Originally shared by Event Horizon
Where does logic come from ? Why should anything necessarily be true or false within logic ? If we, as sentient observers, are a part of a Universe in which logical truths are necessary components of the mathematics upon which the material reality (from which our conscious minds emerge) is built in regards to physics, and we have derived those logical truths from within the fabric and patterned process of that Universe - how can we possess any final certainty or ontological and epistemological anchor from which to be certain about any of these things ?
Ming the Merciless was a very logical (complete and utter) bastard, but his fictional girlfriend was non-fictionally gorgeous which makes him kind of cool.
It's not all that difficult.
ReplyDeleteLogic "works" because we make it up.
Math is a map of reality, not the basis of reality.
Math itself does nothing to inform us which parts can be used for modelling a given section of reality : for that we need to observe that section of reality, and then pick parts of our language of relations (math) that fit with the particular relations observed.
That is what physics is : a specific map, made with our generic mapping tool (math), which we have created ourselves and adapted for the kinds of relations we tend to see in reality.
This shouldn't be any kind of mystery, as it all happened in plain view of history.
We don't get and also don't need certainty. We learn about the world by observing it, and inducing working models from our observations.
Induction is not logically justifiable, but is reflexively justifiable, which is more than can be said about logic.
Induction is of course also able to justify the use of logic, but has a tendency to overrate the utility of it.
Andreas Geisler hi. If we "make up" logic, why should its extrapolation to mathematics possess any correlation to material reality ?
ReplyDeleteOther than that the same material reality provides the conditions within which life, sentience, intelligence and (eventually) mathematics can arise to provide compelling explanations and prediction, in something of a closed-loop; how is it that logical heuristics, analysis or algorithms and theorems possess an apparent identity with the entities, artefacts and relationships they so successfully describe (or map) ?
Is the emergence of mathematics an organic, culturally and historically-contextualised process, perhaps inevitable beyond a certain threshhold of individual intelligence and collective, culturally-sustainable knowledge-retention and transmission ?
How is it that operations on the complex number plane should be so powerful in describing aspects of mathematics and material reality when these inventions are clearly so far removed from intuitive conceptions of number or relational (object) dynamics in the primary human domain of phenomenological sense-experience ?
I agree that certainty is not obtained, but think this occurs at a deeper level which suggests that mathematics and physics are mysterious, or at the very least remain metaphysically and ontologically problematic.
☺
Event Horizon
ReplyDelete"why should its extrapolation to mathematics possess any correlation to material reality?"
The answer is that almost none of them do.
For explanation, this: There is an infinity of infinities of possible extrapolations, and as you must be aware it is only by observation that we find out which tiny subsets can help us describe the behaviors we observe.
To say that the physical reality is made of maths is to fundamentally and irretriveably confuse the map with the territory.
Physics is a discipline, and different from its object of study.
One can certainly argue that physics is made from math, but it is made in a way that is so completely dependent on our training of the systems, bending them to mimic the observed behaviors, that all claims of platonism are patently ludicrous.
Is the universe relational? Sure. Is being relational identical to being made of math? Obviously not.
Again: I find it obviously problematic to call something mysterious which:
1) Was painstakingly built up, in full view of history.
2) Is literally concerned with provability - the very antithesis of mystery.
There is nothing hidden. If we make certain axioms, we get certain results, and we can and do change the axioms in order to get results more suited to our intents.
I think it's subtler than that. If elements of logic, or mathematical descriptions or physical laws, are invented to explain one system, then on what grounds do we have to suppose they are ever applicable elsewhere (e.g. the normal distribution is remarkably prevalent) ? It seems to me we only invented descriptions of logic, not logic itself. Reality isn't logic, but it sure as heck seems to behave with ruthlessly unforgiving logic. Physical laws now, yes, I'll happily grant that we definitely have to make observations to determine the specific processes at work (if we didn't I be unemployed). But logic itself ? That seems absolutely ubiquitous.
ReplyDeleteRhys Taylor Because we get to change them as we wish?
ReplyDeleteArithmetic is the generalization of counting concrete objects.
Math is a generalization of that.
There is no single "logic", rather what we invented is a system for generating logics.
What you seem to be calling "logic itself" is what exactly? Because if you mean that "one thing is proportional to another" or "one thing causes another", then these are not logic, but rather inductive conclusions we have formed.
It is incredibly easy to get caught up in circularities with this, and I am quite confident that circularity is what all platonism boils down to.
Now, normal distributions. I am sure you can look at the formulae that generate a normal distribution and find out why a lot of events would fall into such a pattern. Similarly with how growth patterns sometimes approximate a golden ratio.
Again, provability is the antithesis of mystery. There is no benefit to making this any more difficult than that.
Thats ming’s daughter.
ReplyDeleteGeisler's account of the basis of logic is the generally accepted view. However, various people have questioned, or at least marveled at, why math and logic work so well? Here's what i would add to Geisler's account. Logic as we know it has developed by humans over time by the time honored approach of generate and test, just like evolution. We invent some logical element and if it works well ("correlates to material reality") we keep it. This is possible because the world has enduring regularities and we can observe parts of it which logic merely summarizes. So the original issue should have been why is the world so regular that it admits to a system of logic? That we don't know beyond basic natural science.
ReplyDeleteThe second thing to point out is that logic as we know it is not a perfect accounting of reality, not a simple mapping from concept to observation. Especially problematic is complex systems where all known logic fails in various ways.
But at any rate there's no mystery why logic/math correlate to material reality (it's generated and selected by humans to do so).
It may be interesting to cogitate on the following diagram originally attributed to Penrose. However, don't get too worked up about it because many people think it's meaningless (old conversation by various thinkers on the Edge).
https://lh3.googleusercontent.com/557zCUNw7v9qkMXQJRa7TW5w_pyfnOdinRp3w0lBeospgs0rtUMJ87MxVKvyT_EPxsb6PXkDJ_w2704sreopYb4CiBHa_1pz04o=s0
Host For the End As portrayed by Ornelia Muti.
ReplyDeletehttps://en.wikipedia.org/wiki/Ornella_Muti
Edward Morbius One of the hottest ladies of all time, and the model used by Fumetti(?) for all those great dirty horror comic covers back in the 70s. (The covers are great, the comics are sick & disturbing even by my standards.)
ReplyDeleteBill Brayman I think there is a particular risk, for people who work with axiomatic systems a lot, to inductively form am altogether too high opinion of the applicability of logic.
ReplyDeleteAs Hume pointed out, people are bad at logic, and clearly manage to survive just fine without it, as the capacity for it develops late in life, if at all.
The biggest weakness of deduction is its strength: With deduction, you can prove whatever you want, even things that are patently false in the real world.
This is because most people fail to realize that any act of deduction is an operation not on the real world, but on an imaginary world in which the premises are exactly True.
For this reason, the arguer can simply pick premises and inferences such that the conclusion is as desired.
Is logic about determining truth or falsity, or about determining the validity or invalidity of conclusions based on premises and operations?
ReplyDeleteEdward Morbius I would say that logic is about determining which conclusions are tautological to the axioms within a finite number of steps.
ReplyDeleteBut that might be imprecise :)
Andreas Geisler There are ... different classes of logic.
ReplyDeleteEdward Morbius imprecise it is, then :)
ReplyDeleteAndreas Geisler yes definitely i've seen that narrow view of logic a lot. Formal logic has a lot of limitations. But logic like geometry or anything like that is powerful when used right. The world has it's patterns and regularities. Logic works well when it represents those.
ReplyDeleteAs to the original question where does logic come from, I don't think it is quite as mysterious as it seems. Just like math, there are abstract structures that can be used to model the world effectively. Humans discover those abstract structures and linguistic structures to express and manipulate them, and voila you have math and logic, just like many other aspects of information processing.
It is that basic isomorphism between abstract structure and material structure that allows logic to work.
And like you say not all the world fits into axiomatic structures (so far) and people sometimes overlook the limitations.
Bill Brayman Even worse than overlooking the limitations, they have a fairly massive "survivorship bias".
ReplyDeleteThat they think "This fits really well" while only evaluating the stuff that actually does fit.
For every bit of axiomatic system which can be fitted to a given bit of observed reality-behavior, there is a literal infinity of other such bits of axiomatic system which doesn't fit at all.
They only look at the stuff that makes it past the inductive selection process.
If we look, as we should, at the ENTIRETY of logic, it really cannot be said to fit reality. The two are completely different, even if some patterns in one can be mapped onto some patterns in the other.
This is no different from, say, encrypting a painting by Rembrandt so as to make it identical to a van Gogh, and then claiming the Rembrandt IS the van Gogh.
If there was a universal key to perform such a conversion, that would be something that could be defended, but if there is just a list of mutually independent transformations of each square micrometer of the source, then there is exactly no basis for claiming they are similar.
Yet with logics, people forget that we do not have a universal key that transforms logic into physics. We instead have a feature-by-feature set of transformations that turn observations into logickable components - and since they were specifically selected for having comparable behavior, the correspondence is unsurprising.
Rhys Taylor As just an educated layman i'll press on a bit here. You said: "It seems to me we only invented descriptions of logic, not logic itself. Reality isn't logic, but it sure as heck seems to behave with ruthlessly unforgiving logic."
ReplyDeleteYes, in a sense logic is just another dimension of reality. Now as you might guess, I claim that logic only exists as part of an information processing system. Whatever elements of the universe might be doing, if there is no info processing, there is no logic. Yet, of course, there are patterns and regularities but there is also randomness and chaos all mixed together. Only because we can process information are we able to map logical and mathematical structures onto material reality as shown from our instruments.
We should step back be sure of our terms. Logic is a system with truth semantics. Math is a system with many other semantics, all of which have to do with the notion of structure. Model theory gets into this stuff. You use logic to make assertions about the elements of structures or structures themselves. That's where the truth semantics comes from. Assertions are true or false. And you need a language to express assertions. So humans invented languages and they discovered structures. But structures as analyzable entities are only visible to an information processing system.
I'll return to what I'd intended to start with but steered away from initially: Logic is a set of tools for information processing intended to provide useful inferences and conclusions based on observations, prior knowledge, and models of understanding.
ReplyDeleteIt has different forms. There are informal and formal logic, predicate logic, Boolean logic. But all start with some set of premises, assumptions, observations, states, etc., and try to come up with inferences or conclusions based on these.
To that extent, logic comes from within: it's part of our mental wetware and software for understanding the Universe. But, since we (and our brains) are both part of the Universe, and came up within it, and function and operate within it, logic tends to have a strong conformance with the Universe as well. It's useful because of that.
I see certainty as a red herring. Nothing is certain. But many things are useful.
The ultimate determination of utility is models which can be used to meaningfully interact with the Universe. At some small or large scale.
Our models are necessarily incomplete (that's a large part of what being a model is: incompleteness). The information feeding into them is incomplete. The information and interactions flowing from them is incomplete.
But iterated over a process control loop -- cybernetics, OODA, whatever you will -- we observe a state of the Universe, we process that and apply it to our models, however imprecise, we act, and then judge the outcome against expectations. Often it's close enough, occasionally not, in which case, being flexible meat-computers, we toss out our invalidated models and try something else.
(Or we don't, in which case we're boxed in by our models, or senses, or responses, or some combination thereof, much as an insect will fly against a window or into a flame, based on an inadequate modeling of the Universe.)
Philosophy is a systems science.
Edward Morbius Like Hume, I do not believe logic is part of our wetware.
ReplyDeleteOur brains are induction engines. The basic function of neurons is inherently inductive.
We induce logic, at some point in our development. Perhaps not quite as late as Hume suggested, because he was likely sticking to when we are able to vocalize what we think we're doing when we think we're doing logic - not to when we're actually applying logic-like rules.
One might say induction is a logic, but I find them too dissimilar for that to be useful. That's just semantics, though.
The important part is that induction is capable of functioning without deductive heuristics. Adding such heuristics makes it faster, which by way of some thresholds to concept formation makes some new options possible in the first place.
But we don't need to have it hard-wired in to live.
Andreas Geisler Finding independent instances of a thing can be interesting. Variants of logic in European, Indian, and Chinese philosophy, say (though commerce existed back to Roman times).
ReplyDeleteBetter yet: in American or Australian native traditions.
I'm largely ignorant of most of these.
Edward Morbius When I say we induce it, I mean each human indpendently.
ReplyDeleteSimilarity in inductive conclusions is sufficiently explained by similarities in the input and similarity in the inductive machinery, and both of those are well-evidenced.
Our reality, by and large, behaves in a way that an idea can't be simultaneously true and false.
That becomes much less impressive when we realize that our ideas are generally too imprecise to be considered true, but precise enough to be reliable. But as a heuristic, saying "John was in the Library when the murder was committed in the Dining hall, so he can't have dunnit" generally works out fine.
Andreas Geisler 'We" individually, but also "we" collectively, in that logic is a shared set of tools used in communicating decisions.
ReplyDeleteI'm not arguing that logic is is or is not innate to human brains, only that it's found there, placed by genetics or education, or some combination, it doesn't much matter for my pount above: Logic is a set of tools for information processing.
But yes, logic comes from us, by some set of routes, genetic or cultural.
Well, I think this one has degenerated too far into nuttery for me, so I'm muting this. Y'all have fun though.
ReplyDeleteEdward Morbius Genetic AND cultural. The systems work OK, and people talk about how they use them, which leads to cultural convergence into publicly endorsed systems of reasoning.
ReplyDeleteRhys Taylor Considering that this started with Mathematical Platonism, it is logically inconceivable that it has become more nutty.
Mathematical Platonism is loony bin material :)