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Recently I encountered the acronym ANADEW, which I found to mean A natlang's already dunnit, except worse. Pondering a comment from Logan R. Kearsley where he speculated that "... it's mildly positive in naturalistic circles, since if a natlang already does it, you know you're justified in using it." I began to wonder what did not eventually fit in the ANADEW concept.

I gather that Lojban might be unique in its strong attention to being logical, as explained in two excellent answers to What makes lojban such a “logical” language?. If it is not unique, at least it still is something that I don't thing any natlang has as a strong point.

In the short time that this site's been open, it has struck me that conlangs might be improvements in one way or another over natlangs, yet despite their diversity, they haven't matched the diversity, and utility, of natlangs.

So, what I'm wondering is, other than Lojban and its "logic" is there some other significant traits that some human conlang has which is not found in a natlang somewhere?

I wouldn't consider using never-before-heard sounds as significant, though that's been mentioned in another question. I would have considered having a super minimal verb set significant, as in Kēlen, except that, well ANADEW, or in this case maybe better.

Full disclosure, I am not a conlanger, likely never will be. Nonetheless, I find many fields interesting, and created languages is one of them. With that in mind, please excuse some of my oversights or misconstrued concepts.

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There are a broad range of answers possible here and it would be impossible to list everything. In general, it is rather easy to come up with a feature that does not seem to occur in natural languages: simply take a feature every language appears to possess (for example: phonemes, verbs, hierarchical syntax that can be described with syntax trees, a very large amount of words) and reject it. Then see what you can do with the language. This leads to so-called Engelangs, short for “Engineered Languages”.

Alternatively, one can from the ground up decide to build structure from a different “philosophy”, e.g. build on predicate logic, or stacks (the CS concept), or… well, whatever you can think of that can organize information, really.

To make an example, there is Ithkuil. Ithkuil does not strive to be a naturalistic language. Instead, its goal is to allow for unambiguity. Among the things it does to provide that are a range of grammatical inflections not found in any natural language - too many to list, but one example I can make is its case system. In most natural languages, case is something of a helper to syntax. Case marks words for their syntactic roles and thus helps create the structure necessary to understand a sentence. In Ithkuil however, case marks semantics. The sentence “I hit you” in ithkuil would require different cases for “I” and “you” depending on whether e.g. I was a volitional actor, or whether the hitting was an unavoidable circumstance, or an accident, or mediated by someone else… While traces of such systems are found in natural language, none get even close to the extreme of Ithkuil.

Finally, an interesting anecdote is the Conlang Trigger System, a novel way of structuring languages employed in naturalistic conlangs (i.e. ones striving to be mistakable for natural languages). The trigger system developed from misunderstandings of the way certain Austronesian languages (such as Tagalog) work. It’s a perfectly plausible system… just not actually attested in natural languages. I believe there’s a nice writeup on the whole topic, but cannot find it right now.

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    From the description, Ithkuil fits in the even worse of ANADEW, as you said "traces ... are found in natural language..." Triggers, seems possible, if there is a conlang that uses them successfully, as opposed to the proposition that they could be used to create a conlang.
    – user4
    Commented Feb 8, 2018 at 9:09
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    Trigger systems have absolutely been used in conlangs - they’re pretty much a staple. The important point is that they’re not attested in natural languages but still appear to be perfectly plausible systems that could exist, but just don’t seem to.
    – Sascha Baer
    Commented Feb 8, 2018 at 9:25
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    That, then, does fit what I was looking for. Something as significant as the "logic" of Lojban. What human language could do, yet so far has not. That it "seems" natural/plausible and still never happened is even better.
    – user4
    Commented Feb 8, 2018 at 9:28
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Whilst I also think that this question is too broad as you could argue that almost all conlangs that weren't created to be "naturalistic" have some feature never before seen in a natural language. Wikipedia talks about many a priori languages which, by definiton, contain features not based on existing languages. With that being said, here are some of my favourite (perhaps less well known) philosophical languages that are vastly different from all natural languages.

Pasigraphies

A pasigraphy is a constructed writing system which aims to be intelligible to all people. Unlike other writing systems, pasigraphies generally only exist in written form and cannot be spoken. Some notable pasigraphies include

  • Characteristica Universalis by Gottfried William Leibniz
    Leibniz ws one of the earliest proponents of a universal pasigraphy or "alphabet of human thought" assigned "charactaristics" to objects so that they would be able to be manipulated by means similar to algebra.

  • Real Character by John Wilkins
    The most successful of Wilkins' many philosophical languages and one of the first to gain popular attraction, Real Character is an ideographic system that uses the combination of different symbols to form new concepts.

  • Blissymbolics by Charles K. Bliss
    The most successful pasigraphy to date, Blissymbolics is fundamentally similar to Real Character and are now mainly used to teach people with speech and physical disabilities.

enter image description here (Examples of Blissymbols stolen from All Things Linguistics)

  • Transcendental Algebra by Jacob Linzbach
    Inspired by Leibniz's Characteristica, Transcendental Algebra was created to accompany Edgar de Wahl's international auxiliary Occidental and allows for the "algebraic manipulation" of facts to calculate truth.

I feel like this list wouldn't be complete without a shoutout to Solresol (not having words seems pretty un-natlang-y to me)

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  • The first three, especially the third, seem like simplified Egyptian. Using a "new" writing, even when tied to a new language doesn't seem ground-breaking to me. Nordic priests were combining symbols to make different meanings thousands of years ago. The runes had shapes suggestive of the object that held the meaning for that rune, they had associated numbers that were used to create meanings. I don't know, but have been lead to believe that Chinese characters are created by compounding meanings and thoughts. These don't seem "new" so much as simplified or modernized. I can be wrong, of course
    – user4
    Commented Feb 8, 2018 at 11:26
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    iirc Egyptian Hieroglyphs are logophonetic (the glyphs either mean what they look like or represent a phoneme) and Elder Futhark is an alphabet. If anything you could compare Real Character and Blissymbols to Oracle Bone script, but Oracle bone still couldn't exist without a spoken language (old chinese)
    – as4s4hetic
    Commented Feb 8, 2018 at 12:06