Startling explanatory power, predictive success and technological applications have awarded enormous social prestige to science. Yet, as Husserl lamented in ‘The Crisis of European Sciences,’ the world it depicts is at odds with the “Lebenswelt,” where one finds the everyday table that in 'The Nature of the Physical World’ Eddington contrasted with “the scientific table.” Thus, Sellars (1963, ch. 1) stressed the importance of addressing the “clash” between the “scientific image” offered by science and the “manifest image” emerging from perception, common sense and the semantic structure of natural languages.

This dichotomy is typically put forward metaphysically in connection with the empirical sciences, such as biology, the neurosciences, and most notably physics, where the spacetime of relativity theory and many aspects of quantum mechanics appear to be in stark contrast with commonsense and its world of ordinary objects.

This conflict is usefully extended to logic and the foundations of mathematics, as we distinguish between an “informal” (or “natural”) logic, a system of inferential principles implicitly presupposed in the manifest image and operative in everyday reasoning, and a “formal” logic of the scientific image, involving the explicit formulation of sophisticated logical systems, which respond to phenomena in the light of which the informal logic appears problematic, e.g., future contingents, empty terms, vagueness, intensional contexts, quantum mechanics, and especially the logical and semantic paradoxes, which threaten inconsistency or even explosiveness (the provability of every proposition) (Cantini & Bruni 2017). In sum, we have both a “metaphysical” and a “logical” manifest/scientific dichotomy.

It is well understood that the former poses a “metaphysical trilemma:” S-predominance, the scientific and the manifest images are incompatible and only the former is true; M-predominance, the scientific and the manifest images are incompatible and only the latter is true; SM-Compatibility, the two images are compatible, and both true.

Sellars (1963, ch. 1), Churchland, Dennett and many others have endorsed S-predominance, typically in the light of an adherence to scientific realism (Chakravartty 2017). In contrast, Husserl (Husserliana VI, 129-131, 135; XXXV, 475; XXXVI) and anti-realists such as Duhem (cf. L’évolution de la mécanique) have endorsed M-predominance after noticing that, since science is based on perception, it cannot reject common sense if not by cutting off the branch it is sitting on. However, if science failed to achieve truth, its astonishing success would be unexplainable, as pointed out by the no miracle argument (Chakravartty 2017, §2.1).

This dialectic could go on in dramatic tones. Realists could provocatively argue that, if scientific theories were false, we should refrain from funding and teaching science, and using its advice and products, such as vaccines, drugs, diagnostic devices, agricultural aids, etc. Ironically, we should go back to the pre-modern way of living.

Instrumentalists and “constructive empiricists” (Van Fraassen 1980, Chakravartty 2017, §4.1) could of course reply that we should still use science, because it works in practice.

Realists, however, could rejoinder that one can hardly explain its practically utility, if not by relying on the idea that scientific theories are (approximately) true.

A similar line of reasoning could be applied in the case of common sense and the manifest image, for science arguably relies on the manifest image in taking observational reports at face value, and perhaps in presupposing correspondentist truth and classical logic. Thus, if the manifest image were taken to be false, since science itself is based upon it, we would risk wholesale skepticism. Moreover, since our vision of ourselves and our social relations, crucially involving normativity and moral responsibility, are based on the manifest image, we may face serious cultural disorientation and existential bewilderment.

In the light of these tensions, SM-compatibility appears most palatable. But how can the two images be compatible, since they seem to contradict each other?

The logical manifest/scientific dichotomy poses a similar “logical trilemma:” S-predominance, the formal and the informal logics are incompatible and only the former is valid; M-predominance, the formal and the informal logics are incompatible and only the latter is valid; SM-Compatibility, the two logics are compatible, and both valid.

Tarski supported S-predominance, when he reacted to the semantic paradoxes by declaring that natural language is inconsistent and proclaimed the need for a rigorous system based on a rigid language/metalanguage distinction (Azzouni 2006), and similarly Russell regarded the type-theoretical logic of Principia Mathematica as the appropriate vehicle for progress in scientific philosophy (Landini 2011).

However, here too one may suspect that this revisionary approach cuts the branch on which one is sitting, because we get to sophisticated formal systems by relying on some underlying informal logic, and perhaps we can at least in part see in this light the opposition to formal logic of the so-called ordinary language philosophers of the previous century. And thus again SM-Compatibility seems most palatable.

SM-compatibility requires a better understanding of the two images at both the metaphysical and logical level. As regards the former, analytic ontology on the one hand (Loux 2006), and much contemporary work in the metaphysics of science on the other hand (Ladyman & Ross 2007), can be seen as descriptive and revisionary metaphysics (Strawson 1959), respectively; the former attempts to shed light on the manifest image, and the latter aims at superseding it in favor of the scientific image. The dividing line is not clear-cut though, for a priori analyses typical of the former intermingle with an a posteriori appeal to current science typical of the latter (Armstrong 1997).

Be this as it may, this literature shows that we are far from an agreement on what the two images really amount to on the metaphysical side, and something similar can be said on the logical side. This is made clear by some crucial topics on which we focus in this project from the standpoint of both images: (i) properties, relations (PRs) and related issues, (ii) time, (iii) logical and semantic paradoxes.

As regards the manifest image, at a most general level there seems to be a four-fold distinction of PRs, objects, and states of affairs. Yet, there are competing views of PRs: universals or tropes, abundant and fine-grained or sparse and coarse-grained. The latter divide appears to be correlated with two contrasting intuitions: PRs as semantic values of predicates vs. PRs as endowed with causal roles in the natural world.

To account for both, some have proposed a hybrid view, according to which there are both sparse and abundant PRs. This standpoint however has received little attention (Orilia and Swoyer 2017).

To compound matters, there are also many competing views of the differential application of non-symmetric relations (relational order), i.e. what distinguishes, e.g., Romeo’s loving Juliet from Juliet’s loving Romeo; this issue is intertwined with that of whether or not there are converse relations. For instance, are there both loving and being loved, which differ in “direction,” or only one “neutral” love relation? (MacBride 2016).

At the more specific level of the commonsense conception of time, it is typically taken for granted that it is A-theoretic, dynamic and presentist. Yet, there are many versions of presentism (Ciuni et al. 2013) and it is not obvious which of them, if any, reflects commonsense and its sense of the passage of time.

Moreover, the substantiality of the disagreement between presentism and its rivals has been questioned by many (e.g., Lombard 2010). It appears to require a notion of tenseless existence and predication (Mozersky 2011), but it is not fully clear how this should be understood (Dolev 2016).

As to the logical side, the widespread acceptance of classical logic, its use in introductory logical courses, its predominance throughout the history of philosophy until the flourishing of non-classical logics in the last century, the fact that even non-classical proposals are typically presented with classical logic in the background, either as term of comparison or as used in the metalanguage, strongly suggest that the informal logic encapsulates classical logic.

Yet, some non-classical systems, in particular intuitionistic, relevantist and paraconsistent ones, are often put forward as attempts to capture how we should reason, not only in a scientific setting, but in everyday life, and thus may be regarded as aiming at revealing the implicit informal logic (Haack 1996).

It may be expected that the growing field of experimental philosophy (Alai et al. 2015, Knobe & Shaun 2017) may shed light on the manifest image by appropriately surveying beliefs and intuitions of ordinary subjects with the methods of cognitive science. Yet, no extensive relevant inquiry has been conducted on the above issues, if not the preliminary study in Graziani (2017), which confirms a commonsensical inclination to presentism.

As regards the scientific image, its ontological commitment to PRs, and more generally to unobservable entities, presupposes scientific realism. Yet, there are very powerful scientific antirealists arguments, such as the pessimistic meta-induction, various arguments based on the purported empirical and even theoretical equivalence of theories, Stanford’s argument from unconceived alternatives.

Scientific realism has been defended with interesting replies, e.g., prescribing selectivity as to which assumptions of an accepted theory are true (Alai 2017, Chakravartty 2017, §2.3). This line is particularly popular, but if one follows it, the scientific image ends up depending on the selection.

At the more specific level of the conception of time emerging from science, there used to be wide consensus on the idea that, in the light of relativity theory, a B-theoretical eternalism has the lead (Callender 2011, 2017).

Now there is increasing popularity for the idea that quantum gravity physics favors a vision of spacetime as non-fundamental (Rovelli 2009, Callender 2017), which appears to require a notion of ontological dependence, a fundamental/emergent distinction (Schaffer 2009, Paolini Paoletti 2017) and may call for a radical revision of by now established philosophical beliefs concerning the nature of time.

And at the conservative side of the spectrum, there are “neo-Lorentzians” who argue that there is still place for an A-theory in the scientific image (Smith 2008).

At the logical level, new formal systems that claim superiority to those based on a Tarskian or Russellian approach keep flourishing (Cantini & Bruni 2017, §6).

They typically avoid inconsistency or at least explosion by replacing some prima facie valid principles of the informal logic with circumscribed counterparts.

But no agreement as to which system is the true logic is in sight, and there is even a logical monism/pluralism dispute: either there is one true logic or a plurality of logics, among which we can choose, depending on goals and domains of investigation (Russell 2016).

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