rationalizes them by means of the Bayes theorem.

However, the two perspectives have one thing in common; with evidences shared to the scientific community, the beliefs are drawn to a fixed posterior distribution that we refer to as scientific consensus.

Bayesianism considers the background knowledge. In fact, the probability of the likelihood $P(E|H)$, should not be simply on H alone but on a set of additional hypotheses on instruments, theoretical models and measurement accuracy. This is the truth of modern day science where there is no hypothesis that is ever tested on its own.

The Higgs Boson

The Higgs boson plays a central role in the Standard Model of particle physics: it shows how elementary particles obtain a mass through the process of spontaneous symmetry breaking in the electroweak sector. Peter Higgs, Francois Englert and others proposed it first in 1964, independently.

The theory states that the universe is filled with a scalar field, referred to as Higgs field, which interacts with particles, including W and Z bosons, to give them a mass. The quantum excitation of this field is a new particle, called Higgs boson.

The Higgs boson was the long missing puzzle of the Standard Model: this was true in theory, but the direct observation of it was technically absent. With the help of the data of the previous CERN accelerators, Large Electron-Positron Collider (LEP) and Tevatron, experimental physicists successively narrowed the range of possible masses of the Higgs, with evidence suggesting that should it exist, it would be lighter than 200 GeV.

Therefore, the pre-2012 probability of the Higgs hypothesis being true known as $P(H)$ was large but not definite: even though the Model strongly favored it, the absence of its observation continued to leave the possibilities of having new alternatives.

At one point, CERN constructed the Large Hadron Collider (LHC): a ring of superconducting magnets with a circumference of 27 km with the ability to accelerate protons to 13 TeV and collide them. The detectors ATLAS and CMS were two massive detectors in charge of searching the Higgs boson independently.

Case Study: The Discovery of the Higgs Boson

An example of Bayesian confirmation in modern physics is the discovery of the Higgs boson in 2012 at CERN.

The LHC experiments (ATLAS and CMS) examined events involving billions of proton-proton collisions and reassembled the resultant products to identify excesses that would be associated with the Higgs signal. The Higgs would manifest itself as a narrow resonance at a certain value of the mass which is essentially a bump in the distribution of energies.

Suppose that the hypothesis is as follows; $H$: "The Higgs boson exists and has a mass of less than 200 GeV" and $E$: "an excess number of events are seen". Then the likelihood $P(E|H)$ is the probability of such an excess, had the particle really existed, and the complementary likelihood $P(E|\neg H)$ is the probability of the background fluctuating in the same way to provide precisely the same excess.

These experiments demonstrated that $P(E|\neg H)$ was quite low, of the order of one in 3.5 million, which relates to the $5\sigma$ level of significance. That is, assuming that the null hypotheses were correct, that no Higgs boson existed, then such an excess would occur almost never by chance.

In terms of Bayesian, that is, the probability of $P(E|\neg H)$ was very small, while $P(E|H)$ was immense. Thus, posterior probability that the Higgs exists, $P(H|E)$ being the probability that the Higgs exists given data seen, was also close to one. The Higgs hypothesis made such strong predictions of experimental data, and under the condition of its negation turned them into such improbabilities, that rational belief of the existence of the particle has become almost but not absolutely certain.

This was discovered in bits: initial data of significance of $2\sigma$ or $3\sigma$ statistic slightly raised the posterior probability, but next data gradually confirmed the belief. This incremental updating of confidence is what fits the model of rational learning of Bayesian model.

Moreover, the $5\sigma$ rule of the particle physics community can be interpreted as a decision level that is associated with a sufficiently large posterior probability that is acceptable. Although physicists usually develop their discoveries using frequentist tests, such as using the $p$-values and $\sigma$-values, their structure of inference remains bayesian.

Philosophically, this demonstrates how implicitly even nominally frequentist methodologies justify themselves by Bayesian reasoning. Physicists believe, not only the numerical value of the answer but also its theoretical reasonableness and consistency with previous models and the danger of systematic bias of Bayesian inference.

Also, the ATLAS and CMS results are combined, which proves the Bayesian model averaging practice. The independent likelihood functions that were provided by each experiment; the combination of them allowed the scientists to create a global posterior that represented the totality of available evidence.

This led to the announcement of the discovery on July 4, 2012, of the observation of a new particle that was in agreement with the Higgs boson, the combined significance of which was over $5\sigma$.

What took place here is that some high prior prediction was revised to a almost maximal posterior conviction, a paradigmatic illustration of scientific confirmation.

The Scientific Confirmation

The Higgs case demonstrates several philosophical points of view on the Bayesian concept of science.

To begin with, confirmation is not a binary concept. Scientific belief is a development, by means of the posterior revisions and by the increment of evidence. The monitored boost in confidence of the Higgs is a perfect example of the Bayesian learning curve.

The second one is related to the strong interdependence of the theory and evidence. The data analysis of the LHC relied on complex simulations, with the Standard Model, detector calibration and background models, all aspects that Bayesianism formally formalizes, using conditional probabilities.

Third, Bayesianism clarifies the position of discovery. Physicists never established the Higgs in some absolute sense; they gained a posterior probability that was so likely to be certain that it was irrational to doubt this further. The discovery then not only is not logical demonstration, but is a great probabilistic confirmation.

But Bayesianism is too has its weaknesses. It provides the assumption of a given hypothesis space and unchanging background conditions. In practice, when a scientific revolution appears, as the Newtonian mechanics to the quantum one, the hypothesis-evidence model has to evolve. Bayesian updating has difficulty in responding to these paradigm shifts, as between mutually incompatible conceptual systems there are priors and likelihoods whose meaning has been lost.

In this regard, Bayesianism has a very good explanation of science, but it needs the addition of historical and sociological explanations to comprehend revolutionary science.

However, the Bayesian model is invaluable: it represents the most accurate formal model of confirmation, coherence and rationality existing in the modern science.

Conclusion

Bayesianism constitutes one of the most consistent, realistic philosophical frameworks of scientific reasoning. It regards belief constantly revised with evidence as grades of knowledge and in this way reconciles the empirical experiments of science with their theoretical model.

The Higgs boson was actually found demonstrating this process of gradual learning, where the experimental data gradually changed the theoretical prediction of its existence into a near-certainty, with each new dataset greatly narrowing the posterior belief of the hypothesis until it was discovered to be nearly certain plausible.

However, Bayesianism cannot solve all the difficulties alone: it fails concerning theory change. But Bayesianism has the success that inductivism and falsificationism fail to achieve: it describes the rational processes of belief in the uncertainty of empirical experience.

Science is never successful in achieving any absolute truth, it is successful in dealing with uncertainty, in handling the degrees of our beliefs in the light of the continually increasing data of the world.

Science and Pseudoscience

Science and pseudoscience have always had an ambiguous relationship. We usually know how to recognize, at a glance, what is scientific and what is not. In today's world, immersed in technological progress, this distinction seems almost obvious: science produces medicines, machines, computers and etc.; pseudoscience, on the other hand, seems to be a set of confused and uncertain beliefs. Yet, when we try to transform this intuition into a clear definition, the boundary becomes blurred: what is science? And on what basis can we say that one practice is scientific and another is not?

This is where the problem of demarcation arises: in order to draw a non-arbitrary line between science and non-science, we need to clarify at least two fundamental things:

• how science produces knowledge (the method);
• how and why this knowledge improves over time (progress).

Without a theory of method and progress, we risk defining science in a circular way ("science is what scientists do") or purely sociologically ("science is what the state calls science"), and then it becomes difficult to justify why some practices should be excluded and others accepted.

In this sense, demarcation is not only a descriptive issue ("what scientists do"), but also a normative one: it implies criteria on how they should work to produce reliable knowledge. It is, therefore, inevitable to reflect on the scientific method: not as a rigid¹, but as a set of constraints aimed at reducing error and making our knowledge of the world possible and public.

Scientific Method and the Concept of Progress

There is a saying that it is often more important to ask the right questions than to have the right answers. In fact, science almost always born from a question: about how nature works, about the causes of a phenomenon and about the patterns we observe. Since ancient times, humans have sought answers to questions such as why the sun rises and sets, why the stars move, why the sky is blue and etc.. For long periods of history, explanations relied on myths, legends, or supernatural agents: not necessarily irrational in the cultural context of the time, but often difficult to control and test.

Science, on the other hand, is characterized by a systematic approach: it is not enough to tell a plausible story; explanations must be constructed that can be publicly evaluated and, at least in principle, disproved by facts.² Schematically, a typical cycle includes:

1. Formulation of the problem: they are guided by prior knowledge, conceptual tools (e.g. math), and often by anomalies (something that does not add up).
2. Hypotheses: a clear and binding hypothesis is proposed; it must say not only "what could be true", but also what we expect to observe if it were true.
3. Empirical tests (observations, experiments, measurements): data is collected using transparent, controlled, and replicable procedures (or at least replicable under comparable conditions).
4. Critical evaluation and review: if the data contradict the hypothesis, the hypothesis must be modified or abandoned; if they support it, it does not become "true once and for all", but gains credibility and is subjected to more rigorous testing.
5. Sharing and external control:³ paper publication, peer review, discussion with the community, attempts at replication: science is also a social process, but with rules aimed at reducing errors, bias, and self-deception.

Without a clear idea of method, any practice could present itself as scientific, making the demarcation inevitably arbitrary. Method serves not only to describe what science does, but also to establish constraints: what kind of claims are admissible, how they must be justified, and how they can be challenged.

Similarly, scientific progress does not consist of a simple linear accumulation of facts or notions, but of a continuous improvement of knowledge over time: greater empirical accuracy, more predictive power, better control of errors, and the ability to integrate previously separate phenomena. Theories are not preserved because they are "true once and for all", but because they are, at present, the best available to explain and predict an phenomena.

A central point is that science never claims absolute certainty. At most, a theory is considered highly reliable within a certain domain and with a certain degree of confidence. This fallibility attitude is a strength: admitting the possibility of error does not mean "knowing nothing", but knowing responsibly, indicating limits, conditions, and margins of uncertainty. Pseudosciences, on the contrary, often tend to present dogmatic or refutable theses, avoiding what could disprove them.

Inductivism: Generalization of Facts

Inductivism is one of the responses for the demarcation problem, by which the science forms the general laws basing on the specific cases. A research process starts with observation of phenomena in the reality, by repetition of observations and discovery of regularities, more generalization is developed. For example, we see that, day after day, the Sun rises and sets, of a long succession of such cases, we conclude there is a kind of law of the kind: "the Sun rises and sets every day".

But, here the weakness of induction is obvious: the fact that it is always occurred is not logically bound with the fact of its occurring forever. A vast number of observations do not draw to a generalized conclusion: there is always the possibility, however small, that an exception will be made in some future, or that some other case will be studied to invalidate the generalization. This is not to say that induction is useless: it simply cannot give absolute logical certainty, but only probabilistic and pragmatic support.

This is also significant to demarcation. Whether the science is based on observation and experiments, inductivism appears to provide an easy criterion: what is verified with numerous facts is scientific. This is however not enough as a demarcation criterion. A pseudoscience may pose itself as empirically grounded through the cherry-picking of only positive examples and ignoring the negative ones. This is where cherry-picking comes into the game: it is not hard to find confirmations when one is free to arbitrarily select what observations to pay attention to. This is why it is not the quantity of evidence one (it is still important), but the manner in which the evidence chosen and tested: protocols, controls, replicability, error analysis, comparison with possibly undesirably data.

Another flaw is that observations are not absolutely neutral pure data. They are also restricted to reality and they are always aggregated and interpreted in a theoretical framework: the choice of what to measure, what instruments to apply, what categories to apply, how to deal with noise, is subject to assumptions and models.

In a few words, induction does reveal something true, the empirical concretion of science, but it cannot, of itself, rationally prove universal laws, or decisively distinguish science and pseudoscience.

Popper: Falsifiability

Another possible solution is the principle of falsifiability by Karl Popper. This is because Popper asserts that a theory is only scientific, when it puts itself to the danger of being disproved by observations or experiments: it has to make statements that are clear, to be disproven in the light of potential contrary evidence. In this view, we can go back to the concept, that no theory can be conclusively verified. Scientific advancement is not piling up evidences to the verified side, but subjecting our knowledge to constant and intense stress, to find out how far it will be held and whether there are superior models.

Science is falsifiable, while pseudoscience systematically takes positions against the danger of being disproved. Pseudosciences also have a tendency to come up with vague theories which are difficult to refute, by the expedient of retroactive explanations, semantic ambiguities, or ad hoc hypotheses that have no testable consequences. To the contrary, a good theory explicitly contains what is supposed to happen in the event that it is true and what is supposed to refute it in the event that it is not.

The merits of the Popperian criterion are evident: it is concerned with the importance of empirical testing and why science can only develop through criticism and not through confirmation. Nonetheless, it has significant limitations as well. To begin with, the thesis of Duhem-Quine demonstrates that falsifications are not unambiguous; an empirical test does not impact one disconnected hypothesis, but a system (auxiliary hypotheses, initial conditions, measuring instruments, theoretical models). When an experiment disproves a prediction, it is not logically decided what aspect of the theoretical system to give up.

Second, one can hardly make a distinction between legitimate and ad hoc adjustments made to a theory with the aim to either enhance the predictive power of that theory, or, to avoid its disproving due to the lack of the new empirical material.

In summary, the criterion of falsifiability clarifies the role of empirical risk and criticism in the scientific method and offers a more robust demarcation than inductivism. However, in order to fully explain the actual work of science and its historical dynamics, it must be integrated with considerations of the theoretical context, underlying assumptions, and actual practices of scientific communities.⁴

Kuhn: Science as a Communal Activity

Thomas Kuhn proposes a change of perspective: science is a communal and historical activity. Scientific knowledge is not the product of isolated genius, but the result of collective work involving communities of researchers spread across time and space. In this sense, science is a global job of humanity, rather than of the individual.

Kuhn observes that scientific development alternates between two phases:

• Normal science: stable periods in which a community works within a shared paradigm. The paradigm provides ideal models, conceptual tools, methods, evaluation standards, and criteria for acceptability. In this phase, scientists do not question the foundations of the paradigm, but solve problems within it.
• Scientific revolutions: phases of crisis in which anomalies accumulate, the dominant paradigm loses its explanatory power, and a new paradigm may emerge that radically reorganizes the field.

In this perspective, the demarcation is not given by a single logical criterion (induction or falsifiability), but by the fact that a practice operates within a paradigm recognized by a scientific community. Today, for example, in order to publish an article, it is necessary to comply with shared rules and standards: methodological clarity, comparison with the literature, verifiable and replicable data, transparent use of tools, formal language, and explicit limits. These rules are self-imposed by the community to make knowledge communicable and open to criticism. Without shared rules, rational discussion and progress would become impossible.

Pseudosciences, on the contrary, often lack a stable paradigm: they do not generate problems that can be solved systematically, they do not accumulate comparable results, and they do not have common criteria for evaluating successes and failures.

Kuhn's merit is to describe scientific practice and the dynamics of revolutions realistically, highlighting the importance of the community. However, the main limitation concerns the comparison between paradigms: if each paradigm defines its own standards, how can we say that one is "better" than another without falling into an epistemological relativism? How can we say that relativity is "better" than Newtonian mechanics, or that quantum mechanics is superior to classical physics, without falling into a form of relativism? Kuhn's emphasis on the historical-social dimension aspects, making it more difficult to establish a clear normative demarcation.

Lakatos: Research Programmes

Imre Lakatos attempts to mediate between Popper's falsificationism and Kuhn's historicism. On the one hand, he rejects Popper's idea of immediate and decisive falsifications; on the other, he distances himself from the relativistic risk inherent in Kuhn's notion of paradigm. His proposal is that of scientific research programs, interpreted as historical theoretical structures that develop over time and guide the activity of a scientific community.

A research program includes:

• a hard core, consisting of fundamental assumptions that are not abandoned by its supporters;
• a protective belt, consisting of auxiliary hypotheses, models, and initial conditions, which can be modified to respond to empirical difficulties.

When anomalies emerge, they generally affect the protective belt and not the hard core: this explains why theories are not immediately abandoned and provides an clear answer to the problem raised by the Duhem--Quine thesis: the failure of a prediction does not automatically imply the abandonment of the entire theoretical framework, since it is often attributes the error to correctable auxiliary hypotheses, rather than to the core of the program.

A program is scientifically valid if it produces new empirical predictions, and at least some of these predictions are actually confirmed. Instead, it becomes degenerating when it merely accommodates already known facts retroactively, introducing ad hoc adjustments to the protective belt without increasing the empirical content or predictive power.

Thanks to this, pseudoscience typically takes the form of degenerating research programmes: they do not produce new and risky predictions, but react to refutations only with retroactive adjustments, often without independent empirical consequences. Unlike progressive scientific programs, pseudosciences do not show growth in empirical content over time, nor do they show improvement in explanatory or predictive capabilities.

However, Lakatos' approach also has its limitations. In many cases, the assessment of a program as progressive or degenerating is only clear in hindsight, when the historical outcome is already known. In real time, it is often difficult to determine whether a program is going through a temporary phase of difficulty or whether it is actually degenerating. Furthermore, the line between science and pseudoscience remains unclear: some pseudoscientific programs can survive for a long time by promising future confirmations without providing them, making immediate and definitive judgment problematic.

Feyerabend: Criticism of the Universal Method

Paul Feyerabend criticizes the idea of a universal scientific methodology. There is no methodological criterion that is valid in every era and in every context and, consequently, there can be no universal criterion about the problem of demarcation. The history of science shows that many great innovations have violated methodological rules considered rational and correct in their time. It is not an invitation to total chaos or arbitrariness, but a critique to the idea that there is a fixed methodological recipe capable of guiding and justifying all scientific progress.

From this perspective, scientific progress is not the result of the mechanical application of immutable rational rules, but also depends on historical, social, and cultural contingencies. Decisions about which theories to accept or reject are not always determined exclusively by logical or empirical criteria, but also involve pragmatic, psychological, and institutional factors. The main merit of Feyerabend's position is that it destroys the myth of a rigid science and highlights the role of theoretical plurality, creativity, and even the conscious violation of rules as possible drivers of scientific innovation.

However, it is precisely this radical pluralism that raises a serious problem in terms of demarcation. If there are no shared methodological criteria, it becomes difficult to explain why some practices should be considered scientifically reliable, and others not. In particular, Feyerabend's position risks weakening the distinction between science and pseudoscience: if there is no method and if even breaking the rules can be valid, then a pseudoscientific practice could claim legitimacy as a simple alternative to official science.

In the absence of shared evaluation criteria, the danger is that pluralism will turn into epistemological relativism, making it impossible to distinguish between legitimate scientific criticism and simple rejection of evidence.

In summary, Feyerabend offers a powerful critique of methodological dogmatism and highlights the historical complexity of real science. However, the price of this position is a significant weakening of the normative demarcation between science and pseudoscience.

Case Study: COVID-19 as a Demarcation Case

The COVID-19 pandemic has made visible to everyone, how science operates in conditions of urgency and uncertainty, bringing aspects of the scientific method that are not generally familiar to the non-specialist public.

Throughout the introduction of mandatory vaccination, the "no-vax" movement has gained considerable visibility. One of the most common criticism concerned the possible side effects. Like all drugs, vaccines could cause side effects; however, the vast majority of effects are light and temporary, while serious reactions are extremely rare. The philosophically relevant point, however, is more general: in modern medicine, decisions are never made in terms of zero risk. The "zero risk" option does not exist; every healthcare decision is a choice between different risks, weighed against the expected benefits.

The issue of long-term effects is a particularly clear example of scientific reasoning in conditions of uncertainty. At the start of the vaccination campaign, long-term data were not available; however, this was not equivalent to "gambling", but rather making a decision based on the best available evidence. In this context, science shows its fallibilist character: it does not promise absolute certainties, but quantifies uncertainty and manages it in a rational and transparent manner.

Finally, the debate on vaccines shows why no single criterion of demarcation is sufficient on its own. Induction is vulnerable to arbitrary selection of evidence; falsifiability is not always immediate due to auxiliary assumptions; paradigms evolve historically; research programs are evaluated over time; and Feyerabend reminds us that actual scientific practice is more complex than any rigid methodological scheme. However, taken together, these tools allow us to understand why the scientific response to the pandemic, while imperfect, is epistemically justified: it was based on controlled data, public reviews, critical comparison of alternatives, and transparent management of uncertainty.

Conclusion

Pseudosciences have historically contributed to the formation of epistemic bubbles within societies, separated from the rest of the public debate. These bubbles tend to develop in opposition to shared scientific knowledge, a bit like salmon swimming upstream: a current that, in most cases, represents not an arbitrary imposition, but a collective attempt to protect the common good.

The consequences of such attitudes are not limited to the individual sphere. Vaccine refusal, for example, not only poses a personal risk, but also undermines collective protection, encouraging the possible reappearance of diseases that we considered defeated. Similarly, climate change denial is not a neutral position: it has potentially harmful effects on a global scale, influencing political and economic decisions that affect the entire planet. The examples could be multiple, but the central point is that pseudoscience produces negative externalities, affecting people who do not share those beliefs.

However, it would be simplistic and presumptuous to dismiss these phenomena by attributing them solely to the selfishness or bad faith of the individuals involved. Before judging, it is necessary to understand the conditions that make these dynamics possible in order to address them effectively.

In the end, it is essential to be able to reason in a structured way, not intuitively or randomly, but following the methodological principles that characterize scientific thinking: attention to evidence, awareness of limitations, openness to revision and etc. Only by strengthening these skills can we reduce the influence of pseudoscience and encourage more responsible and rational participation in social and political life.

Introduction

Science has often described scientific practice as a trichotomy of three fundamental elements:

• Theories: build a conceptual framework to explain and predict phenomena;
• Observations: collect data about the world;
• Experiments: allow controlled interventions on a physical system to test hypotheses, laws and models.

However, in many cases, we cannot directly manipulate the system of interest (e.g., gravitational waves, black holes, exoplanets and etc.), nor can we observe the phenomenon "directly" without complex chains of instrumental mediation.

Therefore, scientific practice incorporates tools that fall outside the theory-observation-experiment trichotomy: from thought experiments to computer simulations. These tools share a common trait: they allow us to exercise what we call surrogate reasoning, that is, a reasoning about a "substitute" (mental, mathematical, or computational), to reach plausible conclusions about something else (an object, a process, or a theory).

Sometimes, science goes beyond the traditional, because, the world we want to understand is often non-manipulable, not directly observable, or too complex to be observed without intermediate tools.

Why Scientific Practice Goes Beyond the Trichotomy

The traditional trichotomy works well when the ideal conditions for scientific method are met: we can intervene in the system, repeat the test, isolate variables, produce relatively transparent observations, and compare them with theoretical predictions. But there are at least three systematic reasons why these conditions are not always available.

Experimental Impossibility or Impracticability

Many systems are beyond the reach of human intervention: cosmic events, phenomena on enormous scales, or processes too dangerous to manipulate. Even when an experiment would be possible in principle, it may be economically unsustainable or require unavailable technologies. Here, science cannot do without indirect tools.

Heavily Mediated Observations

Many data are not simple readings of the world, but the output of extraction and transformation procedures (filters, reconstructions, calibrations, statistical inference). In these cases, speaking of observation as "pure raw data" is quite misleading.

Theoretical and Mathematical Complexity

A theory can be well-formulated yet not analytically calculable. Without computational tools, we would be unable to explore the consequences of the theory or produce usable predictions.

These three elements explain why scientific practice develops and uses additional tools. In particular, computer simulations exist in a hybrid zone: they resemble experiments because they allow exploration, manipulation (on parameters), and the production of "data-like" outputs; but they also resemble models, because they are surrogates for the real system and depend on theoretical assumptions. This hybridization is crucial to understanding their epistemic value and the philosophical problems they generate.

Gravitational Waves and Computer Simulations

Gravitational waves are ripples in space-time predicted by general relativity. The idea of detecting them might seem like a simple observational exercise: build a detector and measure. In reality, the process is much more complex and perfectly illustrates why the traditional trichotomy, alone, are not enough.

Interferometric detectors (such as LIGO and VIRGO) measure tiny variations in the length of the interferometer's arms. The expected signal is extremely weak and immersed in complex noise (seismic, thermal, instrumental, and etc.). Consequently, the question is not just "what did the instrument measure?" but "how do we distinguish a real physical signal from a fluctuation or an artifact?" and "how do we assign a precise physical interpretation to the signal?"

This is where simulations come into play in a crucial way. They serve to:

1. Build theoretical templates (waveforms) for different physical scenarios (black hole mergers, neutron stars, and etc.);
2. Perform detection through matched filtering: compare data with expected templates and search for statistically significant matches;
3. Perform parameter estimation: once a signal is found, estimate physical parameters and uncertainties by comparing the data with families of waveforms, obtained via simulation;
4. Assess robustness and significance: build background noise, estimate false positive rates and verify that the event is not caused by known bugs.

A key point is that simulation is not just "post-processing": it is an integral part of the identification criterion of a gravitational wave.

Main Philosophical Problems

Problem of the Theoretical Dependence of Evidence

The identification of the signal depends on templates produced by numerical modeling. It, therefore, seems that the evidence is profoundly theory-based. This raises the question: "are we really observing something in the world, or are we finding in the data what the theory tells us to look for?"

Problem of Justification and Risk of Circularity

If the signal is recognized by comparison with simulated waveforms, is there a risk of circularity: "does the theory produce the templates, and do the templates confirm the theory?"

Problem of the Reliability of Simulations

Numerical simulations require approximations and assumptions about initial conditions. How can we ensure that the outputs are reliable and not computational artifacts?

Problem of the Epistemic Status of Simulations

A simulation produces data-like outputs, but they are not data from the world: they are data from the model. In what sense, then, does it contribute to empirical knowledge? Is it a form of experiment? An extension of theory? A model of an experiment? This point is crucial because it determines how we evaluate the evidential strength of the discovery.

Two Approaches to Addressing the Philosophical Problems

Approach A: Simulations as a Form of Experiment

An immediate way to understand computer simulations is to compare them to experiments. Even if we don't directly intervene in the target system, we can still conduct experiments on its computational counterpart: we set initial conditions, evolve the system according to rules drawn from theories, observe the output, and then repeat the procedure by changing parameters and hypotheses. In this sense, the simulation is a virtual laboratory: intervention consists of varying inputs and assumptions; observation consists of interpreting results, often treated as data.

This perspective clearly explains the operational nature of simulations in contemporary science. Scientists use them not only to calculate theoretical consequences, but also to explore spaces of possibility: they perform repeated runs, compare outputs, look for patterns, study sensitivity to small variations, and sometimes encounter dynamics that are unexpected compared to initial expectations. Calling them "experiments in silico", therefore, captures an important aspect of the practice: the iterative, exploratory, and procedural aspects.

Approch B: Simulations as Surrogate Tools that Model Possible Experiments

A second approach starts from the idea that simulations resemble experiments in many ways, but do not coincide with them. What we call "intervention" in a simulation is not an intervention on the target, but rather on a representational system. Similarly, "observation" concerns outputs generated, according to a prior defined rules and assumptions. Consequently, simulation is best understood as a practice that stages possible experiments: it allows activities analogous to intervention and observation, but in a constructed environment, which provides direct information about what is true in the model and indirect information about the world.

The advantage of this perspective is that it preserves an important conceptual distinction: the simulation output is not automatically empirical data. It becomes, epistemically, relevant only when we can argue that the model captures relevant aspects of the target system, and that the errors introduced are understood and controlled. This also makes it clear how the scientific community treats simulations: as tools to be verified, compared, calibrated, and stressed with sensitivity analyses and cross-checks.

Why I Prefer Approach B

The case of gravitational waves makes it clear that discovery is not the result of immediate observation. Interferometric detectors measure tiny variations in high-noise conditions. Detection is an inferential chain in which raw data becomes evidence thanks to filters, statistical methods, and above all, expected waveforms obtained from modeling and numerical simulations. The central epistemic question is: "why we can say that a certain structure in the data is better explained as a gravitational wave rather than as noise or an artifact?

Approach B responds naturally: the simulation builds a set of physically possible scenarios (given a theoretical framework) and establishes what we should observe if the world realized one of these scenarios. The match between data and template is not an automatic proof, but a step that gains strength only within a set of controls. And this is exactly how the LIGO/Virgo works: reliability does not come from a single model or a single pipeline, but from a system of convergent checks.

For example, multiple and independent pipelines are used; the convergence of results is an indicator of robustness. Significances are estimated by comparing candidate events against an empirical background of noise, quantifying how unlikely it is to obtain a similar result by chance. Injection tests are conducted, inserting simulated signals into the data to verify that the pipelines recover them and to evaluate sensitivity and error rates. Finally, different families of waveform models are compared to understand how much parameter estimates depend on modeling choices. All these practices make sense if simulation is seen as a mediator between theory and data, not as an experimental substitute for the world.

Why I DON'T Prefer Approach A

The "simulations as experiments" approach risks to skip a key distinction: in real experiments, the system can behave in ways that exceed or contradict the model; In a simulation, what happens is bounded by the implemented rules and modeling assumptions.

In the case of gravitational waves, this is crucial, because the simulated output can match a structure in the data even for false reasons: instrumental glitches, rare statistical coincidences, biases introduced in template selection or filtering. Precisely for this reason, the scientific community insists on noise controls and instrument calibration. Interpreting simulations as experiments, risks promoting them to sources of direct empirical evidence, confusing consistency with the model, with confirmation of the phenomenon in the world.

Theoretical dependence does not imply circularity

The concern remains: "If I use general relativity to generate templates and then find a match in the data with those templates, aren't I just confirming what I assumed?" Approach B clarifies why this is not a circularity. The match is not guaranteed: the inferential chain is fallible and could fail at many points (noise, numerical errors, approximations, incomplete models). Credibility arises from the convergence of many conditions: consistency of the signal shape, consistency between detectors, significance with respect to the background, stability of results when pipelines and models vary. In this sense, theory, simulation, instrument, and data do not form a closed circle, but a mutual control loop: theoretical dependence is inevitable in highly mediated contexts, but can be epistemically virtuous when accompanied by robust community practices of validation and comparison.

Conclusion

Contemporary science shows that the traditional trichotomy, while useful, is insufficient to describe real-world practice. In many fields, knowledge arises from tools that act as epistemic mediators: thought experiments, models, and simulations. Computer simulations, in particular, have become indispensable when the target is too distant, too large, too complex, or too difficult to manipulate.

The case of gravitational waves highlights the most philosophically interesting aspect of this phenomenon: the discovery does not consist of a "direct observation", but of a network of inferences supported by simulations, statistical methods, control procedures, and collective validation practices. The approach that interprets simulations as models of possible experiments is more appropriate: it recognizes the epistemic power of simulations without confusing them with experiments on the world. The "simulations as experiments" approach, however, risks attributing excessive empirical authority to simulations, and obscuring their dependence on modeling assumptions and computational implementations.

Understanding science today, therefore, means understanding the traditional trichotomy, but also these intermediate tools and how, in community practice, they are controlled, justified, and integrated into the production of evidence.

Introducton

Since ancient times, space has been studied in various fields of knowledge, from mathematics to physics. However, beyond its theoretical formulations, the nature of space poses a specifically philosophical problem: its ontological dimension is not immediately accessible to experience. Space is not an object that we can perceive directly or manipulate as a material entity; we do not "touch" it in the way we touch a physical body. Furthermore, precisely because we live entirely immersed in it, we cannot observe it "from the outside", as if it were one element among others in the world.

For this reason, our understanding of space depends largely on theoretical models, particularly mathematical and physical ones, which do not merely describe what immediately appears to the senses, but organize, structure, and interpret experience. Such models make intelligible phenomena that would otherwise remain opaque, allowing us to attribute to space properties that are not directly observable, but described by scientific theories.

Space, thus, becomes a central philosophical problem: it is unclear whether space should be established as an entity that exists independently of the objects it contains, or as something that depends entirely on the relationships between those objects. It is precisely this ambiguity that gives rise to one important debate between two conceptions: substantivalism and relationalism.

According to substantivalism, space is an ontologically autonomous reality: it exists independently of material bodies and is a kind of "container" in which objects are located and move. This conception finds a classic formulation in the physics of Isaac Newton, for whom, absolute space exists in itself, even in the absence of matter, and it has its own properties.

Relationalism, on the contrary, argues that space is not an independent entity, but emerges from the relationships between material objects. From this perspective, talking about space means talking about distances, positions, and mutual relationships between bodies; without objects, space would have no autonomous reality. This position is historically associated with Gottfried Wilhelm Leibniz and Ernst Mach, who criticized Newton's idea of absolute space.

This rises the need to address the question of space from three distinct but complementary perspectives, which also constitute the fundamental structure of the philosophical debate on the subject:

• Metaphysics: what is space? Is it a real and autonomous entity (substantialism) or a set of relationships between objects (relationalism)?
• Epistemology: how do we know space? Through sensory experience, through a prior conceptual structures, or through scientific theoretical models?
• Physics: what role does space play in the laws of physics? Is it a passive background or a dynamic structure that interacts with matter and energy?

The Philosophical Problem of Space

Metaphysical

The first question is whether space is a real and autonomous entity or whether it is instead something derived. In particular, the question arises whether space should be conceived as a "container" independent of the material bodies it contains, or whether it exists only as a system of relations between such bodies. In other words, the metaphysics of space seeks to clarify whether space exists in itself or whether it depends ontologically on matter, and whether it can be considered on the same level as physical objects or as something ontologically distinct.

Epistemological

Space is invisible and not directly perceptible, and this makes our knowledge of it problematic. This raises the question of whether knowledge of space derives primarily from sensory experience or from reason. Specifically, the question is whether the geometric structures we attribute to space are learned through observation of the physical world or whether they are instead the result of rational and theoretical activity. The epistemological problem, therefore, is to explain how it is possible to have reliable knowledge of space, despite its unobservability.

Physical

The main questions concern the relationship between space and matter. The question is whether space interacts, in some way, with matter or whether it simply serves as a passive background in which physical phenomena occur. Furthermore, a central issue is establishing which geometry correctly describes space: whether traditional Euclidean geometry is adequate or whether different geometries are necessary.

Substantivalism: Newton's Absolute Space

Isaac Newton's position represents the one of the most influential formulation of substantivalism. Newton developed his theory of classical mechanics by assuming the existence of absolute space and time, conceived as real entities independent of matter, with a three-dimensional Euclidean geometric structure. Space, for Newton, is an immutable container in which material bodies are placed, and relative to which, it is possible to define absolute position, velocity, and acceleration.

Newton's central argument is through the Inference to the Best Explanation (IBB). He observes that there are empirically detectable inertial effects: for example, the distinction between uniform and accelerated motion, which manifests itself through sensations and observable phenomena (such as being pushed backward in an accelerating vehicle or outward on a curve). These effects, according to Newton, cannot be explained by the relative motion of bodies alone. If all motions were purely relative, there would be no basis for physically distinguishing accelerated motion from uniform motion. The existence of inertial effects suggests, instead, that not all reference frames are equivalent, and that there must exist a privileged frame, provided by absolute space.

Relationalist criticisms, developed in particular by Gottfried Wilhelm Leibniz, challenge precisely this point. Leibniz argues that space is not an autonomous entity, but an order of coexistence between bodies, and therefore, speaking of absolute positions or velocities is lacking of empirical meaning. Through thought experiments such as static shift and kinematic shift, he argues that universes differing only by an absolute translation or velocity would be indistinguishable, thus violating the principle of sufficient reason and the principle of identity of indiscernibles.

Newton implicitly responds by insisting that, even if absolute space is not directly observable, it is necessary to explain observable phenomena, such as inertial effects. For him, therefore, the metaphysical cost of substantivalism is justified by its explanatory power, while relationism fails to explain fundamental aspects of dynamics. In conclusion, Newton's position defends absolute space as an indispensable condition for a coherent theory of motion and inertia.

Relativism: Leibniz and Mach

Gottfried Wilhelm Leibniz and Ernst Mach developed two important versions of the relational conception of space, both in opposition to Newton's theory of absolute space. While they shared a rejection of substantivalism, their arguments were based on different philosophical assumptions: rationalist in Leibniz, empiricist and anti-metaphysical in Mach.

For Leibniz, space is neither a real substance nor an independent container, but an order of coexistence or a set of bodies with respect to one another. It exists only as a set of spatial relations between material objects. Consequently, there is no privileged frame of reference: each body can define a valid frame of reference. Concepts such as absolute position and velocity are, therefore, meaningless.

One of Leibniz's main criticisms of substantivalism is based on the Principle of Sufficient Reason (PSR). If absolute space existed, then universes identical in all relations between bodies but located in different absolute positions would be distinct. However, there would be no sufficient reason why the world should be in one position rather than another. Hence, Leibniz supports this argument with the Principle of Identity of Indiscernibles (PII): two states of the universe that are indistinguishable in all observable and relational respects cannot correspond to distinct physical states. He uses the static and kinematic shift thought experiments to show that absolute space creates metaphysical distinctions without any corresponding physical differences.

However, the problem of inertial effects remains, which Newton interprets as evidence for the existence of absolute accelerations. Leibniz responds by observing that, although acceleration is physically detectable, absolute position and velocity are not.

The critique of substantivalism is further radicalized by Mach. From an empiricist perspective, Mach rejects any unobservable entity, such as absolute space, assuming that, it lacked of scientific meaning. For him, the only relevant facts of mechanics are the relative motions of material bodies. In a universe without of other objects, the very notion of motion would be meaningless.

Mach, therefore, proposes a relational explanation of inertial effects: they depend on the overall distribution of matter in the universe, particularly distant stars. In this way, Mach eliminates the reference to space as an autonomous entity and attributes the entire explanatory role to matter.

In conclusion, Leibniz and Mach reject substantivalism because it introduces superfluous metaphysical entities. Leibniz criticizes it for rational and metaphysical reasons, Mach for empirical and epistemological reasons. Both defend relationism as a more effective conception of space, while acknowledging the difficulty of fully explaining inertial effects without resorting to an absolute space.

Personal View

Personally, I closely relate space to the universe, to the point of considering them equally: space is the universe itself, as the totality of everything that exists in a physical sense. However, this identification immediately clashes with our everyday intuitions. We are, in fact, led to attribute familiar characteristics to space: a finite volume, well-defined boundaries, as if it were a room or a delimited container. The universe, however, is probably the least intuitive object we can imagine.

The very question of its finitude is problematic. What we actually observe is not the universe in its entirety, but only a portion of it, called the observable universe: the region from which light has had time to reach us from the Big Bang to the present. This limit does not depend on a lack of instruments, but on a fundamental physical constraint (the speed of light).

Modern cosmology has indeed shown that the universe is expanding faster than light. On large scales, space itself expands, and some regions recede from us at a rate faster than light. This does not violate the laws of relativity, because it is not objects moving through space faster than light, but space itself that is expanding faster than light. Consequently, the light emitted from certain regions has never been able to reach us, and in some cases, it will never be able to do so.

For this reason, we can only observe a finite portion of the universe, while beyond it we are unable to gather any empirical information. However, this does not mean that the universe as a whole is finite: the only possible assumption we can make is that the observable universe is finite or infinite, while the overall structure of the universe remains an open question.

If we assume that the universe is finite, a further difficulty immediately arises: does it have boundaries? Here too, a common intuition misleads us. Talking about boundaries only makes sense if we imagine something "outside", but if the universe coincides with space itself, the idea of an "outside" loses meaning. There is no outside of the universe in the same sense that there is an outside of a room or a building, because the universe is not contained within a larger space: it is space itself.

For this reason, some cosmological models hypothesize a universe that is finite but without boundaries, analogous to the surface of a sphere: it is finite, but has no edges, and has no "outside" within the geometry of the surface itself. Other models, however, admit a spatially infinite universe. In both cases, however, our assertions remain tied to theoretical models, that go beyond what we can directly observe.

These considerations show how the concept of space, while central to physics, is profoundly abstract in nature and not immediately accessible to experience. We live immersed in space and cannot observe it from the outside; we can only infer its properties through indirect observations and mathematical structures. Consequently, seemingly simple questions like "is the universe finite or infinite?" or "does it have boundaries?" reveal the epistemic limits of our knowledge and highlight the delicate balance between intuition, theory, and observation in the scientific understanding of the universe.