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I think the problem of proving the (non) existence of something is as simple as understanding that (most of the time) it can not be deductive. I'd say that when

I think the problem of proving the (non) existence of something is as simple as understanding that (most of the time) it can not be deductive. I'd say that when it comes to existence, it is always inductive. What kind of proof can anyone give me that she/he exists? Or the rest of the world? There is no such thing. Even in mathematics, if one doubts basic entities as numbers and their properties, the whole establishment of mathematics starts to crack, at least for that particualr one human being. All of our reasoning about the world is inference based, hence probabilistic. That's in the nature of science, religion and everything else in between. There is strong evidence for the existence of God, but it's inherently inductive. Not to mention various conceputal complication which follow from in different kind of reasoning about God (in whatever view).

shkkmo 11y ago
You can, in fact, prove non-existence deductively through proof by contradiction. Proofs can be valid even if their premises (assumptions) are not true. Mathematics does not rest on the truth of it's assumptions, but on the validity of it's proofs. If you can create an interesting system of proofs off of an a different sent of premises, then that can also be very useful (see non-euclidean geometry). If you can't create an interesting system, then those premises have no value. I also disagree that all our reasoning about the world is probabilistic. By saying that all reasoning is inductive, you make you earlier assertion that "I'd say that when it comes to existence, it is always inductive." empty because you are claiming that all reasoning is inductive.
Dylan16807 11y ago
> Even in mathematics, if one doubts basic entities as numbers and their properties, the whole establishment of mathematics starts to crack, at least for that particualr one human being. That's not how it works. Numbers are their properties. You are free to use any properties you want when you commit mathematics, and you will get different sorts of behavior from your numbers depending on your choices. There is nothing to doubt about a set of properties being itself. No 'establishment' tells you how numbers work. Use whatever you like.
- danielam 11y ago
  Well, if mathematics is to say anything about the world, then the foundations must be sound (and drawn from experience which brings us back to empiricism). Sometimes the problem isn't necessarily with the concepts in our heads but the formalizations we choose to proceed from. Set theory is a great example. Take Russell's paradox, for instance, and the different responses to it (e.g., ZFC, Lesniewski's mereology). I'm reminded of Duhem's rather humorous "German Science" where he characterizes German mathematics as being disproportionately oriented toward rigorously deducing nonsense from arbitrary axioms as opposed to the French tendency to rely on intuition to arrive at sensible axioms but neglecting systematic rigor afterwards.
  - Dylan16807 11y ago
    Physics says things about the world. Math is a tool to help you make logical conclusions.

shkkmo 11y ago

You can, in fact, prove non-existence deductively through proof by contradiction. Proofs can be valid even if their premises (assumptions) are not true. Mathematics does not rest on the truth of it's assumptions, but on the validity of it's proofs. If you can create an interesting system of proofs off of an a different sent of premises, then that can also be very useful (see non-euclidean geometry). If you can't create an interesting system, then those premises have no value. I also disagree that all our reasoning about the world is probabilistic. By saying that all reasoning is inductive, you make you earlier assertion that "I'd say that when it comes to existence, it is always inductive." empty because you are claiming that all reasoning is inductive.

Dylan16807 11y ago

> Even in mathematics, if one doubts basic entities as numbers and their properties, the whole establishment of mathematics starts to crack, at least for that particualr one human being. That's not how it works. Numbers are their properties. You are free to use any properties you want when you commit mathematics, and you will get different sorts of behavior from your numbers depending on your choices. There is nothing to doubt about a set of properties being itself. No 'establishment' tells you how numbers work. Use whatever you like.

danielam 11y ago
Well, if mathematics is to say anything about the world, then the foundations must be sound (and drawn from experience which brings us back to empiricism). Sometimes the problem isn't necessarily with the concepts in our heads but the formalizations we choose to proceed from. Set theory is a great example. Take Russell's paradox, for instance, and the different responses to it (e.g., ZFC, Lesniewski's mereology). I'm reminded of Duhem's rather humorous "German Science" where he characterizes German mathematics as being disproportionately oriented toward rigorously deducing nonsense from arbitrary axioms as opposed to the French tendency to rely on intuition to arrive at sensible axioms but neglecting systematic rigor afterwards.
- Dylan16807 11y ago
  Physics says things about the world. Math is a tool to help you make logical conclusions.