Fallibilism

Fallibilism is a doctrine created by Charles Sanders Peirce, which consists in stating that we are subject to hold false beliefs, and therefore, we cannot be absolutely sure of anything, not even of the methods of scientific analysis.

By sustaining that there are no absolute truths and certainties, the Peircean doctrine opens space for questioning the truths provided by the sciences, especially by logic and mathematics. And it is precisely because of the uncertainties that fallibilism ends up becoming a doctrine in which it is necessary to be willing to learn new theories, new interpretations and even a renewal in the methods of analysis.

But is it possible to be mistaken about scientific certainties? What about those truths that are presented as self-evident? Can fallibilism extend to logic and mathematics?

What is fallibilism?

We will use the term fallibilism to denote that which is subject to producing false results. The fallibilism proposed by Charles Pierce states that no certainty can be obtained. The Pierceian doctrine has two main arguments:

1) Epistemological argument

We can divide the epistemological argument into two parts:

• All knowledge is fallible: that is, all knowledge may not be true due to (i) methodology: empirical analysis; (ii) cognitive nature: limitation of the means of analysis, such as the senses; (iii) sensory-cognitive dysfunction, intellectual anomalies.
• All knowledge is provisional: that is, beliefs correct themselves over time, but the ideal of truth is something eternal and unchanging.

The epistemological argument is based on the idea that we cannot accurately obtain certainty about anything. This foundation may make us think that fallibilism is identical to skepticism.

But the Piercian doctrine does not claim that it is impossible for us to attain any truth, nor that all scientific methods of analysis are false.

What fallibilism holds is that we cannot be sure that we are really right about a certain object of analysis. For example, we can be sure that evolutionism really happened, but this doesn’t mean that we are right in believing that such a fact is true.

2) Metaphysical argument

The metaphysical argument states that things are constantly evolving, and that the basis of judgments is empirical, so the notion of truth is constantly evolving.

What is infallibilism?

The idea of infallibilism says that things are fixed and immutable, therefore, truths are also fixed and immutable. However, this idea prevents the evolution of knowledge, because presuming to have already found the absolute truth, there would be no reason to continue the investigation of the object of analysis.

For Charles Peirce, since nature is diverse, there should be a cause for this diversity, because having as a principle the idea of cause and effect, there must be a cause still operating for the non-absolute laws that are constantly evolving.

Therefore, if we follow this line of reasoning, we will reach the conclusion that there are no absolute truths, in view of the fact that the means of analysis to reach this conclusion, that is, reality, is not absolute and immutable, therefore all knowledge is mutable.

This would be one of the reasons that make fallibilism more acceptable than infallibilism.

Does fallibilism extend to logic and mathematics?

We conclude that at least when it comes to empirical knowledge, in the Piercian view an absolute truth cannot be reached. But what about the exact sciences? Could “2+3=5” be wrong? Could logic, which is based on the preservation of truth, be wrong? We will analyze these questions. Starting with mathematics.

Mathematics

It should be noted that mathematics analyzes problems that it creates itself, that is, it doesn’t necessarily analyze issues in our world, it is just used. For this reason, it does not have a truth value referring to an object of analysis. Therefore, mathematical knowledge is on a different level from those analyzed so far.

For mathematics to have different criteria of analysis, it would not be possible to make relevant and meaningful criticisms. Mathematics then becomes practically infallible.

Logic

Regarding fallibility in logic, Susan Haack makes the following observation:

Even if the laws of logic are not possibly false, this in no way guarantees that we are not subject to hold false logical beliefs.

That is, even if logic itself does not hold possibly false propositions, we are subject to holding false beliefs; Susan Haack calls this thesis ‘agent fallibilism’.

Other issues regarding fallibilism in logic raised by Susan Haack are that of evidence and analyticity.

By evidence, we mean that which is presented as obvious, true. But according to Susan Haack, the fact that a proposition is obvious does not mean that it is true, since evidence does not provide us with any epistemological guarantee.

In relation to analyticity, Susan Haack argues that not only can we not fail to recognize the truth of a logical proposition, we must also have some way to ensure that we fully understand the logical proposition being analyzed. For this reason, that is, that we can be mistaken about our beliefs, Susan Haack supports, if necessary, making a revision in logic, but only if there are good reasons to do so.