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In ordinary thought and language there are obviously particulars and it is assumed they usually consist of parts. Ordinary language also supports "generalized, reified properties" (I'd say they feel like universals) and abstract entities: "Red is my favorite color", "Einstein discovered E = m c²", ...

But in extra-philosophical discourse claims like "There is no X" happen, even when it is common and not bizarre (in the languages of the world) to speak of X like it is something that exists; or when most people would state that X exists.

The easier examples are odd particulars (?) like holes or semi-legendary figures (Laozi). Then, composed entities are sometimes denied to exist, in favor of only their parts existing ("there's no such thing as society"). Certain properties or groups and abstract objects are also regularly denied to exist (e.g. "biological sex does not exist").

The most basic way of looking at the problem is distinguishing (A) "What is?" and (B) "How is it?". The same state of affairs can be described more in the manner of answering (A) or (B) -- and from this preference it depends on how easy it is to deny existence without coming across as self-contradictory.

E. g. say, historians conclusively (according to their standards) discover that there was indeed a Chinese man named Laozi in the 4th century BC, but he did not write the Tao Te Ching and was an unimportant peasant. Did Laozi not exist (preference A), or did he exist and people just have very wrong beliefs about him (preference B)?

If composed things are denied to exist, but other composed things are not denied existence, what might be the standard applied here? E. g. Margaret Thatcher believed families exist, but not society.

If properties or groups are denied to exist, but not tout court, what might it mean? E.g. someone who denies "biological sex" but not "humanity".

Now I ask if there is any common ground in those assertions of non-existence? What does it mean extra-philosophically for something to not exist (aside from the most uncontroversial and widely accepted non-existences like witches). Is there some common thread behind such claims, are they made somewhat coherently and in good faith, or are they just either some incoherent confusions or rhetorical devices to exert power?

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    Even when non-existence claims are made coherently and in good faith it does not mean that there needs to be any common thread behind them. Words are commonly used to mean different things in different contexts, without declaring the context, and "is" is especially notorious for its promiscuous use. Some of your examples are based on different attitudes towards available evidence. Others are of choosing one or another implicit "foundational" background (physics, biology, microsociology) with everything emergent on it labeled non-existent, i.e. non-"fundamental". Etc.
    – Conifold
    Feb 27, 2021 at 1:49

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Philosophical existence or non-existence is all about deeper reflection and introspection about one's perceptible experience. For most laypeople, their life experience from their living sense organs are all there is and enough for their entire life, the existence or its negation from one's experience is spontaneous and intuitive, some may be impressive, some may be very weak, some pleasant, some painful... The only time one really finds the need for pundit-like philosophical discourse about some existence or non-existence generally occurs when one begins to doubt his or her previous valuations of certain experiences, from one's whatever mundane, tragic, or mystic life experience. Materialism naturally satisfies most laypeople because a super dry and abstract philosophy on top of their already busy business and life seems utterly useless and redundant. However, many people find out their worldly experience is not ideal from their introspection of their values, thus idealism usually emphasize the existence of some other non-perceptible or not-easily-perceptible things, be it concretely testable or abstract-non-testable-yet-but-will-reflect-on-some-concrete. Some philosophers even went to such an extent that they believe sensible matter are actually a reflection (ie, non-existent) of the ideal/mind/zeitgeist/will, etc.

In summary, all existences are relative to one's conscious experience. Non-existence belief ultimately reflects one's less important valuation judgement about something relative to something else...

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Using Wittgenstein's approach to language, this is like asking 'Are the definitively behaviours that are games, and ones which aren't?', and recognising, no, there are no hard borders. But there are 'family resemblances'. And modes of life. Non-existence, like negation, is totally context-set, except as far as a subcontext universalises (can be translated).

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