Epistemology

Mr Wright observes: From time to time it is useful for sane men in an insane world to remind themselves of basic truths.The first truth is that truth is true. A statement that there is no truth, if true, is false. We know this truth is basic because without it, no question can be answered, not even the question of whether or not truth is true.Truth is a subtle and complex topic, but what we mean by the word can be said in a short sentence using words of one syllable: Truth is when one says ‘it is’, and it is as one says.The second conclusion springs immediately from the first. We know that truth is true because to say Read More ›

Two recent remarks in VICE (a telling label, BTW) raise some significant concerns. First, Kevin Buzzard — no, this is not Babylon Bee [itself a sign when it is harder and harder to tell reality from satire] — Sept 26th: Number Theorist Fears All Published Math Is Wrong “I think there is a non-zero chance that some of our great castles are built on sand,” he said, arguing that we must begin to rely on AI to verify proofs. [ . . . ] Kevin Buzzard, a number theorist and professor of pure mathematics at Imperial College London, believes that it is time to create a new area of mathematics dedicated to the computerization of proofs. The greatest proofs have Read More ›

Carroll, here, was responding to a Weekly Standard cover article on the reactions to philosopher Nagel’s publication of Mind and Cosmos: Why the Materialist Neo-Darwinian Conception of Nature is Almost Certainly False : What I find particularly interesting in the captioned clip is the laudatory reference to “a more Scientific WORLDVIEW” which is immediately problematic, as worldviews are matters of philosophical points of view and linked cultural agendas. That is, they are categorically distinct from science in any proper sense. A clue for what is really meant comes from what immediately follows: “and everyone knows that God doesn’t exist.” Really, and how can science actually establish such a thing, especially in a world with literally billions of theists, many being Read More ›

In a current thread, frequent objector, Seversky, posed a one liner objection intended to dismiss an OP: “Argumentum ad consequentiam.“ This raises an obvious issue on logic and linked epistemology, as argument by reduction to absurdity (which is broader than simple logical contradiction) is a well recognised argument type. Where, also, the issue is not emotive reaction to logical or operational consequences, but that that which is false or evil often leads to chaos, logical or existential or both. Thus, for example, we learn from history that certain things are manifestly false or evil. In short, we need a way to responsibly decide on when an argument succeeds as a reductio. For example, dismissing any arguments we do not like Read More ›

In the thread on Jonathan Bartlett and priorities for Math education, I raised two comments that I think it would be profitable to further reflect on. First, from 33 on how the US National Academy of Sciences tried to classify Mathematics as a “science”: https://services.math.duke.edu/undergraduate/Handbook96_97/node5.html The Nature of Mathematics (These paragraphs are reprinted with permission from Everybody Counts: A Report to the Nation on the Future of Mathematics Education. ©1989 by the National Academy of Sciences. Courtesy of the National Academy Press, Washington, D.C.) Mathematics reveals hidden patterns that help us understand the world around us. Now much more than arithmetic and geometry, mathematics today is a diverse discipline that deals with data, measurements, and observations from science; with inference, Read More ›

In looking at time (no. 18) we saw how a suggested form of multiverse is one in which sub-cosmi are speculated — there is no observational base, this is philosophy dressed up in a lab coat — to pop up as fluctuations, exhibiting their own “big bang” events and timelines: However, it was not as simple as that. Wikipedia, speaking against known inclinations, summarised: a Boltzmann brain is a self-aware entity that arises due to extremely rare random fluctuations out of a state of thermodynamic equilibrium [–> the predominant, statistically overwhelming group of accessible micro-states for a relevant entity in statistical thermodynamics]. For example, in a homogeneous Newtonian soup, theoretically by sheer chance all the atoms could bounce off and Read More ›

Dr Carol Wood of Wesleyan University (a student of Abraham Robinson who pioneered non-standard analysis 50+ years ago) has discussed the hyperreals in two Numberphile videos: First: Extended: Wenmackers may also be helpful: In effect, using Model Theory (thus a fair amount of protective hedging!) or other approaches, one may propose an “extension” of the Naturals and the Reals, often N* or R* — but we will use *N and *R as that is more conveniently “hyper-“. Such a new logic model world — the hyperreals — gives us a way to handle transfinites in a way that is intimately connected to the Reals (with Naturals as regular “mileposts”). As one effect, we here circumvent the question, are there infinitely Read More ›

There is a creeping scientism in our intellectual climate. We have been led to think that Science is the gold standard of reliable, substantial knowledge and that institutional science and its leaders are the curators of knowledge. This is of course deeply connected to the wider domination of evolutionary materialistic scientism, which compounds the above with the notion that the stuff studied by the physical and chemical sciences is effectively the limit of credibly, reliably knowable reality. Where, let us note that scientism is a part of the defining cluster of naturalism, in both its metaphysical and “methodological” guises. We can readily see that in that ever so humble source, Wikipedia, speaking confidently and comfortably on its own philosophical bent: Read More ›

Currently, one of the objections on the table to a demonstration on how certain structural and quantitative entities are implicit in there being a distinct possible world is the rejection, dismissal or doubting of certainty of conclusions. This again reflects one of the many problems with thought in our day. Let’s add a quip, for those who doubt that warranted (as opposed to ill-advised) certainty is possible: are you CERTAIN that we cannot be justifiably certain? Accordingly, I took the opportunity to comment in the fallacies discussion thread: [KF, FDT 304:] One of the themes that keeps surfacing is “certainty,” which sets up the issues: warrant, knowledge, reliability, credibility, and responsibility. Given that we ever so often use knowledge in Read More ›

One of the common presumptions of our day is that facts and values are utterly, irreconcilably distinct. That is, that IS and OUGHT are irreconcilably separated by an ugly gulch that cannot be bridged. But, this is again one of those little errors in the beginning that have ruinous consequences as they spread out into our thinking and living in community. Let’s start with Hume’s Guillotine argument from his A Treatise of Human Nature: “In every system of morality, which I have hitherto met with, I have always remarked, that the author proceeds for some time in the ordinary way of reasoning, and establishes the being of a God, or makes observations concerning human affairs; when of a sudden I Read More ›

We live as beings in a world full of other concrete entities, and to do science we must routinely rely on mathematics and so on numbers and other abstract objects. We observe how — as just one example — a fire demonstrates causality (and see that across time causality has been the subject of hot dispute). We note that across science, there are many “effects.” Such puts the logic of being and causality on the table for discussion as part 4 of this series [ cf. 1, 2, 3] — and yes, again, the question arises: why are these themes not a routine part of our education? The logic of being (ontology) speaks to possible vs impossible entities, contingent ones Read More ›

Why is this topic important? (Why a series, now on no 3 (see 1 and 2)?) Here at UD, the phrase “first principles of right reason” and similar ones (e.g. “reason’s rules”) have often come up. Others talk about “the laws of thought,” which in a post-Kant world hints of “the ugly gulch” between the inner world of mental, conscious phenomena and the outer world of things in themselves. In that context, we have often highlighted that evolutionary materialistic scientism is irretrievably self-referentially incoherent and have pointed out how this means it is necessarily false. We have also pointed to “self-evident” first truths and principles, including the principle of distinct identity and its immediate corollaries, non-contradiction and the excluded middle. Read More ›

In a day when first principles of reason are at a steep discount, it is unsurprising to see that inductive reasoning is doubted or dismissed in some quarters. And yet, there is still a huge cultural investment in science, which is generally understood to pivot on inductive reasoning. Where, as the Stanford Enc of Phil notes, in the modern sense, Induction ” includes all inferential processes that “expand knowledge in the face of uncertainty” (Holland et al. 1986: 1), including abductive inference.” That is, inductive reasoning is argument by more or less credible but not certain support, especially empirical support. How could it ever work? A: Surprise — NOT: by being an application of the principle of (stable) distinct identity. Read More ›

One of the commonest objections we meet when we discuss design inferences — especially concerning the genetic code, is that a claim is “just an analogy” (with implied conclusion that analogies are weak or fallacious). This then extends to inductive arguments used. This common error must be corrected and (as will be shown) the principle of distinct identity helps us to do so. Before we show that, let us pause to note from the Stanford Enc of Phil, just to counter-weight the tendency of many objectors to be quickly dismissive of anything said by “one of those IDiots” without bothering to actually address the substantial issue at stake: >>An analogy is a comparison between two objects, or systems of objects, Read More ›

Let us soberly ponder, reading between the lines: Food for thought. END PS: By way of sharpest contrast: