If zero probabilities are never epistemically legitimate assignments in a well-formed credence function, the claimed discrete/continuous asymmetry rests on an artifact of an inadequate probability framework rather than a genuine conceptual difference.

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Reasons For

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Reason for

1.Standard probability frameworks assign zero probability to measure-zero sets arbitrarily, conflating metaphysical impossibility with mathematical convenience.
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2.Regularity conditions (no zero probabilities for contingent propositions) are theoretically coherent and capture intuitions about epistemic openness better than standard frameworks.
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3.If the discrete/continuous distinction vanishes under regularity conditions, the asymmetry reflects framework limitations rather than objective metaphysical structure.
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Reasons Against

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Reason against

1.Regularity conditions create severe technical problems: they're incompatible with conditioning on measure-zero events, essential for continuous probability theory.
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2.Some asymmetries between discrete and continuous cases reflect genuine structural differences (countable vs uncountable additivity), not merely framework artifacts.
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3.Declaring standard probability theory 'inadequate' simply to preserve a philosophical thesis inverts the proper direction of theory justification.
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Key Terms

Credence function(as used in epistemology): A mathematical way of expressing how confident you are in different beliefs, where each belief gets a number between 0 (certain it's false) and 1 (certain it's true).
Discrete/continuous asymmetry(philosophy of probability): A claimed difference in how we should treat two types of situations: discrete ones (separate, countable items) versus continuous ones (smooth ranges with no clear boundaries).
Epistemically legitimate(describing whether revolutionary science qualifies as real knowledge): Worthy of being believed or accepted as genuine knowledge based on how we know things. If something is epistemically legitimate, it has properly justified reasons behind it.
Genuine conceptual difference(philosophy of concepts): A real, meaningful distinction based on how we actually understand the nature of things—not just an illusion created by how we measure them.
Well-formed(as used in logic and formal semantics): Structured correctly according to the rules of logic or grammar, so it makes sense and can be evaluated properly.
Zero probabilities(probability and statistics): Assigning a 0% chance that something could happen—saying it's absolutely impossible, with no possibility whatsoever.
artifact(Contrasted with real cellular structures in evaluating microscopy results): A feature in a micrograph produced by the methods of preparation rather than by actual structures in the cell
probability framework(as used in statistics and logic): A system for thinking about how likely different outcomes are, using numbers and rules to measure uncertainty.

Connections

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Modality & Possibility1 linked

Declaring standard probability theory 'inadequate' simply to preserve a philosop...If the discrete/continuous distinction vanishes under regularity conditions, the...Regularity conditions (no zero probabilities for contingent propositions) are th...Regularity conditions create severe technical problems: they're incompatible wit...

Details

Type: claim
Perspectives: 2 (1 for, 1 against)
Edits: 1 edit