3 ms·

Are you talking about reasoning in general, reasoning qua that mental process which operates on (representations of) propositions? In which case, I cannot unde

Are you talking about reasoning in general, reasoning qua that mental process which operates on (representations of) propositions? In which case, I cannot understand " true reasoning is expressed in terms of probabilities, not axioms " One of the features of reasoning is that it does not operate in this way. It's highly implausible animals would have been endowed with no ability to operate non-probabilistically on propositions represented by them, since this is essential for correct reasoning -- and a relatively trivial capability to provide. Eg., "if the spider is in boxA, then it is not everywhere else" and so on

jvanderbot 1y ago
I suspect, as a layperson who watches people make decisions all the time, that somewhere in our mind is a "certainty checker". We don't do logic itself, we just create logic from certainty as part of verbal reasoning. It's our messy internal inference of likelihoods that causes us to pause and think, or dash forward with confidence, and convincing others is the only place we need things like "theorems". This is the only way I can square things like intuition, writing to formalize thoughts, verbal argument, etc, with the fact that people are just so mushy all the time.
- mjburgess 1y ago
  People are only mushy in their verbalised reasoning, because its the nature of such reasoning to handle hard cases. Animal cognition, at its basic levels, is incredibly refined and makes necessary use of logic, flawlessly, frequently. This naive cynicism about our mental capacities is a product of this credulity about statistical AI. If one beings with an earnest study of animal intelligence, in order to describe it, it disappears. It's exactly and only a project of the child playing with his lego, certain that great engineering projects have little use for any more than stacking bricks.
  - jvanderbot 1y ago
    Well, we disagree fundamentally. And, I applaud the heavy handed use of condescension. Logical propositions ("2+2=4 regardless of my certainty about it") seem a long way from necessary or sufficient to survival for animals. A fuzzy heatmap of "where is prey going" or "How many prey over there" is much closer to necessary and sufficient. The fact that measurements or senses can update those estimates is a long way from a logical deduction. Something more like probability factor graph can do it, without the pernicious use of "concepts" or too much need for implication, which is sticky and overly rigorous. That's all I have to say, and I doubt we'll find middle ground.
    - mjburgess 1y ago
      You can enumerate, all you wish, all the fuzzy judgements we need to make. This confirms a capacity for uncertain reasoning. It says nothing about the trivial and innumerable ways concepts compose both in content (imagine that A and-also B) and in logical relation (eg., imagine that not A and B). The point of my "condescension" was to point out that people of your position are arguing from ignorance, with confirmation bias -- ie., having no study of animal intelligence, and only ever repeating what they know about their own study of irrelevant systems. Your reply evidences this exactly. Zero engagement with any facts on the ground about actual animal intelligence. Are you really actually trying to account for animal intelligence, or as I have claimed twice now, are you only really wishing to maintain your ignorance of it, dismiss any analysis of it, and instead "confirm" that whatever you are aware of "must, presumably, apply". Imagine being faced with such bad faith over and over and over again. It is like arguing with people who insist the world is flat, and when challenged, point to euclidean geometry and the flatness of the pavement under their feet. If I begin by anticipating such behaviour, you can see why.
      - jvanderbot 1y ago
        Hey it's possible you're absolutely right, but our arguments have about equal value (none) because they are both presented as personal opinions with zero external support. I just had the decency to admit that up front.
soulofmischief 1y ago
Propositions are just predictions, they all come with some level of uncertainty even if we ignore that uncertainty for practical purposes. Any validation of a theory is inherently statistical, as you must sample your environment with some level of precision across spacetime, and that level of precision correlates to the known accuracy of hypotheses. In other words, we can create axiomatic systems of logic, but ultimately any attempt to compare them to reality involves empirical sampling. Unlike classical physics, our current understanding of quantum physics essentially allows for anything to be "possible" at large enough spacetime scales, even if it is never actually "probable". For example, quantum tunneling, where a quantum system might suddenly overcome an energy barrier despite lacking the required energy. Every day when I walk outside my door and step onto the ground, I am operating on a belief that gravity will work the same way every time, that I won't suddenly pass through the Earth's crust or float into the sky. We often take such things for granted, as axiomatic, but ultimately all of our reasoning is based on statistical correlations. There is the ever-minute possibility that gravity suddenly stops working as expected. > if the spider is in boxA, then it is not everywhere else We can't even physically prove that. There's always some level of uncertainty which introduces probability into your reasoning. It's just convenient for us to say, "it's exceedingly unlikely in the entire age of the universe that a macroscopic spider will tunnel from Box A to Box B", and apply non-probabilistic heuristics. It doesn't remove the probability, we just don't bother to consider it when making decisions because the energy required for accounting for such improbabilities outweighs the energy saved by not accounting for them. As mentioned in my comment, there's also the possibility that universal axioms may be recoverable as fixed points in a reasoning manifold, or in some other transformation. If you view these probabilities as attractors on some surface, fixed points may represent "axioms" that are true or false under any contextual transformation.
- mjburgess 1y ago
  This response doesn't fill me with confidence. You aren't really engaging with any of the actual issues your position entails. A proposition is not a prediction. A prediction is either an estimate of the value of some quantity ("the dumb ML meaning of prediction") or a proposition which describes a future scenario. We can trivially enumerate propositions that do not describe future scenarios, eg., 2 + 2 = 4. Uncertainty is a property of belief attitudes towards propositions, it isn't a feature of their semantic content. A person doesnt mean anything different by "2 + 2 = 4" if they are 80 or 90% sure of it. > We can't even physically prove that. Irrelevant. Our minds are not constrained by physical possibility, necessarily so, as we know very little about what is physically possible. I can imagine abitary number of cases, arising out of logical manipulation of propositons, that are not physically possible. (Eg., "Superman can lift any building. The empire state building is so-and-so a kind of building. Imagine(Superman lifting the empire state building)"). The infinite variety of our imagination is a trivial consequence of non-probabilistic operations on propositions, it's incomprehensibly implausible as a consequence of merely probabilistic ones. That nature seems to have endowed minds with discrete operations, that these are empirical in operation across very wide classes of reasoning, including imagination, that these seem trivial for nature to provide (etc.) render the notion that they don't exist highly highly implausible. There is nothing lacking explanation here. The relevant mental processes we have to hand are fairly obvious and fairly easy to explain. Its an obvious act of credulity to try and find some way to make the latest trinkets of the recent rich some sort of miracle. All of these projects of "incredible abstraction" follow around these hype cycles, turning lead into gold: if x "is really" y, and y "is really" z, and ..., then x is amazin! This piles towers of every more general hollowed-out words on top of each other until the most trivial thing sounds like a wonder.
naasking 1y ago
> It's highly implausible animals would have been endowed with no ability to operate non-probabilistically on propositions represented by them, since this is essential for correct reasoning Why would animals need to evolve 100% correct reasoning if probabilistically correct reasoning suffices? If probabilistic reasoning is cheaper in terms of energy then correct reasoning is a disadvantage.
- mjburgess 1y ago
  It doesnt suffice. It's also vastly energetically cheaper just to have (algorithmic) negation. Compressing (A, not A) into a probability function is extremely incomprehensibly expensive.
  - naasking 1y ago
    > It's also vastly energetically cheaper just to have (algorithmic) negation. Even if true, that's an argument that it's cheaper to have something, not that it's cheaper to develop it through natural selection. Training time and energy for LLMs shows how energy intensive training to get to the point of grokking/circuit generalization.
    - mjburgess 1y ago
      It is a matter of empirical fact that we can reason with logical relationships. Thus taking an LLM and it's training as a model of conginition is empriically false. It should be obviously doubly so, since as a model -- as you point out -- it makes trivial aspects of our cognition impossibly expensive to acqurie.
      - naasking 1y ago
        > It is a matter of empirical fact that we can reason with logical relationships It is a matter of empirical fact that our ability to correctly reason with logical relationships only has high statistical likelihood, not certainty. This looks less like actual logic and more like a probabilistic model of logic.

jvanderbot 1y ago

I suspect, as a layperson who watches people make decisions all the time, that somewhere in our mind is a "certainty checker". We don't do logic itself, we just create logic from certainty as part of verbal reasoning. It's our messy internal inference of likelihoods that causes us to pause and think, or dash forward with confidence, and convincing others is the only place we need things like "theorems". This is the only way I can square things like intuition, writing to formalize thoughts, verbal argument, etc, with the fact that people are just so mushy all the time.

mjburgess 1y ago
People are only mushy in their verbalised reasoning, because its the nature of such reasoning to handle hard cases. Animal cognition, at its basic levels, is incredibly refined and makes necessary use of logic, flawlessly, frequently. This naive cynicism about our mental capacities is a product of this credulity about statistical AI. If one beings with an earnest study of animal intelligence, in order to describe it, it disappears. It's exactly and only a project of the child playing with his lego, certain that great engineering projects have little use for any more than stacking bricks.
- jvanderbot 1y ago
  Well, we disagree fundamentally. And, I applaud the heavy handed use of condescension. Logical propositions ("2+2=4 regardless of my certainty about it") seem a long way from necessary or sufficient to survival for animals. A fuzzy heatmap of "where is prey going" or "How many prey over there" is much closer to necessary and sufficient. The fact that measurements or senses can update those estimates is a long way from a logical deduction. Something more like probability factor graph can do it, without the pernicious use of "concepts" or too much need for implication, which is sticky and overly rigorous. That's all I have to say, and I doubt we'll find middle ground.
  - mjburgess 1y ago
    You can enumerate, all you wish, all the fuzzy judgements we need to make. This confirms a capacity for uncertain reasoning. It says nothing about the trivial and innumerable ways concepts compose both in content (imagine that A and-also B) and in logical relation (eg., imagine that not A and B). The point of my "condescension" was to point out that people of your position are arguing from ignorance, with confirmation bias -- ie., having no study of animal intelligence, and only ever repeating what they know about their own study of irrelevant systems. Your reply evidences this exactly. Zero engagement with any facts on the ground about actual animal intelligence. Are you really actually trying to account for animal intelligence, or as I have claimed twice now, are you only really wishing to maintain your ignorance of it, dismiss any analysis of it, and instead "confirm" that whatever you are aware of "must, presumably, apply". Imagine being faced with such bad faith over and over and over again. It is like arguing with people who insist the world is flat, and when challenged, point to euclidean geometry and the flatness of the pavement under their feet. If I begin by anticipating such behaviour, you can see why.
    - jvanderbot 1y ago
      Hey it's possible you're absolutely right, but our arguments have about equal value (none) because they are both presented as personal opinions with zero external support. I just had the decency to admit that up front.

soulofmischief 1y ago

Propositions are just predictions, they all come with some level of uncertainty even if we ignore that uncertainty for practical purposes. Any validation of a theory is inherently statistical, as you must sample your environment with some level of precision across spacetime, and that level of precision correlates to the known accuracy of hypotheses. In other words, we can create axiomatic systems of logic, but ultimately any attempt to compare them to reality involves empirical sampling. Unlike classical physics, our current understanding of quantum physics essentially allows for anything to be "possible" at large enough spacetime scales, even if it is never actually "probable". For example, quantum tunneling, where a quantum system might suddenly overcome an energy barrier despite lacking the required energy. Every day when I walk outside my door and step onto the ground, I am operating on a belief that gravity will work the same way every time, that I won't suddenly pass through the Earth's crust or float into the sky. We often take such things for granted, as axiomatic, but ultimately all of our reasoning is based on statistical correlations. There is the ever-minute possibility that gravity suddenly stops working as expected. > if the spider is in boxA, then it is not everywhere else We can't even physically prove that. There's always some level of uncertainty which introduces probability into your reasoning. It's just convenient for us to say, "it's exceedingly unlikely in the entire age of the universe that a macroscopic spider will tunnel from Box A to Box B", and apply non-probabilistic heuristics. It doesn't remove the probability, we just don't bother to consider it when making decisions because the energy required for accounting for such improbabilities outweighs the energy saved by not accounting for them. As mentioned in my comment, there's also the possibility that universal axioms may be recoverable as fixed points in a reasoning manifold, or in some other transformation. If you view these probabilities as attractors on some surface, fixed points may represent "axioms" that are true or false under any contextual transformation.

mjburgess 1y ago
This response doesn't fill me with confidence. You aren't really engaging with any of the actual issues your position entails. A proposition is not a prediction. A prediction is either an estimate of the value of some quantity ("the dumb ML meaning of prediction") or a proposition which describes a future scenario. We can trivially enumerate propositions that do not describe future scenarios, eg., 2 + 2 = 4. Uncertainty is a property of belief attitudes towards propositions, it isn't a feature of their semantic content. A person doesnt mean anything different by "2 + 2 = 4" if they are 80 or 90% sure of it. > We can't even physically prove that. Irrelevant. Our minds are not constrained by physical possibility, necessarily so, as we know very little about what is physically possible. I can imagine abitary number of cases, arising out of logical manipulation of propositons, that are not physically possible. (Eg., "Superman can lift any building. The empire state building is so-and-so a kind of building. Imagine(Superman lifting the empire state building)"). The infinite variety of our imagination is a trivial consequence of non-probabilistic operations on propositions, it's incomprehensibly implausible as a consequence of merely probabilistic ones. That nature seems to have endowed minds with discrete operations, that these are empirical in operation across very wide classes of reasoning, including imagination, that these seem trivial for nature to provide (etc.) render the notion that they don't exist highly highly implausible. There is nothing lacking explanation here. The relevant mental processes we have to hand are fairly obvious and fairly easy to explain. Its an obvious act of credulity to try and find some way to make the latest trinkets of the recent rich some sort of miracle. All of these projects of "incredible abstraction" follow around these hype cycles, turning lead into gold: if x "is really" y, and y "is really" z, and ..., then x is amazin! This piles towers of every more general hollowed-out words on top of each other until the most trivial thing sounds like a wonder.

naasking 1y ago

> It's highly implausible animals would have been endowed with no ability to operate non-probabilistically on propositions represented by them, since this is essential for correct reasoning Why would animals need to evolve 100% correct reasoning if probabilistically correct reasoning suffices? If probabilistic reasoning is cheaper in terms of energy then correct reasoning is a disadvantage.

mjburgess 1y ago
It doesnt suffice. It's also vastly energetically cheaper just to have (algorithmic) negation. Compressing (A, not A) into a probability function is extremely incomprehensibly expensive.
- naasking 1y ago
  > It's also vastly energetically cheaper just to have (algorithmic) negation. Even if true, that's an argument that it's cheaper to have something, not that it's cheaper to develop it through natural selection. Training time and energy for LLMs shows how energy intensive training to get to the point of grokking/circuit generalization.
  - mjburgess 1y ago
    It is a matter of empirical fact that we can reason with logical relationships. Thus taking an LLM and it's training as a model of conginition is empriically false. It should be obviously doubly so, since as a model -- as you point out -- it makes trivial aspects of our cognition impossibly expensive to acqurie.
    - naasking 1y ago
      > It is a matter of empirical fact that we can reason with logical relationships It is a matter of empirical fact that our ability to correctly reason with logical relationships only has high statistical likelihood, not certainty. This looks less like actual logic and more like a probabilistic model of logic.