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It seems to me that the goal of science is to describe with the most precision the world we perceive through our senses. It seems to me that actually science has an axiom:

There exists some final state of human discovery (maybe possible or maybe not possible to achieve) in which we can describe anything we can perceive through our senses.

I would mark that as an axiom because we cannot know whether the things that we perceive through our senses corresponds to reality. We could be a brain in a vat and everything we perceive is just a delusion.

Why should we or shouldn't we mark that as an axiom of science?

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    Obviously, science assume that there is an objective reality to be studied : described, measured, etc. Not necessarily "perceived by the sense" in a naive way: see sub-atomic particles like Higgs boson. – Mauro ALLEGRANZA Oct 28 '19 at 8:34
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    Not only physisc; consider sociology, and history: obviously they assume the existence of socila facts and historical facts. – Mauro ALLEGRANZA Oct 28 '19 at 8:35
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    But it is not an axiom of specific scientifc theories; it is a sort of "regulative principle" or metaphysical assumptions that is presupposed by the scientific practice itself. It is like gambling at casino : do you bet if you really think that there is no objective reality and all is illusion ? – Mauro ALLEGRANZA Oct 28 '19 at 8:48
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    To describe is the goal of reporters, science aims to explain, predict, reproduce and engineer. Even if it was to describe, why there should be some "final state" is supremely unclear, there may be multiple unending chains of better and better "descriptions", "better" is different senses, that do not converge to anything "final". Not to mention, that to do what we are doing today, in science or anything else, we need not assume any "axioms" about future states at all. – Conifold Oct 28 '19 at 8:52
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    Now you know why the scientists in the Matrix could not discover they were in it. . – user20253 Oct 28 '19 at 9:24
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There is no such axiom of science. Actually, I think you can't claim that science "describes" the world we perceive, nor that science has a "goal".

A goal is a social construct, generally adopted with reference to personal objectives, which are inevitably social. Scientists work hard to make scientific progress in order to reach personal goals, not scientific goals.

Scientific knowledge is the ability to predict significant outcomes of events occurring in time. The ability to predict the outcome of events has economic and/or social value, and so confers power on those who have it.

The ability to predict outcomes is achieved by producing a model (or "algorithm", or "theory", or "law", or "principle" or whatever you want to call it) which can be used to predict, given certain preconditions, the occurrence of subsequent likely events and outcomes over time. You might think a model is "descriptive" of reality but it is not - it is only predictive of outcomes. The descriptive element is merely a by-product of the ability to predict, which is the important part. For example, Newton's law of gravity is a model that predicts the behaviour of physical bodies by mathematically modelling the influence of an attractive force between them (which depends on their mass and distance apart etc.). Newton's "law" is really very good at predicting the motions of planets around the sun. However it does not describe the planets themselves or say anything about how this gravitational force is created or sustained. The model does not say "gravity exists". It just says "by using a model of an attractive force between bodies, let's call that 'gravity', we get good predictions of how those bodies will move".

A model is only "useful" if it sufficiently reliably predicts outcomes that have some social significance, desirable or undesirable, and hence have value. This gives the scientist the means to achieve their objectives. The scientist (or others paying the scientist), being empowered by using the scientific model, can then take action that makes (economic or social) use of the predictions in some way. The degree of reliability or accuracy of the model's predictions determines how useful the model is.

Scientific progress by humanity is measured only in terms of the ability of scientific models to predict outcomes previously unpredictable, or more accurately to predict outcomes - that is, if you are able to make predictions of outcomes more accurately than previously possible and this increased accuracy makes the model more useful, then you have made some progress.

The predictive power of a scientific model may also be useful in reverse - that is, starting from observed outcomes, to deduce what must have been the preconditions. For example the science of kinetics can be used to predict the outcomes of interactions between moving bodies, but also to deduce the precursors, and possibly causes, of collisions between bodies by observing the outcomes. Investigators do this when trying to establish the sequence of events preceding accidents.

The "brain in a vat" possibility is not really relevant to the issue. It does not matter whether or not our senses perceive "reality", just like it does not matter if scientific models do or do not describe "reality". Philosophers might be interested in musing on whether, if we knew that we are all brains in vats, our perceptions of ourselves and our moral behaviour would be different in some way, but that's not really a scientific question. Science is interested only if a "brain in a vat" model is better at predicting outcomes than other theories of the universe.

As a philosopher you might wonder whether there will be a future in which humans are able perfectly to predict every outcome of every event. But currently, as far as I am aware, we have no scientific model that could predict such a future. It certainly is not an axiom of science.

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I have not seen an assertion that there exists a final terminus to the state of discovery as being integral to science. I don’t know if anyone who has posed such a thing as a necessary component of science. My read of Popper’s philosophy of science is that it is completely compatible with science being a never ending process.

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There seems to be 2 parts to your claim:

  1. that a final state of human discovery in science is axiomatic and
  2. that the goal of science is describing what we perceive with our senses.

It is fair to say that a goal of science is to describe our environment though it's not the case that that's limited to what we directly perceive with our senses. But there are other goals such as predicting future events and change our environment (and ourselves).

Even if we can agree on a definition of the goals of science, the first part of the claim won't hold. The reason is that, if we remove the axiom, almost all, if not all, scientific activity remains valid. As such it can't be axiomatic.

Arguably, if a Theory of Everything was identified then that may point to a final state. However, even this does not require one.

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