Uncommon Descent Serving The Intelligent Design Community

Sciences and Theology

Science, Mathematics, Philosophy and (Natural) Theology

From IAI News: How infinity threatens cosmology

Peter Cameron writes: "Infinity is back. Or rather, it never (ever, ever…) went away. While mathematicians have a good sense of the infinite as a concept, cosmologists and physicists are finding it much more difficult to make sense of the infinite in nature." Read More ›

At Mind Matters News: Dartmouth physicist slams the Matrix idea that life is an aliens’ sim

Marcelo Gleiser dismisses the notion for physics reasons but he also objects to the way it casts doubt on free will, which we need to tackle our problems. Read More ›

Semi-circles and right angle dilemmas . . .

Daily Mail reports on a class assignment for seven year olds that happened to be set for the daughter of a Mathematics Lecturer at Oxford. Maths lecturer is left baffled by his seven-year-old daughter’s geometry homework and turns to Twitter for help – so can YOU work out if it’s true or false? Dr Kit Yates shares his seven-year-old daughter’s maths homework to Twitter The question asked students whether a semi-circle had ‘two right angles’ or not The maths lecturer, from Oxford, admitted that he was stumped by the problem  People were left baffled by the question and came up with conflicting answers  By Kate Dennett For Mailonline Published: 17:40 GMT, 25 February 2021 | Updated: 17:40 GMT, 25 February Read More ›

Logic and First Principles, 15: On the architecture of being. Or, are certain abstract entities (“abstracta”) such as numbers, natures, truth etc real? If so, how — and where?

For some weeks now, an underlying persistent debate on the reality of numbers has emerged in several discussion threads at UD. In part, it has been cast in terms of nominalism vs platonic realism; the latter being the effective view of most working mathematicians. Obviously, this is a first principles issue and is worth focussed discussion. Now, No. 14 in this series, on objectivity of aesthetics principles as canons of beauty, begins by pointing to an underlying challenge: We live in a Kant-haunted age, where the “ugly gulch” between our inner world of appearances and judgements and the world of things in themselves is often seen as unbridgeable. Of course, there are many other streams of thought that lead to Read More ›

Logic and First Principles, 11: The logic of Ultimate Mind as Source of Reality

After we headlined and began discussing PS on hearing and consciousness yesterday, H raised a significant issue: H, 15: >> . . . the invocation of a Creator who “beautifully designed what each sound should sound like” and “put the special program that can interpret each frequency pattern of air vibration into each sound, thus giving us the sound experience” is an empty explanation, no more useful than claiming that mind arises from matter without any idea how that could happen. >> To this, I replied: KF, 16: >> The concept that the root of reality is Mind, and that mind is at least as fundamental as matter is not an empty claim or assertion. That intelligent, minded designers exist Read More ›

The Fourier series & rotating vectors in action (with i lurking) — more on the mathematical fabric of reality

The Fourier series is a powerful technique that can be used to break down any repeating waveform into sinusoidal components, based on integer number harmonics of a fundamental frequency: Video: This is already amazing, that by summing up harmonically related sinusoids (with suitable amplitudes and lagging) we can analyse any repeating waveform as a sum of components. This then extends to any non-repeating pulse, once we go to an integral, which brings in the idea of a continuous spectrum where some wave “energy” is found at every particular frequency in a band. However, something subtler lurks: As the illustration based on clips from the video shows, a sinusoid can be seen as the projection of a rotating vector (= a Read More ›

Logic and first principles, 5: The mathemat-ICAL ordering of reality

As we continue to explore the significance of logic, the pivotal importance of Mathematics (and of the mathemat-ICAL ordering of reality) has come up. Where, we can best understand mathematics in two frames by using a definition with a bracket: Mathematics is [the study of] the logic of structure and quantity. The study part is cultural, the logic part speaks to an intelligible rational framework inextricably embedded in the existence of a world with distinct identity and then with structures amenable to quantification. So, let us headline a comment from the thread on no 4: 87: >>Let us take a key observation: There is order in the universe and we are good at modelling it mathematically. But that doesn’t mean Read More ›

Logic & First Principles, 4: The logic of being, causality and science

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 ›

Silenced! Selectivity too close to truth?

Should science pursue truth regardless of consequences? Or must we succumb to political correctness? Must selectivity of females always equal males? Consider:
Academic Activists Send a Published Paper Down the Memory Hole – by Theodore P. Hill
“In the highly controversial area of human intelligence, the ‘Greater Male Variability Hypothesis’ (GMVH) asserts that there are more idiots and more geniuses among men than among women. Darwin’s research on evolution in the nineteenth century found that, although there are many exceptions for specific traits and species, there is generally more variability in males than in females of the same species throughout the animal kingdom.” . . . Read More ›

Mathematical Realism/ Platonism (and Nesher on Godel’s Option C)

As we continue to explore the mathematical domain of abstract reality and objective truth, we come to first the Godel point (as summarised by Nesher): where, recall, the domain of facts starts with something like the surreal world of numbers: and then also, we come to the world of Mathematical Platonism/ Realism. So, let me continue by promoting a comment I just added to the objectivity of Mathematics thread: KF, 29 : >>Let’s see how IEP describes Mathematical Platonism (where, no, this is not equal to Plato’s theory of forms): Traditionally, mathematical platonism has referred to a collection of metaphysical accounts of mathematics, where a metaphysical account of mathematics is one that entails theses concerning the existence and fundamental nature Read More ›

Sev, JDK, the value of philosophy [esp. metaphysics] and addressing the intersubjective consensus challenge

In the PZM on the state of atheism thread, some key fundamental issues have emerged: JDK, 12: >>to both ba[77] and kf: because I think your belief in the power and importance of metaphysical philosophy is excessive and misguided . . . >> Sev, 17: >>[to BA77,] You consistently ignore the possibility that a consensus morality can be achieved through inter-subjective agreement.>> Both of these deserve notice, and I responded. This, I now headline, as it goes to the core of the many vexed debates that are going on not only in and around UD but across our civilisation. Pardon, JDK, I here redirect to the correct source: KF, 26: >>a long time ago now, I realised that if one Read More ›

My conclusion (so far) on the suggested infinite past, beginningless physical world: not plausible, likely not possible, here’s why

One of the more astonishing points of debate that has come out at UD is that at least some defenders of the evolutionary materialistic view are prepared to argue for or assume as default that we have had a beginningless past for the physical world.  This has come up several times in recent years and was again discussed last week. I will share my take-away conclusion so far. But first, why are such willing to put up such a spectacularly untestable, unobservable claim? Because, we first know that non-being has no causal powers so if there were ever utter nothing, such would forever obtain. That a world manifestly is implies that SOMETHING always was. The question is what, given that Read More ›

Fun with the hyperreal numbers (and with the idea of an infinite actual past)

The hyperreals are an extension of the real number line that brings to bear a reciprocal relationship between the very large and the very small. By so introducing extensions to the real number continuum, it forms a base for an infinitesimals approach to the calculus and makes sense of a lot of the tricks used by early pioneers of Calculus from Leibniz and Newton to Euler and beyond. (Though, it is clear in retrospect that they missed a lot of the pathologies that are now part of the far more cautious approaches of today.) And yes, here is a case where Wikipedia does some good (likely, in a context where there are few basement trolls capable of making a mess): Read More ›

DI Fellow, David Berlinski: “There is no argument against religion that is not also an argument against mathematics”

He continues (HT, BA77): >>Mathematicians are capable of grasping a world of objects that lies beyond space and time …. … Come again … DB: No need to come again: I got to where I was going the first time. The number four, after all, did not come into existence at a particular time, and it is not going to go out of existence at another time. It is neither here nor there. Nonetheless we are in some sense able to grasp the number by a faculty of our minds. Mathematical intuition is utterly mysterious. So for that matter is the fact that mathematical objects such as a Lie Group or a differentiable manifold have the power to interact with Read More ›