Scientific Metaphysics and Informational Theory Defeasibility

Updated: Jan 19

Theory defeasibility, or the revision and update of theories on the basis of new information and hypotheses, is sometimes misrepresented by pessimistic meta-inductionists, and by instrumentalists, as a flaw in scientific methodology and epistemology. However, it is a natural and necessary outcome of scientific progress. It can be characterised in terms of Robert Nola and Luciano Floridi's conceptions of optimistic meta-induction: overall the trajectory of scientific theorising and methodology is positive, and involves striking practical advances, and publicly verifiable, replicable, and reproducible results (Floridi, 2008; Nola, 2008).

However, nor does it logically, intuitively, or rationally follow from optimistic meta-induction and theory defeasibility that all metaphysical characterisations and theories have equal epistemic weight and are on an equal epistemic and scientific explanatory footing (where scientific means, at minimum, publicly repeatable and verifiable testing, demonstration, and experimentation by a community of expert scientists). That clearly does not follow. It is fair to say that that such an assertion would be just wrongheaded.

I suggest that it does, however, follow from the fact of optimistic meta-induction (which arguably earns the status of fact because science continually works so well) that our best philosophy of science, and our best scientific metaphysics, should also be defeasible on a methodological axiomatic – or at least in-principle – basis. Scientific metaphysics, and scientific-metaphysical theories - should change in accordance with changes in the ontological commitments of our best hard, physical sciences (what those theories say does and does not exist).

Obviously, this really means physics, and not much else. In other words: starting with psychology or even neuroscience, and positing that the universe might just be some enormous, conscious mind type of thing: such an approach is not really science. It does not involve a metaphysics that is ratified by science, either.

Non-apriorist Metaphysics

Expressivists like to tell us that both metaphysics, and scientific metaphysics, are a non-starter anyway. Do not even bother, they say. I agree with them about many kinds of metaphysics that claim scientific authenticity and grounding (especially those varieties that eschew either or both of empiricism or physicalism, or that are anti-naturalistic). However, several expressivist philosophers also tell us that we cannot be realist about any of the observables and unobservables posed by quantum theory (Egg, 2019; Healey, 2013, 2018; Healey & Fine, 1990; Maudlin, 1998).

In many cases I suspect that those forms of expressivism may well be their own reductio ad absurdum, rather than that they demonstrate scientific realism about referents of theory terms and unobservables (apart from some naïve realism) is a mistake. Or else, perhaps they at least reduce themselves to near logical absurdity with respect to some of their premises, precepts, and views.

While logical positivists A.J. Ayer and Rudolph Carnap, and many expressivists, have, quite correctly, rejected a-priorist metaphysics as largely useless for scientific explanation and epistemology: to reject all metaphysics out of hand is a (probably rather silly) mistake. The most significant reason for this is that scientific metaphysical musing and posits constitute a huge part of what working scientists, including theoretical physicists, do on a regular basis as part of the process of scientific discovery (Andersen & Becker Arenhart, 2016; Anderson et al., 1997; Arns, 2001; Beebee & Sabbarton-Leary, 2010; Chalmers et al., 2009; Crupi, 2016; Esfeld, 2010; Maudlin, 2007; Slater, 2009).

The difference with the metaphysics of physicists, and that of other scientists, is that it is usually properly informed by existing scientific knowledge and evidence . It has a very limited a-priorist component where the a-priorism is largely based upon existing empirical evidence. That is: when it does have an a-priorist component, this is either tempered by a lack of belief and epistemic commitment, pending verification via scientific method and process (as in the famous case of Wolfgang Pauli and the Neutrino), or else that a-priorist component is posited based on induction from substantial, existing, experimentally established scientific explanation and evidence.

In many cases, this contributes to the formation of new hypotheses that can be tested in a hypothetico-deductive ‘loop’: Karl Popper’s suggested approach to achieving a stable and efficacious scientific method, which has found many adherents in the sciences – especially contemporary psychology and molecular bioscience (Barbieri, 2002; Liang et al., 2019). This kind of scientific metaphysics – performed within the process of doing science – means that thoroughgoing expressivism about the referents of scientific theories, and their models, is probably wrongheaded (although it is not the only thing that points to that proposal). Ockham’s Razor, or the principle of ontic parsimony, is one thing. Disallowing realism about any kind of scientific theory referent due to logical positivist A.J. Ayer’s war on anything not analytically logicise-able is something else altogether (Hanfling, 1986; Steinmann & Ayer, 1973).

Ontic Parsimony – Again

Ontic parsimony involves not including anything in the ontology (theory or else posited objective) not required to explain, or save, the phenomena (Long, 2019). To ‘save the phenomena’ is just philosopher’s (very old) language for explaining (the natural basis of) a natural system, entity, event, or process. That is, of a natural and physical phenomenon.

It does not necessarily follow that the theory itself has to be simple. The theory might be exceedingly complex. It is also not necessarily the case that a theory with a very inflated ontology will be a very complex theory. The premises, propositions, assumptions, posits, hypotheses, inferences, entailments, and experimental bases of such a theory might be few, and relatively simple.

Use of our most complex scientific theory - quantum field theory – involves temporarily inflating the ontology with a certain kind of mathematical abstracta (I will leave mathematically elegant string theory aside until it is less speculative and has more experimental support). A whole lot of variables associated with what physicists call (mathematical) singularities and infinities get temporarily injected into QFT modelling equations. However, these are necessarily eliminated in the process of renormalisation that is required to finalise the result (Crowther, 2015).

In other words, our best, and most complex scientific theory seems very much to support the principle of ontic parsimony. It tells us that retaining even mathematically indispensable (from the perspective of the turning of the mathematical handle of the system) ontic ‘bloat’ is not a good way to adduce what does and does not exist in the world. Not even if it is temporarily useful in applied mathematical procedures. Temporary explosions of mathematical abstracta as part of the mathematical machinations of the working of equations are okay.

Declaring that such variables have corresponding referents – things in the physical phenomena to which they refer and correspond – is a mistake:

[F]ield theories don’t necessarily make sense to arbitrarily small length scales. If we try to make calculations in the continuum we simply get garbage. This "garbage" is the famous infinities that surround quantum field theory. However, if we introduce some fundamental scale in the game to define our theory, some minimal length beyond which our description breaks down, suddenly everything makes sense again. And using this framework we have been able to recover all those weird experimental facts to an astounding precision. And I do mean astounding. Renormalisation has the best prediction in the history of science. The g-factor of the electron is the quantity that has the best agreement between data and theoretical prediction. Period. No caveats (Melo, 2019, 4).

There is a debate among physicists and philosophers of science about whether the infinities, or singularities, and 'blowups' (multiplying of mathematical abstracta) that occur in QFT prior to renormalisation are information ‘sinks’ - do not really provide any information about the physical phenomenon - or are instead genuinely informational, or genuinely encode information.

Certainly, from the perspective of the philosophy of information, and from the perspective of most interpretations of information theory and theories of signals and transmission: the fact that renormalisation works as part of the method and model of QFT conveys information of some kind. It probably conveys a lot of information. However it is probably mostly information about, and of, the model, its representations, and the workings of the model (although what kind of propositional information may be encoded from it is not necessarily immediately clear).

It may also be information about the nature of the applied mathematics involved. In other words, from the perspective of science, scientific explanation, and especially scientific realism versus anti-realism: it matters what kind of information sources the information of the ‘blowup’ abstracta are telling us about, or else are somehow variously encoded from.

There is also a related, and quite complex, debate about the nature of mathematical abstracta. It is best characterised by the Quine-Putnam indispensability argument and Hartry Field’s demonstration of mathematics free of abstracta (what critics of mathematical nominalism have called the ‘hard road’. (Bueno, 2012; Busch & Morrison, 2016; Colyvan, 2010, 2012; Jandrić, 2020; Yablo, 2012)) However, for the sake of argument in this post, we can assume no one is quibbling about the existence of causal Platonic abstracta in physical fields, nor in the phenomena modelled by QFT (although there are certainly Platonist philosophers of mathematics that do hold such positions ). Put otherwise: most physicists are presumably not endorsing the idea that a mathematical abstractum can exert – either practically or in-principle – physical, causal influence on any physical system.

It is certainly an interesting question whether the informational ‘blowup’ of mathematical abstracta associated with QFT modelling is an indication of what is going on in the modelled physical phenomena or quantum systems. However, the preponderance of scientific opinion still regards the proliferation of mathematical singularities and infinities that occurs in that process as largely non-informational with respect to the actual material phenomenon of quantum fields. Most physicists do not think that the ‘blowup’ mathematical entities in question exist in the phenomenon as information sources: in the physical fields being modelled by the mathematical representations of those fields and the mathematical manipulation of those representations (this is further complicated by an overarching question about the veracity of realism about quantum fields, which I will avoid here for the sake of brevity and simplicity).

This has not a little to do with the nature of infinities and the relationship between different kinds of mathematical infinities and concepts of physical infinities. The 'blowups' and singularities might be informational, but the information that they provide is likely to be about the model, rather than being information about, from, or of, the modelled phenomenon. If information encoded by the blowups is about the physical systems being modelled, then it is likely to be indirectly indicative of something which may be outside of the phenomenon, rather than any kind of informational representation of what exists in the physical system being modelled.

Science is replete with useful explanatory fictions, and abstract mathematical constructs, that no scientist thinks require additions to the material ontology of the universe. Frictionless planes, centres of gravity, and absolute vacuums all have this illustrious and respectable explanatory status. Centres of gravity cannot exist apart from whatever entity they are a centre of gravity for. They are an intrinsic property of material entities only, and such are the necessary condition for the existence of centres of gravity. Yet even centres of gravity are arguably more real ‘fictions’ than such fictions as frictionless planes, the ball model of atoms, perfect spheres, and absolute vacuums. Yet, these are all just arguably abstract devices used to get a model to easily explain what is happening in a set of physical systems or phenomena.

The mathematical abstracta that are eliminated in a QFT renormalisation are also probably not as real as centres of gravity. How much they are like centres of gravity, and how much they are like fictions, is not so easy to adduce. What is clear, however, is that physicists must rid the solution of them by way of renormalisation to achieve the best predictive results in the history of science. That may constitute perhaps our strongest confirmation yet of the robust veracity of ontic parsimony. It may also be an endorsement of the practical indispensability of mathematical abstracta in scientific theories, but realism about such entities does not necessarily follow from this (Azzouni, 2015; Baker, 2005; Bangu, 2013; Hjortland, 2019; Miller, 2016; Pincock, 2012).

Since infinities are conceptually tricky in general, let us try to get a better handle on the idea with the concept of the continuum. The mathematical continuum is such that one can pick any two rational or irrational numbers as close together on the mathematical number lines as one likes, and there is guaranteed to be an infinite supply of values in between them. You can pick another number in between the two you started with, and then pick another number in between that number and either of the existing two, and you can continue this process indefinitely (in principle). Few, if any, applied scientists think that the mathematical continuum necessarily exists, or can be realised in such a way, in any physical system.

For example: a neural synapse may have a range of electrical potentials that it can realise, but it does not follow that it can produce or adopt every potential value available in the mathematical continuum between those two values. The natural discretising limits of the physical and electrochemical system will prevent this. Pick any two values for an electric potential in an axon terminal and across a synaptic cleft. The mathematical continuum in between them is infinite, but the synapse cannot produce, or realise, all these values.

The Nature of Information, and Structure, Again

It does not necessarily follow that the intrinsic information in any given system is always finite. That is a more difficult question, and it depends upon the entire structure of a physical system, and especially upon whether structure in physical systems has any bottom, or reductive lower limit (Psillos, 2006; Saunders, 2003). This is because the information of information sources and information source states reduces to their structure, or existentially depends upon their structure.

It may also depend upon other things, but structure is non-negotiable. Put otherwise: information is necessarily grounded in, or by, physical structure, or else by structure that reduces to, or else supervenes upon, physical structure. No structure: no information.

This appears to be trivial matter, until one considers existential questions about information, and about what the conditions for the existence of both structure and information are. Is there any real information in, of, or about, abstract mathematical entities (if these even exist)? (Armstrong, 1978; Bueno, 2005; Colyvan, 2012, 2013; Knowles & Liggins, 2015; Marcus, 2015; Pincock, 2004). How could that possibly be transmitted or generated? If this is the wrong question, then: is it the wrong question because subjectivism about information is necessarily correct, and information cannot exist without a consumer or a receiving subject of some kind? (Scarantino, 2015; Stegmann, 2015). Does information existentially depend upon logic, or language, or – is it the other way around? (Sagueillo, 2014; Sequoiah-Grayson, 2008)

Stephen Hawking famously stated that the information of a quantum system is finite. However, firstly, this claim is made within a very specific problem domain. Secondly, this correspondingly seems to be based upon theoretical limits set in accordance with scale variance. It seems also to be confined to certain measurement scales relevant to the modelling being done (Jentschura & Nándori, 2014; Lyre, 2012; Nozick, 2001; Van Leeuwen, 2014).

Structure is both a necessary, and a sufficient, condition, for information. Even if an entity with only boundaries but no internal structure could be used as a symbol to convey many bits of information apart from some external structure, say, as part of a structured arrangement of other structureless entities: such a structureless entity, system, or process would carry no intrinsic information within it.

I should offer a note to the uninitiated in the philosophy of information. Pluralism about the nature of information (colloquially: information is different things to different people/theorists, and the term ‘information’ means different things in different scientific contexts) still largely prevails in philosophy of science, and for good reason. However, care must be taken with respect to the levels of explanation and abstraction at which a given conception of information holds, or is applied (Bauer et al., 2008).

The sciences tend to deliver a broad conceptual pluralism about the nature of information. The concept of information in psychology often differs from that used in physics, for example. In psychology, information is often defined in terms of the information processing theory of cognition, according to which the existence of information is dependent upon cognitive and neurological processes (although the degree to which this is true varies between theorists). There’s a corresponding distinction to be found between cognitive and non-cognitive ‘types’ of information (a distinction which I investigate in depth in my forthcoming monograph). However: 1. The classical Shannonian statistical conception of information is used across the sciences, and 2. Metaphysical concepts of information are far more stable within single disciplines, such as within physics (although there is certainly significant variation to be found even within physics).

I endorse a scientific metaphysics about information, which means (most centrally) that I think that the ontology of information (or theories about, and concepts of, the nature of information, and about how it exists) should be driven by scientific usage of the concept of information, and by references to information in scientific theories (this is somewhat of a ringing endorsement of positive scientism.) Some philosophers of science have even proposed that information is not a real thing in the ontology: not something that we should even think of as real, but instead just a nominalist (just a name or label) placeholder for different values and concepts.

Although I disagree with this, it is far from an incoherent position. This is especially so in the field of biology and in molecular bioscience (although the theorists that I know of that previously held this position now instead endorse various kinds of teleo-functional realism about information: information is realised by the properties of evolved, teleonomic, and functional systems, for example). I am a realist about information, and a physicalist-statisticalist about the nature of information, which is a less popular position among philosophers (but probably more palatable to scientists.)

Scientific Theories as Encoded Information

Scientific theories are encodings of information from many heterogeneous sources and channels. The various channels providing access to the information of those sources are noisy and have limited bandwidth. Encoding processes that convert information from the sources and channels into representations in scientific models are partial, and limited by physical, causal, cognitive, epistemic, and processing limits (among others).

As new information, including evidence from repeated publicly verifiable experimentation, is made available: scientific theories are apt to change as they update that information that their representations and models encode. This is a natural upshot of hypothetico-deductive types of information encoding cycles, coupled with information-encoding principles as applied to scientific models (representational partiality, loss, code conventions, and recognised sets of possible source states, among other variables).

The information encoding involved in scientific theorising is complex and partly cognitively enacted. In other words: scientist’s brain-minds are (obviously) involved in the processing and encoding of the new information that is put into revised and updated theories. This very much includes the low-level processes of neural encoding of information that psychologists and neuroscientists frequently discuss. However, it also includes higher level cognitive encoding of complex lexical and phonological information which is further encoded by higher executive brain function and metacognitive processes (Bang et al., 2018; Brown, 1987; Dennett, 2001; Derakshan & Eysenck, 2009; Shea & Frith, 2019; Taylor, 2013; Yeung & Summerfield, 2012). The encoding of defeasible theories thus happens at multiple levels of abstraction, and across internal cognitive and external non-cognitive boundaries, which means that cognitive and psychological noise must also be accounted for. This is, of course, one reason for the importance of public expert reproducibility and replication of experimental results.

Defeasibility – or updating and change of theories based upon the invalidation of existing theory elements and the refreshing, updating, or turnover, of information encoded into representations in models – is thus an intrinsic and ineliminable element of the updating of scientific theories, just as it is an ineliminable element of individual and group epistemic updating (Adami, 2012; Brigandt, 2012; Bueno, 1999; Bueno & Da Costa, 2007; French & French, 2014; Friston et al., 2016; Ladyman, 2011; Liu & Liu, 2011; Manero, 2019; Motoura, 2017; Van Benthem, 2007; van Eijck, 2014). The lossy-ness (limited fidelity) of information transmission, the limited bandwidth and noise of information channels, restrictions on encoding processes and code sets (rules for encoding), and the corresponding necessary informational-partiality of any token information-encoding representations and models: all of these mean that scientific theory revisability, and defeasibility (revising based upon the removal and replacement of misinformation or pseudo-information with better information) has a sound basis in information theory, and an information theoretic model of scientific practice and methodology.


There is still work for non-a-priorist scientific metaphysics to do both within science, and at the boundary of science and philosophy. Philosophers and philosophers of science have proven indispensable to scientific method and progress, as Popper’s hypothetico-deductive methodology has demonstrated. Philosophy is still the capable handmaiden of science in at least this sense: the sense in which scientists are still naturalistic natural philosophers (Thomasson, 2009). Scientists are arguably natural philosophers whenever they make yet untested posits, or propose untested hypotheses, that have naturalistic ontological implications and entailments.

If that is too strong for the naturalist-scientist reader, then perhaps it is less controversial that scientists are natural philosophers when the implications and entailments are very hard to test, but can be reasonably proposed based on, say, evidence and natural nomic constraints (natural laws). Such scientific metaphysical hypotheses and posits both motivate, and are driven by, the updating of information in theories, and the encoding (cognitive-psychological, instrument based, and experimental-methodological) of newly available (empirically and experimentally) and better information into the models and representations of existing theories.


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