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What do you mean by “no”? Computers and information theory most definitely rely on logical and axiomatic systems, and particular ones at that. Mathematics is a

• naasking 4y ago
  > What do you mean by “no”? Computers and information theory most definitely rely on logical and axiomatic systems, and particular ones at that. I mean "no" to your implicit assertion that such basic logical and axiomatic systems would not evolve in any alien species capable of mathematics. Any such alien will distinguish true and false, will have AND, OR and NOT connectives, and will understand a form of implication (it's inherent to causality). That's all you need to build an understanding of most of our formal systems. Yes the particular expression of our information theory and computer science depends on specific syntactic choices which implies a surface dissimilarity, but the underlying structure will be the same even when expressed in alien math. For instance, an alien species might evolve in an environment in which hyperbolic geometry is more natural (say a species large enough that they can sense gravity directly), and so they develop that geometry first. This will have an isomorphism to our formal model of hyperbolic geometry, and we can then explain Euclidean geometry to them from there. Edit: > Mathematics is also shaped by our thinking, which was my point. Yes, but ultimately irrelevant. This drives the pace of mathematical discovery, and what kinds of mathematical formulae we develop or find most interesting, but this is ultimately irrelevant to the fundamentals which underpin all math, which is what this really comes down to.
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  • illogical_spock 4y ago
    > Any such alien will distinguish true and false, will have AND, OR and NOT connectives, and will understand a form of implication (it's inherent to causality). Implication doesn't have anything to do with causality and in fact the concept of implication in mathematical logic is broken. See: the paradoxes of material implication: https://en.wikipedia.org/wiki/Paradoxes_of_material_implication https://en.wikipedia.org/wiki/Paradoxes_of_material_implicat... To simplify, F -> T (true if false) is a true implication so, for example, I can say that "I am the pope therefore it rained yesterday" and, if it rained yesterday, then the implication is true even though I am not the pope. There has been endless grumbling among philosophers and mathematicians because of this kind of paradox but it is an inevitable result of the axiomatic definition of implication by means of a truth table, and there's no way to correct it without also changing the truth tables of disjunction and negation (because A OR NOT B is equivalent to NOT B THEREFORE A, i.e. because of the way disjunction and negation work, false implies true; you will have to work through this on your own and hit your head on your desk very hard, many times, just as I did when I first realised what a mess this is). In other words, either we accept human axioms of logic, and we have paradoxes of implication, or we don't have paradoxes of implication but then we don't accept human axioms of logic. An alien civilisation may well choose to not accept any axioms of logic that lead to paradoxes of material implication, so they won't have human axioms of logic and, if their formal system is sound, they won't have human logic, and therefore, no human mathematics. In other words, no, aliens will not necessarily have the same mathematics as humans.
    • naasking 4y ago
      > Implication doesn't have anything to do with causality and in fact the concept of implication in mathematical logic is broken I disagree, it's seems very obvious that if-then connectives are a crude causal description. Yes, the crude form is problematic because it's crude.