"All models are wrong, some are useful"*
... no models are [true]—not even the Newtonian laws. When you construct a model you leave out all the details which you, with the knowledge at your disposal, consider inessential.... Models should not be true, but it is important that they are applicable, and whether they are applicable for any given purpose must of course be investigated. This also means that a model is never accepted finally, only on trial.
— Rasch, G. (1960), Probabilistic Models for Some Intelligence and Attainment Tests.
Your second proposition ("Sciences busy themselves with achieving truth...") is not strictly accurate. Sciences work with observations, models, predictions and theories. Using the most relevant observations, a model attempting to describe aspects of reality is defined. It is then repeatedly compared to new observations, and its predictions provide leads for other relevant observations. As long as a model "survives" those, it is considered valid, and the most sturdy models are used to define scientific theories - but strictly speaking, models and theories are never proven right - they can only be proven wrong. And even when they are proven wrong, they can still be useful - for example, the Newtonian laws of motion's predictions are far less accurate than Einsteinian relativity's predictions - and in some places where these differences matter (GPS, precise prediction of planetary motion etc.), the Einsteinian model is used. But for many practical applications, the much more simple Newtonian model is good enough, and is used instead (e.g. construction and engineering, artillery, aerodynamics etc.).
Just as different types of maps may disagree (e.g. which continent looks larger, what is the length of the Nile, etc.), none of those flat projections of a single scale, for a specific point in time can accurately represent every aspect of the ever-changing, spheroidal face of the Earth. They can't be absolutely accurate and complete, but they just need to provide a correct representation of the relevant information.
Bottom line - different scientific models may disagree, but typically that's because their utility is different - this doesn't mean multiple, contradicting truths - just as even something as seemingly straightforward as the length of a road will be measured differently by using a satellite photo, an aerial photo, measuring with a step counter, measuring with a measuring wheel or from the perspective of an ant that crawls over the non-flat asphalt surface.
Which of those measurements is the truth?
*: See the Wikipedia entry for this statement.
Of course the findings of one science should not contradict those of another but with or without that axiom, can you provide any useful examples?
– Robbie Goodwin Oct 16 '23 at 21:09