If the prior probability of every universal hypothesis is zero how would you have to rate the probability of the statement that unicorns (at least one) exist?

Probability of an event = number of outcomes that would fall under this event / total possible number of outcomes.

To say that prior probability of every universal hypothesis is zero is Popper's view that total possible number of outcomes is infinite (thus 1/infinity = 0). No matter how many theories you falsify, there are an infinite number of theories that have not been tested, and so your remaining theories out of this infinite possibility space is zero.

But what about a verifiable existential claim like "at least 1 unicorn exists" be probabilistically assessed?

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    Priors are more Bayesian than Popperian concept:"Priors can be created using a number of methods. A prior can be determined from past information, such as previous experiments. A prior can be elicited from the purely subjective assessment of an experienced expert. An uninformative prior can be created to reflect a balance among outcomes when no information is available." Popper was skeptical of Bayesian confirmation approaches, although he sometimes used some related mathematics. – Conifold Jul 21 '17 at 4:41
  • So what do you think Popper would say if he had to answer what the probability of the statement that unicorns exist is and why? – user18135 Jul 21 '17 at 4:55
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    Popper considers that only universal statements qualify as theories. This is covered in Logic of Scientific Discovery chapter 3, section 15. An existential statement such as "at least one unicorn exists" is not a proper scientific hypothesis for Popper because it is not universal and hence not falsifiable. Thus the assessment that theories have zero prior probability does not apply to it. By contrast, "no unicorns exist" is a hypothesis and is falsifiable. – Bumble Jul 26 '17 at 7:44

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