In the accepted answer to: The difference between an analogy and a metaphor? an insightful conclusion was reached that the analogy is what is expressed and the metaphor/simile are how it is expressed. I think for most cases this is a perfect rule of thumb.

For the purposes of this post, I want to pose the question, that under very specific circumstances we can have an analogy itself only. In other words, an analogy without a metaphor or a simile. This may need certain assumptions about the clarity of the analogy. Take this analogy for example:

You cannot have a rainbow without rain, and you cannot have success without hard work.

The above example doesn't fit as a simile. I'm not sure if its fair to consider it a metaphor either, it doesn't seem to fit the spirit of most metaphors I've seen: "speak daggers", "time is money" … While "rainbow" and "success" are being compared, it lacks the figurative dimension, and so, to me at least, it seems to be a stretch to call it a metaphor. Maybe it's simply a comparison.

Question: What is the best classification for my above example? Is it conventional to argue an analogy can be expressed on its own, as I have speculated? Or does this example fall into the category of metaphor after all?

Another noteworthy example:

Time travel felt as if I was in a runaway carriage.

Edit I just noticed there was an "as" in that line. It could be substituted with "similar to" to escape the simile jurisdiction.

A better one yet:

Imposing a tarrif won't address the root problem of why we have such a big trade deficit, by the same logic: putting a bandage over a skin cancer growth won't change your prognosis.

No obvious simile hallmarks: "like" or "as" (maybe like/as are not mandated for similes?) Also, doesn't strike me as a metaphor. It seems like analogy is the best term for it, but maybe that's just me.

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    I would call that a simile. The comparison is implied rather than explicit, but it’s there, and it’s clearly not a case of identification (ie a metaphor). If you have other, possibly more compelling examples, we might be able to dig into this deeper. – Dan Bron Jul 9 '18 at 14:19
  • @DanBron I have added another example; maybe I'm thinking on a different wavelength. I'd be curious to see what others think about them though. – Arash Howaida Jul 9 '18 at 14:33
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    These are philosophical issues, not English issues per se. – Lambie Jul 9 '18 at 14:34
  • I agree that analogy is the best term for your examples. They don’t strike me as being metaphors either. – user305707 Jul 14 '18 at 17:41
  • I’m sorry to say that to me it seems the best classification for the example: “You cannot have a rainbow without rain, and you cannot have success without hard work” is a mistake. The first part of the comparison is axiomatic; the second is false, thus so must be any analogy. I’d allow, the tariff-cancer example is better and still, addressing the root problem and changing the prognosis aren’t really comparable. – Robbie Goodwin Jul 27 '18 at 19:47

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