Alexander Pruss's Blog

• Doxastic moral relativism 2025-05-21
  Reductive doxastic moral relativism is the view that an action type’s being morally wrong is nothing but an individual or society’s belief that the action type is morally wrong. But this is viciously circular, since we reduce wrongness to a belief about wrongness. Indeed, it now seems that murder is wrong provided that it is […]
• Sacraments and New Testament law 2025-05-20
  Christians believe that Jesus commanded us to baptize new Christians. However, there is a fundamental division in views: some Christians (such as Catholics and the Orthodox) have a sacramental view of baptism, on which baptism as such leads to an actual supernaturally-produced change in the person baptized, while others hold a symbolic view of it. […]
• Semantics of syntactically incorrect language 2025-05-14
  As anyone who has talked with a language-learner knows, syntactically incorrect sentences often succeed in expressing a proposition. This is true even in the case of formal languages. Formal semantics, say of the Tarski sort, has difficulties with syntactically incorrect sentences. One approach to saving the formal semantics is as follows: Given a syntactically incorrect […]
• Truth-value realisms about arithmetic 2025-05-13
  Arithmetical truth-value realists hold that any proposition in the language of arithmetic has a fully determined truth value. Arithmetical truth-value necessists add that this truth value is necessary rather than merely contingent. Although we know from the incompleteness theorems that there are alternate non-standard natural number structures, with different truth values (e.g., there is a […]
• Possible futures 2025-05-09
  Given a time t and a world w, possible or not, say that w is t-possible if and only if there is a possible world wt that matches w in all atemporal respects as well as with respect to all that happens up to and including time t. For instance, a world just like ours […]
• Unrestricted quantification and Tarskian truth 2025-05-06
  It is well-known—a feature and not a bug—that Tarski’s definition of truth needs to be given in a metalanguage rather than the object language. Here I want to note a feature of this that I haven’t seen before. Let’s start by considering how Tarski’s definition of truth would work for set theory. We can define […]
• Immortality of the soul and the soul's proper operation 2025-05-03
  This is an attempt to make an argument for the natural immortality of the soul from the premise that the soul has a proper operation that is independent of the body. The argument is going to be rather odd, because it depends on my rather eccentric four-dimensionalist version of Aristotelian metaphysics. Start with the thought […]
• Aquinas' argument for the immortality of the soul 2025-05-02
  Aquinas argues that because the human soul has a proper operation—abstract thought—that does not depend on the body, the soul would survive the destruction of the body. I’ve never quite understood this argument. It seems to show that there could be a point to the soul surviving the destruction of the body, but that doesn’t […]
• Snakes and finitude 2025-05-02
  For years I have thought the finite to be mysterious, and needs something metaphysical like divine illumination or causal finitism to pick it out. Now I am not sure. I think snakes and exact duplicates can help. And if that’s right, then the argument in my other post from today can be fixed. Here are […]
• A dialectically failing argument for truth-value realism about arithmetic 2025-05-02
  Truth-value realism about (first-order) arithmetic is the thesis that for any first-order logic sentence in the language of arithmetic (i.e., using the successor, addition and multiplication functions along with the name “0”), there is a definite truth value, either true or false. Now, consider the following argument for truth-value realism about arithmetic. Assume eternalism. Imagine […]
• Causation and counterfactuals 2025-05-01
  Suppose that an extremely reliable cannon is loaded with a rock, and pointed at a window, and the extremely reliable timer on the cannon is set for two minutes. Two minutes later, the cannon shoots out the rock causing the window to break. The Lewisian counterfactual account of causation accounts for the causation by the […]
• Temporal purism 2025-05-01
  Say that a fact is temporally pure about an instantaneous time t provided that it holds solely in virtue of how things are at t. (The term is due to Richard Gale, but I am not sure he would have wanted the “instantaneous” restriction.) Thus, that Alice is swallowed the fatal poison at noon is […]
• Laziness is the mother of invention 2025-05-01
  For about 20 years, we've been using a set of Logitech Z-2200 speakers as our TV speakers. But they have an inconvenient volume control that requires one to get up from the sofa to turn the knob. Most of the time, it's enough to adjust the volume with the TV's internal control, but sometimes the […]
• Presentism, multiverses and discrete time 2025-04-29
  Suppose time is in fact continuous and modeled by the real numbers. It seems odd indeed to me that the real numbers should be the only possible way for time to run. The real numbers are a very specific mathematical system. There are other systems, such as the hyperreals or the rationals or even the […]
• Darwin and Einstein against the shared-form interpretation of Aristotle 2025-04-29
  Assume an Aristotelian account of substantial form on which forms are found in the informed things. A classic question is whether substantial forms are shared between members of the same kind or whether each individual has their own numerically (but maybe not qualitatively) distinct form. Here’s a fun argument against the shared-form view. For evolution […]
• Inferentialism and the fictitious isolated hydrogen atom 2025-04-28
  This is another attempt at an argument against inferentialism about logical constants. Given a world w, let w* be a world just like w except that it has added to it an extra spatiotemporally disconnected island universe containing exactly one hydrogen atom with a precisely specified wavefunction ψ0. Suppose that in in the actual world […]
• Probabilities of regresses of chickens 2025-04-28
  Suppose we have a backwards-infinite sequence of asexually reproducing chickens, ..., c−3, c−2, c−1, c0 with cn having a chance pn of producing a new chicken cn + 1 (chicken c0 may or may not have succeeded; the earlier ones have succeeded). Suppose that the pn are all strictly between 0 and 1, and that the infinite product p−1p−2p−3... equals some […]
• Inferentialism and the completeness of geometry 2025-04-28
  The Quinean criterion for existential commitment is that we incur existential commitment precisely by affirming existentially quantified sentences. But what’s an existential quantifier? The inferentialist answer is that an existential quantifier is anything that behaves logically like an existential quantifier by obeying the rules of inference associated with quantifiers in classical logic. Here is a […]
• Some issues concerning eliminative structuralism for second-order arithmetic 2025-04-27
  Eliminative structuralist philosophers of mathematics insist that what mathematicians study is structures rather than specific realizations of these structures, like a privileged natural number system would be. One example of such an approach would be to take the axioms of second-order Peano Arithmetic PA2, and say an arithmetical sentence ϕ is true if and only […]
• Causal Robinson Arithmetic 2025-04-23
  Say that a structure N that has a distinguished element 0, a unary function S, and binary operations + and ⋅ is a causal Robinson Arithmetic (CRA) structure iff: The structure N satisfies the axioms of Robinson Arithmetic, and For any x in N, x is a partial cause of the object Sx. The Fundamental […]