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

I don’t know what you hope to gain by saying that something that is impossible is merely hard.

Of course you can vary it. However you cannot do so without reducing it's ability to explain the phenomena in question. It's hard to vary. That's my point. So, a theory is not good just just because it a prediction or that it's falsifiable. For an explanation to be good is must also be hard to vary. 2 + 3 = 5 is extremely hard to vary. Religious beliefs are not. They can be varied significantly and still explain the same phenomena just as well. I don't know why you find this so difficult to grasp, since I've applied it Paley's rock and watch, with some level of agreement here. The watch is hard to vary without reducing it's ability to tell time, if even at all, while the rock is easily varied without reducing it's ability to tell time, because we can use it as a sundial. I'm simply pointing out the same thing in respect to explanations. Perhaps an example discussion on the Fabric of Reality list would help to clarify this…. The question asked was if is 2+2=4 falsifiable. Someone proposed the following test.

If Tommy has two cupcakes in a box and then Tommy puts two more cupcakes in a box and Tommy doesn't now have 4 cupcakes in a box then the idea has been proven false.

David Deutsch, the Oxford Physicist and author whom's work the list is based on, pointed out the the problem with this conclusion.

The thing is, if carried out under the conditions implied, the outcome would not refute the theory that 2+2=4 but rather, it would refute the theory that the Tommy-cupcake-box system accurately models the numbers 2 and 4 and the operation of addition. This is exactly analogous to why, as I argued, [a single] fossil rabbit in the Jurassic stratum would not refute the theory of evolution: experimental testing is useless in the absence of a good explanation. What would a good explanation that 2+2 doesn't equal 4 look like? I can't think of one; that's because the theory that it's true is, in real life, extremely hard to vary. That's why mathematicians mistake it for being self-evident, or directly intuited, etc. And it is of course my opinion that 2+2 does in fact equal 4, so I'm not expecting to find a contrary theory that is at all good as an explanation. But, for instance, Greg Egan's science-fiction story Dark Integers explores essentially that possibility (albeit only for very large integers). The analogy between the theory of evolution and the 2+2 theory is in fact closer than the mere difficulty of imagining a good explanation to the contrary. Both of them, if false, would seem to involve there being laws of physics that directly mess with the creation of knowledge, in what we would consider a malevolent way. This makes for very bad explanations, but that doesn't affect the logic of the issue so here goes: The analogue of creationism being true, then, would be something like that there is really no such entity as the number 4 because the axioms of arithmetic as we know them are blatantly inconsistent, and that the laws of physics act on neurons to make us unconsciously confabulate excuses for ignoring the physical effects of that.

In case this isn't clear, given the observations of the experiment, we would assume that something was tampering with Tommy's box, the cupcake, our neurons, etc., rather than conclude that 2+2 doesn't equal 4. This is because the explanation that 2+2 actually equals 4, in reality, is very hard to vary. Nor can we think of a better explanation as to why 2+2=4. Other possiblities exist, however they are based on the idea that there are laws or forces that interfere with the creation of knowledge in malevolent ways. Can we rule this out as being true with 100% certainty? No, we cannot. But neither can we rule out that 2+2 equals something other than 4. This are bad explanations. So, to summarize, Hume showed us the problem of induction, Karl Popper showed that our use of induction in science was a myth (which caused a shift to falsification in science), and now Deutsch has pointed out that the creation of knowledge is based on seeking good explanations, which are hard to vary, not just making predictions or being falsifiable. I have no bias against the supernatural, per se. I want is good explanations. Bad explanations are not limited to the supernatural. The claim that you can cure the common cold via eating a foot of grass isn't supernatural, yet it's a bad explanation because it lacks an explanation as to how eating grass cures colds. Saying the biosphere was designed by an authoritative and inexplicable mind that exists in an inexplicable realm that operates via inexplicable means and methods is not a good explanation. critical rationalist

CR "2 + 3 = 5, is hard to vary." If by "hard," you mean "impossible," you are correct. I don't know what you hope to gain by saying that something that is impossible is merely hard. Barry Arrington

J-Mac, you know quite enough to understand what Orthodox Christian teaching is regarding God as triune. The unity and diversity refer to distinct aspects of being, so are not contradictory. Likewise, prayer NEVER informs God of our needs that he otherwise would be ignorant of. It is a relational exercise of submission and acknowledgement of Jehovah Jireh, Provider; which inter alia so changes our heart-attitude that it is safe to grant us things that would otherwise be to our detriment. For me, that I have life today is answer to my mom's prayer of surrender. And I doubt that it is mere accident of coincidence that I literally met my wife on a visit home from school, sitting in my parents' pew at church. Where the specific passage you tried to twist into sounding ridiculous actually points to this: obedient unto death as a servant, as in Gethsemane's prayer, if it were possible let this cup pass, nevertheless not my will but thine be done. And more. KF kairosfocus

CR, your strident objections to self-evidence fail. Kindly explain to us how it is not manifest to one who understands, that: || + ||| --> ||||| Where to suggest otherwise, e.g. that the result is 4 leads to something patently absurd like: || + ||| --> |||| That is, to try to deny this SET leads to the absurdity, 1 = 0; by way of an instructive example. In short, self-evidence is shown. It is no mistake. And BTW, Error exists is also self-evident. KF PS: JB, redefining what + means is imposing an equivocation. kairosfocus

Continuing, here (as there is need for posting images): https://uncommondesc.wpengine.com/mathematics/fun-with-the-hyperreal-numbers/ KF kairosfocus

CR - just as a point of interest, basic addition is easily modified when the number line is converted into a circle, as happens in modular arithmetic. 2 + 3 can equal all sorts of things in a rigorous, non-contradictory way. Think about the clock. If I start at 2AM, and add 25 hours, it will be 3AM. The clock is a number circle, and knows nothing of days. That is modular arithmetic, and it is a well-studied system in mathematics. johnnyb

Jmac says, “If God exists, he has no entry in spacetime because he would have to have created it and then he would have to heave restricted himself to something he created…” Well, that is exactly what he did when he came as Jesus, the man, restricting himself to the body of a man. See Philippians 2:5-11 Yeah.. yeah... yeah... Was this incident before or after God as Jesus decided to pray to himself? J-Mac

CR @ 15: The initial conditions being fundamental is a necessity for sane, consistent materialism; as making the initial state arbitrary kicks the door wide open for something more. Judging by the oft recurring theme of cosmic fine tuning on this site, I doubt you'll find much argument from your "religious" opposition on the contingency of the universe. LocalMinimum

Sure their is. Religious beliefs are easily varied, while mathematics, such as 2 + 3 = 5, is hard to vary. That's why we mistakenly think that 2 + 3 = 5 is self evident. This also assumes the idea that the initial conditions as fundamental. But why should we?

The prevailing conception regards the initial state of the physical world as a fundamental part of its constitution, and we therefore hope and expect that state to be specified by some fundamental, elegant law of physics. But at present there are no exact theories of what the initial state was. Thermodynamics suggests that it was a ‘zero-entropy state’, but as I said, we have no exact theory of what that means. Cosmology suggests that it was homogeneous and isotropic, but whether the observed inhomogeneities (such as galaxies) could have evolved from quantum fluctuations in a homogeneous initial state is controversial. In the constructor-theoretic conception, the initial state is not fundamental. It is an emergent consequence of the fundamental truths that laws of physics specify, namely which tasks are or are not possible. For example, given a set of laws of motion, what exactly is implied about the initial state by the practical feasibility of building (good approximations to) a universal computer several billion years later may be inelegant and intractably complex to state explicitly, yet may follow logically from elegant constructor-theoretic laws about information and computation (see Sections 2.6 and 2.8 below). The intuitive appeal of the prevailing conception may be nothing more than a legacy from an earlier era of philosophy: First, the idea that the initial state is fundamental corresponds to the ancient idea of divine creation happening at the beginning of time. And second, the idea that the initial state might be a logical consequence of anything deeper raises a spectre of teleological explanation, which is anathema because it resembles explanation through divine intentions. But neither of those (somewhat contradictory) considerations could be a substantive objection to a fruitful constructor theory, if one could be developed.

IOW, assuming the initial concisions are fundamental is parochial choice, which is unnecessarily narrow in scope. critical rationalist

F/N: Let's roll the tape from the OP:

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 elementary particles or accelerating forces. But these are precisely the claims that theologians have always made as well – that human beings are capable by an exercise of their devotional abilities to come to some understanding of the deity; and the deity, although beyond space and time, is capable of interacting with material objects . . . . What I do believe is that theology is no more an impossible achievement than mathematics. The same rational standards apply. Does the system make sense; does it explain something? Are there deep principles at work. Is it productive?

Food for thought. KF kairosfocus

Good point, Allen Shepherd @ 12. Truth Will Set You Free

Jmac says, "If God exists, he has no entry in spacetime because he would have to have created it and then he would have to heave restricted himself to something he created…" Well, that is exactly what he did when he came as Jesus, the man, restricting himself to the body of a man. See Philippians 2:5-11 Allen Shepherd

db writes,

The same rational standards apply. Does the system make sense; does it explain something? Are there deep principles at work. Is it productive?

No math and religion are most definitely not alike in these regards. jdk

J-Mac https://pbs.twimg.com/media/BAWYAbbCQAAycy5.jpg bornagain77

BA77 Do you realize what "on related note means"? How about semirelated? J-Mac

Truth Will Set You Free, I get it, but I was raised in a religion where there were no maybes...It was either Catholic view or not view... While things have changed over the years within the catholic faith, that doesn't mean that catholic religion has no contradictions...No religion is free of that... That's why we have religious faith... If God exists, he has no entry in spacetime because he would have to have created it and then he would have to heave restricted himself to something he created... J-Mac

Of related note:

Naturalism and Self-Refutation - Michael Egnor - January 31, 2018 Excerpt: Mathematics is certainly something we do. Is mathematics “included in the space-time continuum [with] basic elements … described by physics”? It seems a stretch. What is the physics behind the Pythagorean theorem? After all, no actual triangle is perfect, and thus no actual triangle in nature has sides such that the Pythagorean theorem holds. There is no real triangle in which the sum of the squares of the sides exactly equals the square of the hypotenuse. That holds true for all of geometry. Geometry is about concepts, not about anything in the natural world or about anything that can be described by physics. What is the “physics” of the fact that the area of a circle is pi multiplied by the square of the radius? And of course what is natural and physical about imaginary numbers, infinite series, irrational numbers, and the mathematics of more than three spatial dimensions? Mathematics is entirely about concepts, which have no precise instantiation in nature as described by physics.,, https://evolutionnews.org/2018/01/naturalism-and-self-refutation/

Of related interest to this notion of 'perfect' geometric objects occupying a Platonic mathematical world,,,

Platonic mathematical world – image https://image.slidesharecdn.com/quantuminformation2-120301000431-phpapp01/95/quantum-information-14-728.jpg?cb=1330561190

,,, Is this 'platonic' geometric object,,:

Artist’s rendering of the amplituhedron, a newly discovered mathematical object resembling a multifaceted jewel in higher dimensions. https://d2r55xnwy6nx47.cloudfront.net/uploads/2013/09/amplutihedron_2000.jpg A Jewel at the Heart of Quantum Physics - September 17, 2013 Excerpt: Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality.,,, Interactions that were previously calculated with mathematical formulas thousands of terms long can now be described by computing the volume of the corresponding jewel-like “amplituhedron,” which yields an equivalent one-term expression. “The degree of efficiency is mind-boggling,” said Jacob Bourjaily, a theoretical physicist at Harvard University and one of the researchers who developed the new idea. “You can easily do, on paper, computations that were infeasible even with a computer before.”,,, The amplituhedron, or a similar geometric object, could help by removing two deeply rooted principles of physics: locality and unitarity.,,, Locality is the notion that particles can interact only from adjoining positions in space and time.,,, The amplituhedron is not built out of space-time and probabilities; these properties merely arise as consequences of the jewel’s geometry. The usual picture of space and time, and particles moving around in them, is a construct. “It’s a better formulation that makes you think about everything in a completely different way,” said David Skinner, a theoretical physicist at Cambridge University.,,, The amplituhedron itself does not describe gravity. But Arkani-Hamed and his collaborators think there might be a related geometric object that does.,,, But the new amplituhedron research suggests space-time, and therefore dimensions, may be illusory anyway.,,, Even without unitarity and locality, the amplituhedron formulation of quantum field theory does not yet incorporate gravity. But researchers are working on it.,,, Beyond making (quantum field theory) calculations easier or possibly leading the way to quantum gravity, the discovery of the amplituhedron could cause an even more profound shift, Arkani-Hamed said. That is, giving up space and time as fundamental constituents of nature and figuring out how the Big Bang and cosmological evolution of the universe arose out of pure geometry. https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics/

Quote:

“Geometry is unique and eternal, a reflection from the mind of God. That mankind shares in it is because man is an image of God.” – Johannes Kepler (1571-1630) quoted from his book Harmonices Mundi:

bornagain77

J-Mac @ 5: He is not talking about the various religions and how they contradict one another. He's talking about the concept of something existing beyond space and time, neither coming into existence nor going out of existence at any particular point in time. Perhaps numbers are not the only such things. Perhaps there is an eternal Mind that shares those attributes. I like his thinking! Truth Will Set You Free

"“There is no argument against religion that is not also an argument against mathematics." The problem with religion is that it can, and often does, contradict itself...Whereas mathematics is either right or wrong. It can't contradict itself... J-Mac

as to; "Aren’t abstract entities such as Lie groups causally inert?" Darwinists/Atheists, I repeat myself, have long contended that information itself was 'just a metaphor', i.e. just a causally inert abstract entity. As is usual for claims from Darwinists, advances in science have rendered that claim false To further back up Berlinski's claim that mathematical objects have the power to interact with elementary particles, it has now been shown that immaterial information has a thermodynamic content and that immaterial information is its own distinct entity that is separate from matter and energy. A distinct physical entity that, in spite of being immaterial, does indeed have the power to interact with matter and energy. Here are a few references that drive this point home.

Information is Physical (but not how Rolf Landauer meant) - video https://www.youtube.com/watch?v=H35I83y5Uro Demonic device converts information to energy – 2010 Excerpt: “This is a beautiful experimental demonstration that information has a thermodynamic content,” says Christopher Jarzynski, a statistical chemist at the University of Maryland in College Park. In 1997, Jarzynski formulated an equation to define the amount of energy that could theoretically be converted from a unit of information2; the work by Sano and his team has now confirmed this equation. “This tells us something new about how the laws of thermodynamics work on the microscopic scale,” says Jarzynski. per Scientific American Information: From Maxwell’s demon to Landauer’s eraser – Lutz and Ciliberto – Oct. 25, 2015 – Physics Today Excerpt: The above examples of gedanken-turned-real experiments provide a firm empirical foundation for the physics of information and tangible evidence of the intimate connection between information and energy. They have been followed by additional experiments and simulations along similar lines.12 (See, for example, Physics Today, August 2014, page 60.) Collectively, that body of experimental work further demonstrates the equivalence of information and thermodynamic entropies at thermal equilibrium.,,, (2008) Sagawa and Ueda’s (theoretical) result extends the second law to explicitly incorporate information; it shows that information, entropy, and energy should be treated on equal footings. http://www.johnboccio.com/research/quantum/notes/Information.pdf J. Parrondo, J. Horowitz, and T. Sagawa. Thermodynamics of information. Nature Physics, 11:131-139, 2015. Matter, energy… knowledge: - May 11, 2016 Running a brain-twisting thought experiment for real shows that information is a physical thing – so can we now harness the most elusive entity in the cosmos? https://www.newscientist.com/article/mg23030730-200-demon-no-more-physics-most-elusive-entity-gives-up-its-secret/ New Scientist astounds: Information is physical – May 13, 2016 Excerpt: Recently came the most startling demonstration yet: a tiny machine powered purely by information, which chilled metal through the power of its knowledge. This seemingly magical device could put us on the road to new, more efficient nanoscale machines, a better understanding of the workings of life, and a more complete picture of perhaps our most fundamental theory of the physical world. https://uncommondesc.wpengine.com/news/new-scientist-astounds-information-is-physical/ Information engine operates with nearly perfect efficiency - Lisa Zyga - January 19, 2018 Excerpt: Physicists have experimentally demonstrated an information engine—a device that converts information into work—with an efficiency that exceeds the conventional second law of thermodynamics. Instead, the engine's efficiency is bounded by a recently proposed generalized second law of thermodynamics, and it is the first information engine to approach this new bound.,,, The generalized second law of thermodynamics states that the work extracted from an information engine is limited by the sum of two components: the first is the free energy difference between the final and initial states (this is the sole limit placed on conventional engines by the conventional second law), and the other is the amount of available information (this part sets an upper bound on the extra work that can be extracted from information). To achieve the maximum efficiency set by the generalized second law, the researchers in the new study designed and implemented an information engine made of a particle trapped by light at room temperature. Random thermal fluctuations cause the tiny particle to move slightly due to Brownian motion, and a photodiode tracks the particle's changing position with a spatial accuracy of 1 nanometer. If the particle moves more than a certain distance away from its starting point in a certain direction, the light trap quickly shifts in the direction of the particle. This process repeats, so that over time the engine transports the particle in a desired direction simply by extracting work from the information it obtains from the system's random thermal fluctuations (the free energy component here is zero, so it does not contribute to the work extracted). One of the most important features of this system is its nearly instantaneous feedback response: the trap shifts in just a fraction of a millisecond, giving the particle no time to move further and dissipate energy. As a result, almost none of the energy gained by the shift is lost to heat, but rather nearly all of it is converted into work. By avoiding practically any information loss, the information-to-energy conversion of this process reaches approximately 98.5% of the bound set by the generalized second law. The results lend support for this bound, and illustrate the possibility of extracting the maximum amount of work possible from information. https://phys.org/news/2018-01-efficiency.html What is information? - animated video (May 2016) Quote: “If information is not (physically) real then neither are we” https://www.youtube.com/watch?v=2AvIOzVJMCM

In the following article, George Ellis argues for the Causal Efficacy of Non Physical entities. Of particular interest is his argument for the causal efficacy of computer programs. Ellis goes on to persuasively argue that physical evidence for the reality of the immaterial mind is the computer sitting right in front of you

Recognising Top-Down Causation – George Ellis Excerpt: page 5: A: Causal Efficacy of Non Physical entities: Both the program and the data are non-physical entities, indeed so is all software. A program is not a physical thing you can point to, but by Definition 2 it certainly exists. You can point to a CD or flashdrive where it is stored, but that is not the thing in itself: it is a medium in which it is stored. The program itself is an abstract entity, shaped by abstract logic. Is the software “nothing but” its realisation through a specific set of stored electronic states in the computer memory banks? No it is not because it is the precise pattern in those states that matters: a higher level relation that is not apparent at the scale of the electrons themselves. It’s a relational thing (and if you get the relations between the symbols wrong, so you have a syntax error, it will all come to a grinding halt). This abstract nature of software is realised in the concept of virtual machines, which occur at every level in the computer hierarchy except the bottom one [17]. But this tower of virtual machines causes physical effects in the real world, for example when a computer controls a robot in an assembly line to create physical artefacts. Excerpt page 7: The assumption that causation is bottom up only is wrong in biology, in computers, and even in many cases in physics, ,,, The mind is not a physical entity, but it certainly is causally effective: proof is the existence of the computer on which you are reading this text. It could not exist if it had not been designed and manufactured according to someone’s plans, thereby proving the causal efficacy of thoughts, which like computer programs and data are not physical entities. http://fqxi.org/data/essay-contest-files/Ellis_FQXI_Essay_Ellis_2012.pdf

Although the preceding evidence is certainly very strong evidence for the physical reality of immaterial information, the coup de grace for demonstrating that immaterial information is its own distinct physical entity that is separate from matter and energy, is Quantum Teleportation where it is shown that the photons aren’t disappearing from one place and appearing in another. Instead, it’s the information that’s being teleported through quantum entanglement.,,,

Quantum Teleportation Enters the Real World – September 19, 2016 Excerpt: Two separate teams of scientists have taken quantum teleportation from the lab into the real world. Researchers working in Calgary, Canada and Hefei, China, used existing fiber optics networks to transmit small units of information across cities via quantum entanglement — Einstein’s “spooky action at a distance.”,,, This isn’t teleportation in the “Star Trek” sense — the photons aren’t disappearing from one place and appearing in another. Instead, it’s the information that’s being teleported through quantum entanglement.,,, ,,, it is only the information that gets teleported from one place to another. http://blogs.discovermagazine.com/d-brief/2016/09/19/quantum-teleportation-enters-real-world/#.V-HqWNEoDtR

Of related interest:

Darwinian Evolution vs Mathematics https://www.youtube.com/watch?v=q3gyx70BHvA

Verse:

John1:1 “In the beginning was the Word, and the Word was with God, and the Word was God.” of note: ‘the Word’ in John1:1 is translated from ‘Logos’ in Greek. Logos is also the root word from which we derive our modern word logic

bornagain77

DS, I think he is referring to the constraints in mathematically formed natural laws. They do have impacts good enough to predict. I have suggested that logic of structure and quantity -- mathematics -- is core to reality. And yes that raises questions of mind at work, ever since Plato in The Laws Bk X. KF kairosfocus

I don't have any significant disagreements with Berlinski here, but this passage has always troubled me:

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 elementary particles or accelerating forces.

Aren't abstract entities such as Lie groups causally inert? daveS

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