Could someone explain in layman's terms the difference between truth conditions

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Could someone explain in layman's terms the difference between truth conditions and assertability conditions, and what is at stake between them? Thanks for your time.

Truth conditions are often held to be independent of assertability. Thus, the claim that 'snow is white' or '6 is the smallest perfect number' are true, regardless of whether anyone is warranted in asserting these claims. The reason why some philosophers might object to this format is that it appears to open the door to a radical skepticism, e.g. it may be claimed that there are truths that elude our best cognitive posers. Such philosophers thus advance what may be called an epistemic understanding of truth that would make it incoherent to think there are truths that outstrip our warranted assertability. Although I am not a radical skeptic, I am inclined to think that a wide-ranging skepticism is at least coherent --why limit truth to what we have (or ideally might have) justification in asserting?

You might find the work of Roger Trigg of interest in such matters, e.g. Reality at Risk.

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