[HN Gopher] In the 17th century, Leibniz dreamed of a machine th...
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In the 17th century, Leibniz dreamed of a machine that could
calculate ideas
Author : MichaelMoser123
Score : 72 points
Date : 2023-07-28 09:34 UTC (1 days ago)
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| dwheeler wrote:
| Leibniz dreamed that we would be able to completrly determine if
| some claim was true or not. We can't do that for all claims, but
| at least in mathematics, we can prove with absolute certainty
| that some axioms will lead you to other claims. So at least a
| little piece of his dream is a reality.
| dvt wrote:
| Leibnitz followed very closely in the footsteps of the
| Neoplatonists and he was what you'd call a _rationalist 's_
| rationalist. He would be later rebuked by Hume (the famous is-
| ought problem made moral-- _ought_ --problems fundamentally
| distinct from rational-- _is_ --problems) and Kant would put the
| nail in the coffin of the rationalist-empiricist debate in the
| next century (with his earth-shattering _Critique of Pure Reason_
| ). And if that wasn't enough, as the logical positivists of the
| early 20th century were still clinging to some form of
| mathematical completeness, Godel proved that the project dreamed
| up by Leibnitz (and more distantly by Plato) was a dead end, to
| Wittgenstein's, Russell's and many others' dismay. Some things
| (even true ones!) are simply unprovable.
|
| I love this story as it spans more than 2000 years, and even
| though the idea itself proved to be untenable, this search gave
| us the enlightenment, the industrial revolution, the computer
| age, and beyond.
| smokel wrote:
| Hmm. Do I understand your comment correctly in that thoughts
| should be either rational or not?
|
| I think different kinds of thinking have their applications in
| different contexts. Godels theorems are hardly ever relevant to
| most of mathematics and not in the least to computers (which
| are finite).
|
| I also doubt that industrialism has anything to do with Leibniz
| or Hume. That part of history is most likely fuelled by greed
| for money, not for philosophical thought.
| routerl wrote:
| > Do I understand your comment correctly in that thoughts
| should be either rational or not?
|
| You didn't understand correctly. "Rationalist", in the OP, is
| a historical label which can retrospectively be applied to a
| specific set of thinkers, who defended specific beliefs, from
| the 16th to the 18th centuries.
|
| None of them were claiming they were the only people who
| thought "rationally"; rather, they were mostly claiming that
| _only_ rational thought could reach truth, and empirical
| evidence need not factor into it.
|
| In modern parlance, the Rationalists believed that all
| knowledge would end up being deductive, like math.
|
| > Godels theorems are hardly ever relevant to most of
| mathematics and not in the least to computers (which are
| finite).
|
| https://en.m.wikipedia.org/wiki/Halting_problem
|
| > I also doubt that industrialism has anything to do with
| Leibnitz or Hume. That part of history is most likely fuelled
| by greed for money, not for philosophical thought.
|
| In this time period, the intellectual circles that Leibniz
| and Hume frequented are _exactly_ the circles that gave rise
| to modern economics, the ability to measure longitude at sea,
| the ability to calculate rates of change over time, using
| steam to power machines, etc. In other words, we 're
| literally talking about all of the intellectual developments
| that directly led to the industrial revolution.
| [deleted]
| routerl wrote:
| > the project dreamed up by Leibnitz (and more distantly by
| Plato)
|
| More distant than that. It all comes from Euclid. Who, you
| know, was actually tremendously successful in that project.
| dvt wrote:
| > More distant than that. It all comes from Euclid. Who, you
| know, was actually tremendously successful in that project.
|
| I of course know of his Elements, but is there any evidence
| that Euclid was an axiomatic reductionist? Was he trying to
| turn _everything_ into an axiomatic system? I regrettably don
| 't know enough about him and should probably rectify that
| (any book suggestions?).
| routerl wrote:
| I don't have any real suggestions, but the two important
| Euclidean books were the _Elements_ and the _Data_ ; the
| latter is about what exists, and the former is about the
| relations between what exists.
|
| You're right that Plato was the first to write that there
| are non-mathematical relationships, and to try to formalize
| them, but what he meant by "non-mathematical" basically
| meant "non-geometric"; recall that we're talking about a
| few hundred years before the invention of algebra.
|
| This laid the seed for Aristotle to formally declare that
| logic is its own discipline, rather than just the method
| used in geometry, and _this_ is when we see these projects
| extend to _everything_ , but no longer as axiomatic
| pursuits.
| thomasjv wrote:
| Kurt Godel was a rationalist.
| https://plato.stanford.edu/entries/goedel/#GodRat
| johndhi wrote:
| What do we dream of now?
|
| I've been reading 70s and 80s sci Fi and loving all of the ideas
| of the future they had. I don't see them today but I don't know
| what to read.
| gpderetta wrote:
| I think cyberpunk was pretty spot on?
| johndhi wrote:
| That's the 90s though, right? What about now?
| MichaelMoser123 wrote:
| Also Newtons method/gradient descent + calculus play a big role
| in backpropagation/ML (Leibnitz was one of the inventors of
| calculus).
| moffkalast wrote:
| _Newton has left the chat_
| cubefox wrote:
| (2019)
|
| Note that this article precedes both ChatGPT and GPT-3. When it
| was written, Leibniz' idea of a machine reasoning by manipulating
| symbols was still science fiction. Now it is very much reality.
| anthk wrote:
| I was about to mention Ramon Llull, but it's there.
| readyplayernull wrote:
| Unless a symbol is as fuzzy as the bray of a donkey of Buridan.
| divbzero wrote:
| _The Baroque Cycle_ contains a fun digression describing the
| combinatorial logic behind this machine.
| sublinear wrote:
| > Swift's point was that language is not a formal system that
| represents human thought, but a messy and ambiguous form of
| expression.
|
| Yep even the greatest minds are susceptible to false dichotomy.
| We now have linguistics and computer science, yet some aspects of
| thought remain forever intractably messy.
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