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Source: 6 minutes 4 seconds juncture, Lecture 12-4 (transcription), ... How to Reason and Argue,
by Prof Ram Neta PhD (U Pittsbugh; in Philosophy)

But not every attempt at reductio ad absurdum works. Consider this one.

[1.] Premise: Some things exist even though no one is thinking of them.

[2.] Conclusion: Therefore, reality exceeds the reach of the mind.
[ie:] There's more to reality than there is in the mind.

Now suppose someone challenges [1] [...] as follows. They say, look,
you're saying that some things exist even though no one is thinking of them,
but as you're saying that, presumably you're not just mouthing the words.
You're really thinking it. You're thinking that some things exist even though no one is thinking of them. But if you're thinking that proposition, then you are thinking of those things.
So whatever those things are that illegibly exist, even when no one is thinking of them, well you're thinking of them right now. And so the proposition
[...] that some things exist even when no one is thinking of them [...]
is not true; because you're thinking of those very things right now
(Those very things that exist even though allegedly no one is thinking of them.) [...]
What's wrong with this attempt at a reductio ad absurdum of the premise of this argument?

Please clarify and explain what is wrong?

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    It is impossible to know all the permutations of what you call reality. You cannot know all the shapes of pots that clay can be formed into, but you can know the nature of clay from which all pots are formed. – Swami Vishwananda May 30 '15 at 5:13
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  1. by contemplating a statement such as "everything that exists" you are not actually thinking of everything that exists.

  2. you cannot be thinking of those things that no one is thinking of anymore than you can "turn up the gas quickly enough to see how the darkness looks."

  3. thinking of those things that no one is thinking of is suspiciously like the set which includes all the sets which do not include themselves, from Russell's paradox

  4. you can legitimately think of something now, as you contemplate if it existed one moment ago when nobody was thinking of it, including yourself.

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Some things exist even though no one is thinking of them.

What's wrong with this attempt at a reductio ad absurdum of the premise of this argument?

Answer: The premise is not putting forth a condition 'no one is thinking of them' to the category in question that is 'existence of somethings'.

Rather, what it is claiming that no matter somebody thinks of the existence of some things, it is going to exist any way. it exists any way whether one thinks or not - the existence of those things not dependent over anybody's thinking of them. so this is what is wrong with this premise in attempting at a reductio ad absurdum.

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Kants antinomies showed that there were limits to reasons reach; hence one has other modes of thought, which though not neccessarily truthful in the sense of reason may have significance or truth in their own mode.

This is why, for example, in Badiou system, he had four modes of truth - which he calls truth procedures - science, art, love & politics (notably not religion, as he's an athiest); philosophy he suggests, produces no truths itself; in this he's aligning himself with the Socratic procedure of critical enquiry and being a 'mid-wife' to truth-procedures pregnant with truths, whilst keeping truth procedures honest.

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This falls under the Fallacy of Equivocation, where the ambiguity in natural language is exploited.

A. Some things exist even though no one is thinking of them

B. You're thinking of those very things right now

In the first case, the person means at a minimum that people are specifically and individually thinking of a thing. The second statement uses "thinking of" in a much more abstract and general sense. So the second speaker is pointing out the absurdity of a premise that the first speaker never actually committed to.

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