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So I have formulated a set of arguments to argue certainty is not possible in science. Did I make an illogical argument here or like is there anything amiss in my argument?

Opinion: Science can reach an absolute truth, but we will never be certain of it.

Argument: We are limited by our consciousness. Every experimental design we construct is limited by our thinking. Every observation we make is made through the human lens. We don’t have the ability to detect unseen realities. Therefore, we cannot test if they are there or not. This is why we can’t be sure our model of reality is absolute truth.

Argument: We are not fortune-tellers Since science is prohibitive (rules out possibilities), some ideas don’t fit our reality, others do. We create theories and test them. But we don't have the ability to tell if the next experiment will prove the theory wrong. A theory that withstands all the tests so far could easily fail at the next so we can’t be certain that it holds. So certainty that our theory is absolute truth is not possible. This pattern of new models replacing old ones is a paradigm shift and what is common today was radical before.

Argument: We make assumptions Every theory we construct is based on a set of assumptions. For example, the theory of relativity matches really well with what we measure but it assumes the speed of light is constant which we do not know is true. Since we make assumptions which, for the above paragraph reasons, we can never be certain, then the theory built upon it has no 100% certainty of being true either.

Conclusion: So maybe a better way of defining science is not a process to find the absolute truth but rather a continuous process of modeling what we see to the best accuracy possible.

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  • Comments are not for extended discussion; this conversation has been moved to chat.
    – Geoffrey Thomas
    Jul 28 at 10:17
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    I'm pretty sure your better way to define science is just the definition of science.
    – philosodad
    Jul 28 at 21:08
  • Your arguments are on headed in the direction of well worn tracks. You'd be interested in en.wikipedia.org/wiki/Fallibilism?wprov=sfla1
    – J D
    Jul 29 at 3:00
  • Have you ever misremembered something? Can you perfectly recall every object in your house? Of course not. Then how could one ever think they could be certain about anything.
    – Tvde1
    Jul 29 at 9:18
  • Are you assuming there is such a thing as absolute truth here?
    – terdon
    Jul 29 at 11:11

9 Answers 9

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Science is not a goal, it is a methodology. Within this paradigm is the certain knowledge that the results of scientific endeavor will always be tentative, subject to further refinement as technology advances and as new models of physical phenomena are proposed.

So, Aristotle thought that rocks fall because their natural state is on the ground. Newton proposed that rocks (and apples) fall because of an inverse-square law in three spatial dimensions that is scaled by the product of the gravitating masses and a constant of proportionality to make the units come out right. Einstein then showed that Newton's gravity was caused by spacetime curvature and would yield incorrect results in the extreme case of enormous masses of small size (which were unknown in Newton's time). And it is already well-known that Einstein's model of gravity will fail to furnish correct results when we try to apply it to the singularity inside a black hole.

In the push to advance scientific understanding, we are no longer limited by our human senses: we have telescopes and microscopes that allow us to make images of things our eyes cannot see, and thereby remotely detect the falling of trees in forests we do not inhabit.

For example, the SLAC linear accelerator allowed us to probe the insides of a proton and determine its internal structure, giving us the ability to detect the "unseen realities" there in the same way that the Hubble and Webb telescopes let us probe the unseen realities that lie within galaxies that are 10 billion light-years away from us.

Regarding fortune-telling, I don't know what your point here is exactly but I will say that all models have limited ranges of applicability outside of which they cannot provide correct predictions- but that this characteristic does not disprove the model within its range of applicability.

Regarding assumptions, note that it is a very common exercise to discard specific assumptions when building models and then seeing what if anything the resulting model will correctly predict. If the predictions remain true, then the initial assumption was in fact unnecessary. If the predictions become false, then the model requires the discarded assumption- which in and of itself provides further clues to understanding the way the universe works.

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    Isaac Asimov's essay "The Relativity of Wrong" - hermiene.net/essays-trans/relativity_of_wrong.html as I write this - approaches the "science is a process" part this from another understandable direction. Basically: "Earth is flat" is very wrong; "Earth is a sphere" is wrong, "Earth is an oblate spheroid" is slightly wrong, and science is the process of refining that shape (among so many other things).
    – minnmass
    Jul 27 at 16:08
  • "giving us the ability to detect the "unseen realities" there in the same way that the Hubble and Webb telescopes let us probe the unseen realities". What if these realities are just a distorted vision? What if there is a supreme being out there who deliberately distorts our data or our observations? This is the problem Descartes was trying to get over. Jul 27 at 23:11
  • @LawrenceBragg You bring up a completely different issue here. For what it's worth I do not take Descartes' concern seriously and IMHO neither should you. Jul 27 at 23:28
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    Your reality already includes distorted vision. Most of your visual field is hallucinated, false-color, motion-compensated, and has blind spots filled in. If you mean instead that you're concerned about superdeterminism, then indeed that is a completely different question.
    – Corbin
    Jul 28 at 4:36
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    @corbin, Lawrence Bragg raised the issue, not me. Whatever defects we may have in our visual field, that does not stop us from activities like designing, building and flying airplanes. I do not know what you mean by superdeterminism. -NN Jul 28 at 4:47
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Opinion: Science can reach an absolute truth, but we will never be certain of it.

No it can't for the simple fact that for that we'd need to measure with absolute certainty and that is, so far, considered to be a physical impossibility. For example Heisenberg's Uncertainty relation argues that location and momentum can't be measured at the same time with "high" accuracy, so together they can't be more exact than 34 decimal places. So you won't really see the effect of that in real life but if you wanted to get to the bottom of physics and describe small things with the best precision that you can get, you get into the trouble that this isn't even physically possible.

And that's just one problem, there's also quantum mechanics where we can't actually measure the thing itself but just the probability and the combination of the previous two with chaos theory, that is the problem that little variations in the starting conditions of certain experiments can lead to huge deviations of the results over time means that "truth" is kinda out of reach.

So what ever "truth" is produced by science will always have a margin of error. Or in other words won't be a truth to begin with.

Argument: We are limited by our consciousness. Every experimental design we construct is limited by our thinking. Every observation we make is made through the human lens. We don’t have the ability to detect unseen realities. Therefore, we cannot test if they are there or not. This is why we can’t be sure our model of reality is absolute truth. _whatisscience_Scientific method

Yes but no. As long as we can perceive that effect in any possible way we might construct a device that can measure or amplify it so that we can detect it and at that point we can describe a lot of things with reasonable certainty that no human has ever see with their own eyes (directly).

Argument: We are not fortune-tellers Since science is prohibitive (rules out possibilities), some ideas don’t fit our reality, others do. We create theories and test them. But we don't have the ability to tell if the next experiment will prove the theory wrong. A theory that withstands all the tests so far could easily fail at the next so we can’t be certain that it holds.

Ironically that is the process of science. We try to tell the future using only our models and if they are good, then the future actually comes out as predicted, if not we scrap or update our models. If it were just for that we could actually find truth, but as said we build models on flawed data and so we can't get around the margin of error. But as Popper defined it. Science is always wrong. Being wrong and having the ability to be proven wrong is not a weakness but a strength. A theory that explains everything perfectly and can predict the future wouldn't need science.

Argument: We make assumptions Every theory we construct is based on a set of unquestioned assumptions. For example, the theory of relativity matches really well with what we measure but it assumes the speed of light is constant which we do not know is true. _whatisscience_science is a human construct

Yes and no. I mean there are fundamental assumptions about the world, but if reality showed them to be wrong, they would still become subject of scrutiny if that's what you're trying to say.

Conclusion: So maybe a better way of defining science is not a process to find the absolute truth but rather a continuous process of modeling what we see to the best accuracy possible.

Isn't that already the definition of science?

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    The Heisenberg uncertainty principle doesn't say that you can't measure position and momentum to arbitrary precision at the same time, it is that a particle cannot have an arbitrarily precise spread of momentum and position at the same time. These are very different statements, saying that there are underlying values which just can't be measured implies what's called a hidden-variable theory, which are generally considered to be most likely wrong due to their nonlocality (though not verifiably so).
    – llama
    Jul 27 at 18:15
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    Heisenberg's paper is nearly a century old, we've learned a lot since then. The problem is not just that you can't measure them, it's that quantum states with those properties do not exist. This difference is more obvious if you look at uncertainty relations with angular momentum of atoms or squeezed states of light.
    – llama
    Jul 27 at 18:54
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    Two questions a) is that level of precision relevant to the answer beyond ruling out the naive assumption that this is just a problem with our measuring devices (which it is not). b) I'd say that is still describing the problem that you can't measure these two properties at the same time because measuring one interferes with the other isn't it?
    – haxor789
    Jul 27 at 19:10
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    @LawrenceBragg: You're assuming the Law of Excluded Middle, which isn't constructively valid. But it gets worse; truth is not formally definable. Suppose there is an algorithm for deciding absolute truth; then we can do a Gödelian trick to force it to lie. So there is no such algorithm.
    – Corbin
    Jul 28 at 4:28
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    @haxor789: The nuance that llama points out is non-negotiable; the Kochen-Specker lemma shows that there are observable properties of (spin-1) particles (like squared spin) which might be undetermined before the measurement, in the sense that we can derive a contradiction from the assumption that it's a determined property.
    – Corbin
    Jul 28 at 4:32
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No method we know of can determine "absolute"/objective truth, because all knowledge builds on our subjective and limited perception of reality.

This is already accepted as true by many/most people, or at least most philosophers, skeptics and scientists. So no argument to support this is necessary.

Science is the best we've got though, and it's essentially just the formalised process for how humans (and other animals) naturally gain knowledge.

Every theory we construct is based on a set of unquestioned assumptions.

Kind of, but not really, no.

All knowledge is based on some assumptions, but science and the scientific community is pretty good at breaking down, questioning and "proving" or "disproving" (i.e. providing evidence for or against) those assumptions.

Whether assumptions are questioned is not a function of science itself, but rather of the humans applying said science. If you think specific theories are based on specific assumptions that should be questioned, but aren't, and you can present a good reason why it should be questioned, or why it might be false, scientists would probably like to know that.

Although science isn't typically so much about building on "unquestioned assumptions", as much as it's about trying to come up with the simplest explanation for observed reality. Sometimes we observe more things so that explanation stops being the simplest one (or breaks apart altogether). In that case, we come up with another explanation. Or if we come up with an explanation that's simpler or better explains reality, we opt for that instead. This is exactly what makes science as useful and powerful as it is: it's constantly improving and refining itself as our knowledge of reality expands, and it typically doesn't add unnecessary or unjustified assumptions when our observations can be explained without those assumptions.

... but it assumes the speed of light is constant

This sounds like a good example of an assumption we've questioned (directly or indirectly). We've tested the speed of light quite extensively.

Although I suppose it depends on in which way you think we're not questioning whether it's constant (and why and how this would impact the theory of relativity).

[defining science as] a continuous process of modeling what we see observe to the best accuracy possible

This is a reasonable (if incomplete) representation of how science is already defined, based on how scientists and many laypeople already view it. You'll probably also need to include the systematic nature of the process, and the usage of the scientific method, in the definition though.

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  • While I personally agree with "So no argument to support this is necessary.", there are cases when someone may need reminding that science does not provide certainties, such as the IPCC... earthscience.stackexchange.com/a/24061/21388 With that in mind, it's worthwhile to be able to formulate a clear and easily understandable argument to have beneficial discourse with like minded people. I'm still stuck relying on quoting people better at that than myself.
    – TCooper
    Jul 27 at 19:43
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    @TCooper 1) Sometimes it makes sense to use absolute and certain terms for science, even if not technically philosophically accurate, because (a) if even your basic perception of reality is subjective, words like "objective" would be somewhat pointless outside of philosophy (so any use of "objective" there can presumably be assumed to mean "as objective as our subjectivity allows") and (b) many laypeople dismiss good science because it may still be proven wrong (like all science can be), despite it being much more reliable than whatever method for discovering truth they're opting for instead.
    – NotThatGuy
    Jul 27 at 21:50
  • 2) Sometimes scientists get it wrong and use more certain terms than they should. I won't comment on whether the IPCC got it wrong or whether what they said made sense (especially when I don't have the exact quote in front of me - I did check both the report 4 from 2007, as well as 6.3, which was the most recent published prior to the linked question, but couldn't find the word "disproved" in either with a quick Ctrl+F). But I do tend to be quite critical of those pointing out the imperfection of science, because it's usually pointed out to unjustifiably deny science.
    – NotThatGuy
    Jul 27 at 21:50
  • @NotThatGuy "tested the speed of light extensively" What test has proven it? youtube.com/watch?v=pTn6Ewhb27k Jul 27 at 23:16
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    @LawrenceBragg If you want a conclusive absolute proof of the speed of light, then you may not quite have understood my answer, as science accepts or rejects ideas based on evidence; it does not prove or disprove them. And if we're talking about evidence, then the very video you linked to references some of that. That video doesn't seem to disprove anything as much as it questions an assumption, which perfectly compatible with my answer and how a lot of scientific discovery starts. Although for scientific discovery to occur, we need to have a reason to doubt an assumption and a way to test it.
    – NotThatGuy
    Jul 28 at 1:34
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Science can't reach infallible truth, but scientists can create knowledge we can act on, as explained by the philosopher Karl Popper among others.

Argument: We are limited by our consciousness. Every experimental design we construct is limited by our thinking. Every observation we make is made through the human lens. We don’t have the ability to detect unseen realities. Therefore, we cannot test if they are there or not. This is why we can’t be sure our model of reality is absolute truth.

This is wrong. All of our observations are conducted using experimental apparatus that is constructed in such a way that they can distinguish between two or more theories about how the world works. If theory A is true the result will be X; if theory B is true the result will be Y. So if we get X A might be true and if we get Y then B might be true. If we get some other outcome Z then they might both be wrong. When we get a result that is incompatible with some theory, that is a problem for the theory and has to be addressed either by discarding the theory or by pointing out a problem with the experiment. So we can eliminate theories through experiment.

Argument: We are not fortune-tellers Since science is prohibitive (rules out possibilities), some ideas don’t fit our reality, others do. We create theories and test them. But we don't have the ability to tell if the next experiment will prove the theory wrong. A theory that withstands all the tests so far could easily fail at the next so we can’t be certain that it holds. So certainty that our theory is absolute truth is not possible. This pattern of new models replacing old ones is a paradigm shift and what is common today was radical before.

This is true.

Argument: We make assumptions Every theory we construct is based on a set of assumptions. For example, the theory of relativity matches really well with what we measure but it assumes the speed of light is constant which we do not know is true. Since we make assumptions which, for the above paragraph reasons, we can never be certain, then the theory built upon it has no 100% certainty of being true either.

Your theory is either right or wrong. So there's no point in trying to attach probabilities to theories. Rather, you should judge a theory as either true or false - you should say yes or no. Your judgement might be right or wrong and you should look for criticisms of your ideas, but that's not the same as attaching probabilities to theories.

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  • I agree that a theory is either right or wrong. Let us pretend there is a theory that is absolutely right. Can we ever be absolutely certain that it is absolutely right? Aug 8 at 9:08
  • You can feel certain about a theory if you like and you can have a feeling that you interpret as a degree of certainty. None of that has anything to do with epistemology.
    – alanf
    Aug 8 at 10:59
  • no we are not talking about whether its possible to feel certain. we are talking about whether its rightful to feel 100% certain. I'm pretty sure there is a term for this which is fallibilism Aug 10 at 2:04
  • @LawrenceBragg No. Fallibilism is the idea that people are fallible and that we ought to take account of this. That has doesn't imply that you can assign a number to how certain your are and there are problems with that such assignments so you should reject them, see curi.us/1595-rationally-resolving-conflicts-of-ideas
    – alanf
    Aug 11 at 6:27
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What you conclude is generally agreed upon, give or take a few word choices. That being said, I find the phrasing of the conclusion to be rather thorny. It is pounced upon by many detractors of science, making debates more difficult than they need to be. Instead, I like to start with the opinion that science, and more specifically the scientific method, is a part of Empiricism, a school of thought about truth that argues that truth is derived from sensory experience. To my knowledge, this is a universally agreed upon opinion, making it a useful first step. Your first two arguments, the "limited by our consciousness" argument and the "we are not fortune-tellers" argument are fundamentally tied to Empiricism, not just the scientific method. And it is generally accepted that empirical methods "make assumptions," although that one might have to be debated more carefully. So we can widen the net from making these statements about science to making these statements about empirical thinking in general.

I find this to be value added because the debate about knowledge and truth has been going on for a long time, and those particular word choices have a great corpus of content to work with. For example, Empiricism is considered to be a part of epistemology, the study of what can be known/is known. Another major branch of epistemology is skepticism, which is interested in the limits of human knowledge. If I may read between the lines a bit, I believe your argument is very much a skeptical one, and it is possible to look at the works of skeptics who argue these properties not only apply to science or empiricism, but human knowledge as a whole.

These are worthwhile because they point to a thorny reality that anyone who is doubting science's ability to derive truth (a well founded doubt, as described here) also need consider whether the same arguments apply to any other system or approach they might compare and contrast with the scientific method. They tie the topic into the much larger debates about knowledge that have been refined quite literally over millennia.

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I doubt very much that most leading scientists believe that they are seeking absolute certainty. I have the impression that they are looking for models that are increasingly complete, descriptively valid, and with a high probability of making the correct predictions in new situations. That is far from absolute certainty search.

Maybe, we can agree or disagree on that, but what I see as very weak are the arguments presented:

Argument 1: We are limited by our consciousness.

There are indirect ways to corroborate things, if we are right one thing will happen if we are not right something else will happen. Moreover, technology continually opens up new ways of testing old ideas, and since science is a collective enterprise, the limitations of an individual consciousness do not restrict science as a collective enterprise.

Argument 2: We are not fortune-tellers

Indeed, we have no way of predicting whether each new experiment will confirm the predictions of the theory. But we do have the possibility of reformulating the theory to obtain models that are more likely to fit the experimental data (this is incontrovertible historical evidence).

Argument 3: We make assumptions

Yes, that is also true, but as the history of science has shown, with time there is a way to test the validity of one's assumptions, to revise them and, if necessary, to reject them.

In short, I do not believe that any of the three arguments is a serious obstacle to the purpose of science as conceived by most scientists. There are other difficulties more notorious than those mentioned, and yet it is not clear that this will prevent a continuous improvement of science, although it may be the case that some questions are permanently scientifically ungraspable.

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  • Please elaborate on whether my arguments show absolute certainty is not possible Jul 29 at 4:48
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The statement of the title is wrong as it is state: Math is a science, and math yields results with certainty. True, math builds only upon abstract definitions, and thus can only infer results about abstract things. Nevertheless, math is a science. The science of thinking logically, to be precise. As such, it is at the root of any other science. Physics and chemistry are nothing without math.

As I said, math is limited to the abstract world. It cannot make any conclusions about the physical world, whatsoever. If we want to get knowledge about the physical world, the methods of math alone are not enough: In a way, math starts with the rules, and works its way down to the specific. However, we do not know the rules that the physical world obeys, apriori, therefore we cannot apply the same deductive method on the physical world. We can only conduct experiments to test the specific. From those specific results, we are trying to work our way back to the rules, but this is an error prone process.

In fact, the process of inferring rules from specific experimental results is so error prone, that we can never be sure that we actually inferred a correct rule, i.e. a rule that the universe actually fully obeys. Since we can only ever run specific experiments, we may simply have forgotten about that one experiment that would prove our theory to be false. In this way, physics, and the other natural sciences may never yield results with certainty.

Nevertheless, we have run enough tests on all the established physical theories up to general relativity and quantum mechanics, that we are confident enough to trust them right up to the bounds of where we know they must break down. I.e. we know that neither theory is "correct", yet both are exceedingly precise approximations to the physical world. Enough certainty to use them confidently for every conceivable purpose, but not enough certainty to stop trying to disprove the theories. (Testing quantum mechanics and general relativity has become somewhat boring though: With the perfect track record of both of these theories, nobody is ever surprised when yet another experiment fails to report a deviation.)

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  • In spirit of the question - even if math can produce certain results, how do we know that we reach them correctly? There are lots of errors in important publications that have been tracked only after several years, when in the meanwhile erroneous results from these publications have been used in subsequent publications, etc. Jul 29 at 8:48
  • @მამუკა ჯიბლაძ Mistakes happen, we are all human, after all. Nevertheless, the number of errors in math proofs is exceedingly low. Simply because every mathematician knows that errors are to be avoided at all costs, and no mathematician wants their name connected with a ridiculous blunder. What happens much more frequently in math is, that a proof contains a leap that is not justified. I.e. a transformation is applied that the author believes in good faith to be valid, while in reality, they have not rigorously proven that the transformation is actually fully valid. Jul 29 at 9:44
  • @მამუკა ჯიბლაძ Usually, these holes in a proof can be filled in later, but from time to time, later mathematicians find that a hole cannot be filled, that the proof actually was incorrect. Therefore, we must treat all new proofs with a certain degree of mistrust. Nevertheless, every proof explicitly states the proofs it relies upon, and when a wrong conclusion is discovered, the dependent proofs can be reconsidered. And, for the entirety of math that is used in physics, you can be certain that it does not contain such errors. It's just too mainstream, and too well tested. Jul 29 at 9:50
  • Two things. First, at least one very important mathematician held a different opinion - Vladimir Voevodsky. Second, purely on formal level, regardless of human errors, according to the Gödel's second incompleteness theorem no consistent mathematical theory is self-contained enough to establish its own consistency. Jul 29 at 10:11
  • @მამუკაჯიბლაძე Can you sketch Voevodsky's thoughts on the matter? Or point me to some text where he makes them? Thank you. Regarding Gödel: Well, Gödel proved for certain that, for sufficiently elaborate logic systems, there must be true theorems that cannot be proven. That is something very different from saying "certainty is not possible". To be precise, if certainty were not possible in math, we could not be sure that 1+1 is indeed 2 with 1 and 2 being natural numbers. But we are certain about that. Absolutely certain. And we are certain about quite a few other things as well. Jul 29 at 17:35
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Science can reach an absolute truth. A hypothesis may be absolutely true (leaving aside the possibility that there are no absolute truths). A given body of evidence may support that hypothesis so strongly that all scientists believe it and it is in all the textbooks. That is what we mean when we say that science has reached the conclusion that something is true.

It may be that the evidence could also be explained by some other (false) alternative hypothesis that no one has thought of. That is beside the point because scientists and textbooks aren’t thinking about that alternative hypothesis.

So in this case, science has reached an absolute truth by accident.

As for whether we can be certain that science has reached an absolute truth, the answer is yes!

People have the capacity to be certain of things. Whether the things they are certain of are true, or even justified based on evidence is only tangentially related to the psychological state of being certain.

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'Certainty is not possible in science' Hmm, I'm not sure a mathematician would agree (I'm not a mathematician, so I could be wrong!). The part of the answer uses the phrase 'absolute truth'. I posit that there is no such thing. All 'truth' is relative (NOT subjective).

I had a lecturer who presented some well-known theories of science and observations; then proceeded to demonstrate how these were predicated on some assumptions, and changing the assumption altered the very shape of the universe.

This created a very bewildered class, who asked "How do we know that the theories and equations are correct?"

His answer was "We know they are correct because we can use them to design and build things that work. We can design a bridge that withstands the required loads, an airplane that flies, a silicon chip that functions."

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