The Inconceivability Argument

The paper contrasts the traditional conceivability argument against physicalism with a new inconceivability argument. Using P for the totality of physical truths and Q for a phenomenal truth, the standard conceivability argument infers physicalism’s falsity from the conceivability and hence possibility of P and not-Q. The author is less persuaded by conceivability considerations and instead emphasizes inconceivability: it seems (ideally) inconceivable that phenomenal truths are wholly constituted by physical truths. The paper formulates the inconceivability argument with two core premises: (I1) it is inconceivable that Q holds wholly in virtue of any set of physical truths Φ, and (I2) inconceivability is a guide to falsity. The central comparative thesis is that the inconceivability argument is more rationally compelling than the conceivability argument: one may reasonably endorse the former while rejecting or suspending judgment on the latter, but not vice versa. The paper outlines the plan to clarify key notions (physicalism, ideal positive (in)conceivability, and grounding), to question the transition premise of the conceivability argument, and to show that proponents of the conceivability argument are committed to the premises of the inconceivability argument.

The work situates itself within debates on epistemic-gap arguments against physicalism, including the conceivability and knowledge arguments (Jackson 1982), and engages extensively with Chalmers’s two-dimensional semantics and conceivability–possibility principles (Chalmers 2002a, 2002b, 2004, 2009b, 2010, 2012). It discusses the distinction between narrowly and broadly physical truths, connecting to Russellian monism (Russell 1927; Eddington 1928; Chalmers 2015; Stoljar 2015; Goff 2017), and adopts the narrow (structure-and-dynamics) understanding of physical truths. The paper draws on the metaphysics of grounding (Fine 2001, 2012; Schaffer 2009; Rosen 2010), including Ground Necessitarianism and internality. It highlights Schaffer’s (2017; in press) challenges to 2D-CP via cases where conceivability outstrips possibility (e.g., No-Set and No-Sum) to undermine the transition premise of the conceivability argument. It evaluates the phenomenal concept strategy (Loar 1990; Papineau 2002; Tye 2003; Balog 2012) and argues it does not threaten the inconceivability argument’s transition premise. Additional related discussions include Block and Stalnaker (1999), Yablo (1993, 1999, 2002), and debates on necessity of grounding (Leuenberger 2014; Skiles 2015; Trogdon 2013; Litland 2015).

The paper employs analytic philosophical methodology: conceptual clarification, formulation of precise arguments, and modal-epistemic analysis. It defines physicalism as the thesis that phenomenal truths are fully grounded in narrowly physical truths (structure-and-dynamics). It analyzes ideal positive conceivability and inconceivability, individuating propositions finely (Fregean style), and treats grounding as a factive, explanatory constitutive-dependence relation. The author compares two argument schemas: the conceivability argument (moving from conceivability to possibility) and the proposed inconceivability argument (moving from inconceivability to falsity). He scrutinizes transition principles: 2D-CP for the conceivability argument and restricted intelligibility principles for the inconceivability argument. He uses formal modal assumptions (S5) and Ground Necessitarianism (and its strong form) to derive commitments. The methodology includes: (1) reductio against the conceivability of psychophysical grounding by showing that, with 2D-CP + Ground Necessitarianism + S5, it would contradict the core conceivability argument’s premises; (2) intuitive case method contrasting clearly conceivable grounding cases (traffic jam, death) with clearly inconceivable grounding claims (Strange Traffic Jam, Strange Death, Pink Lump, Pinkish Experience); (3) a stepwise “structure-and-dynamics” argument for a General Inconceivability Thesis; (4) defense of a transition premise via restricted Intelligibility principles (Physical Intelligibility and Ground Intelligibility), supported by auxiliary principles (Conceivability Excluded Middle and Strong Ground Necessitarianism).

• The inconceivability argument: (I1) it is inconceivable that phenomenal truths (Q) are wholly grounded in any set of narrowly physical truths (Φ), and (I2) if such grounding is inconceivable, it is not the case that Q holds wholly in virtue of Φ; together with (I3) that if Q is not grounded in physical truths, physicalism is false, yields the anti-physicalist conclusion.
• Comparative thesis: One can reasonably endorse the inconceivability argument while rejecting or suspending judgment on the conceivability argument, but one cannot reasonably endorse the conceivability argument without also endorsing the inconceivability argument.
• Challenge to the conceivability argument’s transition premise (2D-CP): Schaffer-style cases (No-Set; No-Sum) are conceivable yet (given orthodox metaphysics) impossible, undermining the move from conceivability to possibility even when expressions have coincident primary/secondary intensions. These cases do not threaten linking inconceivability to falsity.
• The phenomenal concept strategy, which expands the domain of the conceivable to explain away P&¬Q conceivability, does not undercut the inconceivability argument’s transition premise (I2); it targets (C2) by liberalizing conceivability rather than showing real truths are inconceivable.
• Proponents of the conceivability argument are committed to (I1): If Psychophysical Grounding were conceivable, then by 2D-CP and Ground Necessitarianism (plus S5), Φ would necessitate Q, contradicting the conceivability (and thus possibility) of P&¬Q.
• Independent support for (I1): A General Inconceivability Thesis holds that truths purely about structure and dynamics cannot be positively conceived to wholly ground phenomenal truths. Intuitive comparisons show many grounding claims are clearly conceivable (traffic jams, death) while others (e.g., a pink experience wholly in virtue of spherical shape) are not.
• Defense of (I2): Rather than full Intelligibility, restricted principles suffice: Physical Intelligibility (all physical truths are conceivable) and Ground Intelligibility (if A and B are individually and jointly conceivable, and B holds wholly in virtue of A, then the grounding truth is conceivable). These imply that if <Q wholly in virtue of Φ> is inconceivable, it is not true. Proponents of the conceivability argument are especially committed to these restricted principles (they already accept P’s conceivability and rely on Ground Necessitarianism).
• Auxiliary principles supporting Ground Intelligibility: Conceivability Excluded Middle and Strong Ground Necessitarianism (a strengthening of Ground Necessitarianism and a consequence of grounding’s internality).

The findings support the central hypothesis that inconceivability-based reasoning provides a stronger route to anti-physicalist conclusions than the traditional conceivability argument. By focusing on the inability (even ideally) to conceive that phenomenal truths are wholly grounded in structural-dynamical physical truths, the argument avoids vulnerabilities in the conceivability-to-possibility transition (e.g., Schaffer’s counterexamples to 2D-CP). The author shows that the physicalist’s primary counterstrategies (two-dimensionalism and the phenomenal concept strategy) either fail to challenge the inconceivability argument or commit them to principles that actually support it. The defense of (I1) via a General Inconceivability Thesis parallels and matches the intuitive force of the standard General Conceivability Thesis used to support P&¬Q’s conceivability, but targets grounding rather than variation. The defense of (I2) via restricted Intelligibility principles grounds a plausible link from inconceivability to falsity without overcommitting to universal Intelligibility. Consequently, the argument reshapes the dialectic: anyone accepting the conceivability argument’s assumptions is already bound to accept the inconceivability argument’s premises, while those skeptical of conceivability–possibility links can coherently endorse the inconceivability argument alone. This strengthens the broader anti-physicalist case by providing a more robust epistemic-gap route that better aligns with our intuitions about grounding and intelligibility.

The paper introduces and defends the inconceivability argument against physicalism, built on (I1) the inconceivability of psychophysical grounding and (I2) the principle that such inconceivability indicates falsity. It argues that these premises are independently plausible: (I1) follows from a General Inconceivability Thesis regarding structure-and-dynamics, and (I2) is supported by restricted Intelligibility principles (Physical and Ground Intelligibility). The comparative thesis is established: one can reasonably reject or suspend the conceivability argument while endorsing the inconceivability argument, but not conversely; proponents of the conceivability argument are committed to the inconceivability argument’s premises and to their motivating principles. Future work could further analyze the scope and limits of Intelligibility, reassess the necessity of grounding and its internality, explore implications for non-standard physicalist positions (e.g., Russellian monism), and investigate whether any structural truths might ever ground phenomenal truths without violating the General Inconceivability Thesis.

The argument relies on substantive modal and metaphysical assumptions (e.g., S5 modal logic, Ground Necessitarianism and its strong form, and grounding internality), though the author argues these are orthodox and dialectically required by the conceivability argument itself. Judgments about ideal positive (in)conceivability are fallible and may vary; the author acknowledges that (I1) is not conclusively established, appealing instead to strong intuitive support and stepwise structure-and-dynamics reasoning. The case presumes a narrow, structural-dynamical construal of physical truths; if this construal is contested, the reach of (I1) could be affected. The defense of (I2) avoids full Intelligibility but still assumes restricted forms (Physical and Ground Intelligibility), which, while plausible, could be challenged. The possibility of fundamental inconceivable properties is allowed, potentially limiting the generality of Intelligibility. Finally, as a philosophical argument, conclusions depend on the stability of intuitions about grounding and conceivability across idealization.