Arguments, Cognition, and Science. André C. R. Martins

modes of reasoning solid enough for our purpose of diminishing errors? The first step is to ask what we mean by solid enough. By that I do not mean that they will actually end the possibility humans will make mistakes; that seems to be unavoidable. But there might be ways that allow our arguments to be inspected for errors. That is, we are looking for tools we can use to detect erroneous reasoning. Those tools should be such that, when errors are found, we would all agree there is a mistake there.

      As discussed above, acceptance of those tools should be universal. They might need a lot of training to understand and use, of course; but anyone who learns how to use them should be able to agree with the conclusion. A sound argument should be seen as sound by any person who understand the rules of sound argumentation. That way, we can hope that our preferences for particular ideas should not interfere with our conclusions. Or, at least, they should interfere as little as possible.

      Luckily, those modes of argumentation do exist. In the cards problem, once we understand it, we all agree which cards can prove the rule is false and which ones cannot. Disagreeing with the conclusion—once we understand the problem well—seems to be a form of insanity, an incapacity to perform the most basic reasonings. Of course, species insanity is possible, even if we guess it would be improbable, but that is a possibility we might be forced to ignore if some solution is to be found. We can do the best we possibly can, but no better than that.

      Logical reasoning and sound philosophical arguments are natural places to start the search. Those areas have been trying for millennia to achieve certainty (if that were possible at all) or something close to that. Solid reasoning is an old problem, one where we have not found a final solution yet or, as we will see, a complete solution that can actually be implemented.

      Such a task might sound identical to the basic positivism program. In particular, by placing logical reasoning as a high standard, the similarities to Bertrand Russell’s (Whitehead and Russell 2011) and Rudolf Carnap’s ([1937] 2002) approaches are obvious. But we have learned since those brave attempts that basing knowledge on pure logic faces too many difficulties that have never been solved. Attempts to reduce mathematics to no more than a consequence of logic have failed. More than that, both Kurt Godel’s incompleteness theorem (Godel 1962) as well as Alfred Tarski’s undefinability theorem (Tarski 1983) clearly show that such a program might not be feasible.

      Logicism has a deep problem, if it were to be used as the basis for defining knowledge about the world. Its goal was to establish logic as the basis for mathematics. It was assumed that, once we had mathematics, physics and the description of the world would follow. That program, however, was in a deep contradiction with its own goal of avoiding metaphysics. Assuming that mathematics is the actual language of the universe is not something we should do lightly. We just don’t know if that is the case. We can say mathematics has allowed incredible advances in our scientific knowledge as well as in our technologies. The results of using it are unexpectedly precise. That means it is very reasonable to wonder if mathematics plays a central role in the universe. While the question is perfectly valid, we have no reason to answer it one way or another with any degree of certainty. Whatever answer we choose is no better than an educated guess. Mathematics is incredibly useful. If we do aim to find standards of reasoning, we can use mathematical reasoning if it is solid enough, but we cannot be sure the world obeys it or not, certainly not at this point of investigating the problem. We should not trust the intuition of those who love mathematics any more than we could trust the complaints of those who are unable to use it. We must remain skeptic about its role in the universe, unless we find unquestionable evidence that it is indeed the case that the universe was built from mathematics. As we will see, understanding how we can confirm—or not—a mathematical theory about the real world has many problems. Applying logic to that task is less straightforward than most scientists know—or even imagine.

      If we do not find evidence, we can still try to use logic to prove how the world is, but we will need to find a different road. We still need to correct our human tendencies to defend ideas instead of verifying which ones are better. Giving up any attempts at finding certainty might prove to be unavoidable, given the tools we have today. Our next step is to investigate what logical and mathematical methods can actually say. We need to understand their limitations. Even if logic is as solid as possible as a reasoning tool, we must know what conclusions it allows about the world—if any at all.

      My goal in this book is to explore what we can do in our search for correct answers while avoiding the traps our rationality seems to impose on us. If your main objective is only to fit inside your group, experimental results suggest you might already be well adapted. Though not perfectly adapted, there is always room for improvement when using finite resources, but we seem to be already quite competent at that task. In that case, your intuition should serve you well. Your reasoning will make the proper adjustments. It will also probably prevent you from noticing evidences that your group might be wrong.

      If, on the other hand, your goal is, as I hope it is, to look for best answers and to get as close as possible to correct ideas, you must be wary of your intuition. That is the road we will take here. We had to see how well and why we reason; to understand we must look for more solid grounds for knowledge than our own natural argumentation. The search for epistemological methods has often been based on what we feel to be correct. Quite often, there was also an assumption that scientists are doing it right, even if they cannot explain the details. Science is too successful. At least in those areas where advances have been more spectacular, the argument goes, researchers should be working as well as possible. That assumption might seem a good first approximation, but its logic is flawed. We need to state clearly what we know and what we do not know. There is indeed very strong evidence science has been far more successful than all other attempts at understanding the world, but that is a relative comparison. When you notice one method worked better than its competitors, it becomes very plausible to say that method is better. But being better is very different from being the best possible method. As scientists are humans, they are bound to suffer from the same bias common to all humans.

      That means that we must try to avoid as much as possible any arguments based on what we feel to be correct. Looking at arguments of that type might be interesting, to see how and when they might go wrong. To do that, we need ways to inspect them, and we need to be on more solid ground. Therefore, we will investigate how far we can get if we only accept very solid reasoning, that is, arguments of the type any sane (and intelligent) person would consider correct. The first step, therefore, is to keep going until we find and understand standards that allow us to say something about the world—and then see what that something is and what it is not.

      References

      Carnap, R. (1937) 2002. The Logical Syntax of Language. Open Court.

      Claassen, R. L., and M. J. Ensley. 2015. “Motivated Reasoning and Yard-Sign Stealing Partisans: Mine Is a Likable Rogue, Yours Is a Degenerate Criminal.” Political Behavior, 1–19.

      Godel, K. 1962. On Formally Undecidable Propositions of Principia Mathematica and Related Systems. New York: Basic Books.