We make statements like "This table is composed from atoms". This statement must be true or false. But what if tomorrow the atomic theory is completely abandoned and we work with another theory where the concept of "atom" isn't contained. Would the statement now be true or false? If it is false then this clearly shows that the statements depend on what model/theory we adopt.

Example 1 Here is a link for the definition of sea from Wikipedia. Suppose that one day suddenly all the salt from all the "seas" disappear (but nothing else change). Now would it make sense to say for example "A shark swims in the sea"? This contradicts our notion of "pictorial" (I don't know the technical term) understanding of what "sea" means. Even if nobody knew that all the salt went off just by looking he can see that "A shark swims in the sea". Now is this statement true or false?

Example 2 Suppose someone is asked to answer the following question. "We have a box with 2 oranges. Now we add other 3 oranges. How many oranges we have? Would it matter if we added had initially 3 oranges and then added 2?" If he answers, "Look it depends if the real world works like maths do, i.e. the commutative property works etc", I think everyone will laught at him. We haven't find a single example where the maths doesn't work in real world. But this doesn't mean we won't find. And of course this doesn't mean that math don't work if we find one. But when we make statements we use theories or maths in order to evaluate their truth value. Why we do that if the statements should be evaluated only according to real world?

  • Perhaps you are not aware there are different types of truth. You seem to assume there is only on type which in your examples are purely sense based: your sight, taste, smell touch and hearing. There are contingent TRUTHS which can vary due to time & circumstances. One day x is true another day x is false. Then we also have a category of permanent truth values that NEVER CHANGE: once true x is forever true, once false x is forever false -- it does not flip flop value as contingent truths do. If a statement is contingent then it can be true & later be false. Which type of truth do you mean?
    – Logikal
    Aug 1 '20 at 17:27
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    "This clearly shows that the statements depend on what model/theory we adopt" is false. It may happen, however unlikely, that the atomic theory is wrong, but then "table is composed from atoms" is already false today, we are all just mistaken about it. The truth does not change, only our state of knowledge does, and us stating that something is true does not make it so, or otherwise.
    – Conifold
    Aug 2 '20 at 2:37
  • @Logikal Isn't "The table is composed from atoms" a contingent statement? What I am saying is if the truth value of the statement depends on the theory because the terms we use in the statement are relevant to the theory (e.g. atoms). Can we say that because we have proved wrong the theory (e.g. atomic) then the above statement is false irrespective of the fact that we thought it was true as Conifold said?
    – ado sar
    Aug 2 '20 at 22:11
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    Technically yes but you may agree that is a bit extreme. You can add all the information you actually posses about the subject that is relevant: location, size, color, posture or position of the subject and so on. If I read your sentence & can ask you three or more question about your original sentence then try harder to be more detailed & specific. No one should have to read vague or poorly worded sentences that leave reader WONDERING what is meant. There should be no open ended sentences or vague terms that are not defined. We see this frequently in regular life & they wait to be questioned.
    – Logikal
    Aug 2 '20 at 22:49
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    We can agree this what you discrrbe is what happens frequently between people. However are you telling me the conversation NEVER EVER EVER gets interpreted incorrectly. Suppose the conversation was more complex: let's say a moral topic is your preference ALWAYS going to work? You like other people do stuff because it is EASIER FOR YOU than to add all these specific and details. That is MORE WORK. When the more complex conversations arise those details and specifics will COUNT FOR SOMETHING. All the stuff you are trying to avoid will make your life easier when the tougher conversations occur.
    – Logikal
    Aug 2 '20 at 23:04

Science does not define what is true. Science is just a type of knowledge (obtained using the scientific method... etc., etc.). In any case, science would seek for empirical truth, that is, the truth that fits better to experience.

Knowledge is subjective (you and me would provide a quite different description of what a rainbow is), therefore truth is subjective (because is based on knowledge). It is you that decide what knowledge you consider true. Normally, science can be trusted, because it fits better our experience (fits better each one's experience). But nobody is forced to believe in science.

Two theories, for example, evolutionism an creationism, have not intrinsic value as such, no one is better than the other per se. It is each individual that chooses which one to use as the one that fits his experience.

When a theory is replaced by a new one in science, we use the latter not because it is new, but because it usually adapts better to our experience. But any individual is free to believe in what he chooses to.

  • Can we say that with science/scientific theories we get closer and closer to truth? I mean if you leave two ball from a height they will fall. This is not subjective. The explanation/description is subjective. E.g. Special Relativity and Newtonian mechanics both can explain the ball falling.
    – ado sar
    Aug 5 '20 at 11:23
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    @adosar: Not to 'truth', not to any 'noumenon'. Only, to what we have evidence for - that is all science can approach. And if our imaginations fail to generate the ideas we truly need to encompass the workings of our world, then our progress will cease. See Popper on hypothesis generation.
    – CriglCragl
    Dec 27 '21 at 21:07

But when we make statements we use theories or maths in order to evaluate their truth value. Why we do that if the statements should be evaluated only according to real world?

Because we already use theories or math when making statements. Words have no meaning without theories or math. If two people agree on the meaning of a word, that just means they share a theory.

Instead of maths and science, it is possible to evaluate truth by using other theories, but it is impossible to not use any theory. No theory means no language.

We haven't find a single example where the maths doesn't work in real world.

The opposite is true. Science has many times found cases where previous models or even math were wrong, and had to be fixed. See https://mathoverflow.net/questions/879/most-interesting-mathematics-mistake for examples. Also there are likely more mistakes in current models. There are also known unsolved and unsolvable problems in representing the real world using math. https://en.m.wikipedia.org/wiki/List_of_unsolved_problems_in_physics but for those problems, there are no better alternatives.


Classical logic assumes a principle called the "Law of the Excluded Middle", which assumes that all claims must be either true or false. https://en.wikipedia.org/wiki/Law_of_excluded_middle. Logicians have developed multiple alternate logics to classical logic, and many of them do not accept the law of the excluded middle. See this discussion on three state logic: https://en.wikipedia.org/wiki/Three-valued_logic

What you have discovered is that empiricism, and science, are premised on violating the Law of the Excluded Middle. Science operates on a 4-state logic for claims:

  • Sufficiently evidenced to accept as a working hypothesis
  • Sufficiently evidenced against to reject as an invalid assumption
  • Currently indeterminate in support or counter-evidence
  • Incoherent or unevaluatable in principle, can be dismissed without evidence as evidence is impossible

NONE of these four logic states are either true or false, so all are violations of the Law of the Excluded Middle.

This four-state tentative, fallibilistic, empirical approach to inferring reality is intrinsic to indirect realism. And indirect realism is how science operates.

The realization that our best methods of acquiring knowledge do not cohere with classic logic, has contributed to the recently developed consensus among logicians in favor of logical pluralism. https://www.cambridge.org/core/journals/think/article/abs/guide-to-logical-pluralism-for-nonlogicians/EDFDFA1C9EB65DB71848DABD6B12D877

Also, there are multiple examples of simple arithmetic not working in the real world. One straightforward example -- add three animals to the two in your box, and come back a few days later, and there may be two, five, or five dozen, depending on what predator/prey/breeding relationship applied to those animals.

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