Statement about rigor

Antirigor argument: rigor slows you down, permits you to cover less
stuff and make fewer advances. Anyway in physics one is often using
mathematical models of reality which we know are only approximate, so
why demand rigorously valid reasoning about those models?

Prorigor argument: if you (or you in combination with everybody else
in the field in the future and past) are using a chain of N logical
implications (piling N lemmas on top of one another) then if each link
in the chain has correctness probability p (.99, say), then the
probability of total correctness is p^N, i.e. exponentially small. So
it is essential to make p as large as possible otherwise everything is
useless. Also only with rigor do we have true understanding, as
opposed to sweeping troublesome issues under the rug.

My feelings: Both arguments above are valid (although I don't
like the final sentence in the antirigor argument  it depends
if the mathematical model is of independent interest).
But what is inexcusable
is the tendency to claim proofs when one knows full well one does not
have them; to try to disguise and hide the presence of nonrigorous
steps. If you can only make a conjecture, or a partial proof, or
a proof depending on unproved assumptions, fine. Say so. Explicitly
state the assumptions and highlight the gaps in the reasoning to
aid eventual further progress. Do NOT
pretend to have a "demonstration" of something you don't; don't
make vague statements  make precise ones, whether theorems or conjectures.