How to express in a diplomatic, but not too subtle, way that an old (and popular) notion should be dismissed in favor of a new (and better) one?

Question

I'm comparing two (mathematical) notions, say 'functoid' and 'punctoid' (these are fictitious names for the sake of discussion), and I'm arguing that punctoids should be definitely preferred to functoids for a series of reasons.

To convey this idea, I would like to use an expression that is neither too strong nor too subtle. I have been thinking about something like the following:

In a way, what we have just remarked makes the notion of functoid à la Craig and Daniel overruled by punctoids.

But I'm not sure about my use of the term 'overruled'. I had also thought of replacing it with 'shelved', but this sounds too soft to my ears. Please note that I need to stick to a formal register, as this is intended for a publication.

Any suggestions?

Answer 1

supersede, as defined by Dictionary.com

to set aside or cause to be set aside as void, useless, or obsolete, usually in favor of something mentioned; make obsolete: They superseded the old statute with a new one.

Steven Weinberg (Nobel Prize winner in Physics, 1979) used supersede in this way in his book Lectures on Quantum Mechanics, page 21:

It was hopeless to use matrix mechanics to solve more complicated problems, like the hydrogen molecule, so wave mechanics largely superseded matrix mechanixs among the tools of theoretical physics.

The OP's sentence thus becomes:

In a way, what we have just remarked makes the notion of functoid à la Craig and Daniel superseded by punctoids.

I suggest rewriting the sentence to say:

In a way, what we have just remarked means that punctiods supersede the notion of functoids a la Craig and Daniel.

Footnote about the use of a la in a math article: See Using the Mathematics Literature.

Answer 2

Consider "deprecated". See https://www.merriam-webster.com/words-at-play/deprecate, however.

According to this note, it's been used since the 1980s to imply obsolescence, although MW questions this use.

You can be more positive by noting that the punctoid is superior or better in a variety of ways (more flexible, less prone to error, whatever).

Thus:

The functoid should be deprecated in favor of the punctoid.

A milder approach is to say that the funtcoid approach should be replaced.

Answer 3

In a way, what we have just remarked makes the notion of functoid à la Craig and Daniel overruled by punctoids.

Overruled is the wrong word since the punctoids are not sitting in judgment over the functoids, but the real problem with the phrasing is the makes. What you've just shown (supposedly) proves that functoid is inferior (not as good) or obsolete (no good at all any longer).

You can certainly use à la but in English it's associated with ice cream and is precious verging on twee. You were trying to avoid sounding weak, so you need a substitute.

In a way is just incorrect. Either you've established the point or you haven't. (If it's the latter, you shouldn't be saying the functoids are obsolete at all.)

These factors establish that Craig and Daniel's notion of functoid is fundamentally inferior to XYZ's punctoid.

or

These considerations, taken together, show that the notion of functoid (as seen, e.g., in Craig and Daniel) has been rendered obsolete by punctoid.

Answer 4

It’s not often used, but should be recognizable and understood:

Obsolesce

Transitive Verb

: to make obsolescent

^{(Meriam-Webster)}

where obsolescent means becoming obsolete, and obsolete is a fairly common word. It has precisely the meaning you intend, and that meaning is clear to anyone familiar with obsolete, which most English-speakers are.

So your statement could be

In a way, what we have just remarked makes the notion of functoid à la Craig and Daniel obsolesced by punctoids.