We synoptically describe having achieved the unprecedentedlogicist cognitive computational simulation of quantified ver-sions of any n-level (FBTn, ∀n ∈ N) false-belief task, andhence of what we call the infinitary false-belief task (FBTω);the achievement is enabled by the automated reasoner Shad-owProver. Logicist cognitive computational simulation of thelevel-one (or, as it’s currently known, “first-order”) false-belieftask (FBT1) was achieved circa 2007 by Bringsjord et al. Butsubsequently cognitive science has seen the arrival such mod-eling and simulation successfully applied to the second-orderfalse-belief task (FBT2); see e.g. (Blackburn & Polyanskaya,forthcoming). (This is the level-two FBT in our hierarchy oftasks.) But now, courtesy of what we report, logicist cognitivecomputational simulation of any FBTn is accomplished for thefirst time, and hence the infinitary false-belief task (FBTω) isreached as well

According to the received view in the psychology of reasoning, Piaget's view that: F Humans naturally develop a context-free deductive reasoning scheme at the level of elementary first-order logic. has been overthrown by the poor performance of educated adult subjects on specific logic problems (e.g., Wason's selection task). I propose that Piaget's F (or at least a variant) is alive and well, because the subjects in question are simply victims of a defective education. With a modicum of the right sort of logic training, humans reason deductively on logic problems well enough to vindicate Piaget.

Darwins /Origin/ doesn’t discuss the evolution of the human mind. He saved treatment of this topic for the subsequent/Descent of Man/, in which he advanced two claims: (C1) If the cognitive powers of nonhuman animals are discontinuouswith those possessed by humans, then the human mind isnt the product of evolution by mutation and natural selection. (C2)The cognitive powers of nonhuman animals, including specifically reasoning powers, are continuous with those enjoyedby humans; continuity is established. Penn, Holyoak, and Povinelli (2008) have in /BBS/ written “Darwin’s Mistake,” inwhich they purport to refute C2 by establishing discontinuity (they don’t affirm C1). Many vehemently disagree with PHP,and the debate remains intense, and unresolved. Yet, (1) the hitherto informal concept of continuity can be formalized,and (2) that formalization, applied to the debate, settles it. We provide the formalization, and with it settle the debate (infavor of PHP).