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Pythagoras' Dream:

Is reality mathematical?

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  • The Debate

    Pythagoras' Dream - technology brought to you by BT/Polycom

    Pythagoras' Dream

    Pythagoras thought he had discovered the key to the universe: mathematics. Was Pythagoras right? Should we see mathematics as the ultimate character of the world or is this a limited vision?

    The Panel

    Theoretical physicist Lee Smolin live from Toronto, Oxford philosopher Peter Hacker and metaphysician Hilary Lawson dismantle the foundations of reality.

  • Find out more about speakers

Jump to what you want to see in the debate
  • Peter Hacker
    The Pitch
    Oxford philosopher scorns reducing everything to mathematics
  • Lee Smolin
    The Pitch
    Unconventional theoretical physicist contends his colleagues' assumptions
  • Hilary Lawson
    The Pitch
    Anti-realist philosopher weaves in the power of our thought
  • The Debate
    Theme One
    Is reality mathematical?
  • The Debate
    Theme Two
    Why is mathematics successful?
  • The Debate
    Theme Three
    The challenge from non-realism
Want to learn more about our speakers?
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Lianne on 03/02/2016 1:19am

I agree with Carlos.

Aside from that, I think anyone who doesn't think that mathematics has the at least the possibility of being the language for the structure of reality must not have explored fractal geometry or chaos theory. I find it odd that neither of these, which are contemporary and will almost positively bring mathematicians and physicists that much closer to fully and concisely describing our complex and changing reality, are mentioned at all in the debate.

reachers on 15/07/2015 10:51pm

Carlos you sound like a classic mathematics-doctrinal 'liar' no different than all fraudulent theists pushing the 'concocted' inexplicable blessed-trinity lie in a blatant pseudo attempt to make the 'alleged-god' a reality! It is inventing another 'mystery' to fraudulently explain an inexplicable lie. Mathematics is merely an abstract concise 'invented' measure of any quantity, the most complex mathematical equation ever concocted is merely an extrapolated version of a simple 12" ruler made complex on each side of the = sign, get a reality! It even goes to the extreme of one theoretical physicist's equation running for 40 pages and still just an extension of a simple 12" ruler, stop concocting phoney 'blessed-trinities'! It is merely stating 1 Banana = 1 Banana and adding massive unnecessary quantities each side of the = sign! You can do this for the remainder of your days on earth stupid! You cite "E.g Lowenheim-Skolem-Tarski Theorem, Tychonoff's Theorem and Zorn's Lemma are all interderivable." EVERYTHING in human external observable existence is interderivable wacko! Because you want it to be; you are all pushing an abstract product in the same way lying theists do! Do you know why? Because you can! with abstract 'anything' and particularly mathematics! Turkey, you just don't get that applying mathematics can be made to everything with absolutely no relation with each other to describe completely different and unrelated things and end up with statements that can be derived from one another. You are all 'reality-frauds'. And the puke-making part of these frauds are that they all reside in PPR (Permanent-Paid-Retirement) in ACEDEMIA! get a reality. Einstein was a 'liar', he concocted the Cosmological Constant to make his General Relativity lie compute because it DID NOT!. Then when Hubble showed it could not describe reality, he completely and fraudulently altered the math to 'fix-it' to work with Hubble 'demonstrating' reality, he was a LIAR! You can 'seasonally-adjust' anything in the cosmos with math!!! And you deliberately make it impossible to read to justify your fraudulent salaries just like mullahs, priests and rabbis do with 'concocted' doctrine! Like all theists you can only be 1. A Liar, 2. An Imbecile, or 3. A Charlatan (which is anyone stating NOTHING when you are implying you are saying something). The most egregious phoney alive today is Stephen Hawking, a disgusting charlatan concocting the black-hole lie, the space-time lie, the time lie, the beginning-lie, the nothing-lie; and when the space-time lie cannot be explained in reality calling (concocting) it a '4th dimension'! How outrageous! The same 'blessed-trinity' lie the theists use! In my view you are all FRAUDS! get a real job. Keep concocting reality it's a 'good little earner'! Just like the lying theists Best regards Yuri Knall (just takin the piss)!

Carlos Tr on 09/11/2013 8:47am

If mathematics are historical artifacts created by us, then how come unrelated theories end up been interderivable when they speak about completely unrelated subjects? E.g Lowenheim-Skolem-Tarski Theorem, Tychonoff's Theorem and Zorn's Lemma are all interderivable. If all mathematical entities are historical artifacts or inventions, how do mathematicians ever agree? How come mathematicians with absolutely no relation with each other who describe completely different and unrelated things end up with statements that can be derived from one another? This points to a deeper structure of reality that can not be explained by the "creation of mathematicians". To say that Mathematics is an invention is to completely ignore its dynamics and history. Mathematics points to a deeper structure of reality and yes there are mathematical facts which can be proven and also (some of them) can be applied to structures of the physical world, but also to any structure, which makes mathematics universal for any structured set of phenomena. That is completely different than saying that everything is reducible to mathematics, it is tantamount to saying that whatever object or set of objects that has a structure can be described mathematically. I am sorry to say this, but the arguments of the philosophers of this debate are pretty lame.

Cliff Harvey on 06/11/2013 12:28am

Sorry to have to go there, but does Peter Hacker really know anything at all about math? What kinds of math courses has he ever taken? High school calculus? Somehow I doubt he even got that far.

His position of mathematical denialism is patently absurd. The whole point and definition of math is to uncover universally valid facts about logical structures. Once you have proven that "A implies B" it is then forever an undeniable fact that any structures that satisfy or express property A in any possible universe, must also express property B. Sorry, but to think that these structures exist only due to human beings is to completely fail to understand what math is. Hasn't he seen the movie Contact, where we communicate with an alien civilization by our common recognition of a universally important structure, the sequence of prime numbers?

The only thing that you can even argue depends on humans at all is the choice of which directions to look in and what structures are important. Emphasis may be human-dependent but mathematical truth is demonstrably not.

If even mathematics "doesn't exist" then certainly the entire body of work of Peter Hacker would have no hope to be regarded as any universal truth, as opposed to merely a fleeting product of a human imagination. If the space of logically provable propositions is "unreal", then certainly some ill-defined subjective opinion is infinitely more unreal. I'm genuinely curious what Hacker thinks he's doing exactly. Does he also regard himself as a mere "artisan"? If so I could at least admire his consistency, but it doesn't seem likely because based on what he says, logic is not a constraint on truth but instead something more like a fashion trend.

As for the rest of the debate, it left me pretty unsatisfied due to the lack of anybody on the other side, like Max Tegmark, to advocate for a more fundamental role for mathematics in our conception of Nature. Now that would be a genuinely interesting topic to debate, but you can never get there if you can't even agree on basic properties of mathematics. Lee Smolin is also a poor representative of the the theoretical physics community, and without that perspective this debate couldn't have gotten very far.

Lucian on 17/10/2012 7:44pm

Hi Johan

One idea we're considering for this year is 'Are There Laws of Nature?', which will tackle the issues Lee raises, so watch this space!

In the mean time you might be interested in other debates that explore the limits of scientific knowledge and the question of if and why we can understand reality at all: "Alchemy, Anarchy and Science", "The Ultimate Particle" and the "Ultimate Map of Reality". These can be found under Science and Technology and Metaphysics and Language respectively on the IaI TV homepage search box.

Johan_0_o on 12/10/2012 12:21pm

Having at first been persuaded by the ideas of our creating the system of mathematics, I then found it odd that both the physicist and that Oxford philosopher spoke about nature being 'kind to us'. What does that mean? nature gently conforms to our systems through some mysterious divine providence?

Is there another debate anywhere that actually delves into this latter question? if not, do one about that - specifically. Is nature kind to us? for building humans who can create systems that fit withitn it rather than jarring with it?

WhereWithAll on 04/10/2012 1:14pm

Peter Hacker's description of math as a human invention and not a human discovery surely applies not only to the status of mathematical entities but that of all scientific creativity. Are numbers any more of an invention than forces, particles, or any of the other concepts that underpin what we think of as reality? If gravity is just an invention I'd like to see someone make do without it...

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