Introduction

The closure principle in epistemology deals with the logical consequences of what one knows. It poses profound questions about the nature of knowledge and its limits. This article explores the two versions of the closure principle, outlines the debates surrounding it, and examines its relevance to external world scepticism.

The Two Versions of Closure Principle

There are two main versions of the closure principle: a strong version and a weak version.

Strong Version

The strong version of the closure principle asserts that if one knows a certain fact, one also knows all of its logical consequences. For instance, if you know that Smith has 17 cars, you would also know that Smith has a prime number of cars. This example makes it clear that the strong version of the closure principle is untenable. It is impossible to know all the logical consequences of every fact one knows, as demonstrated in this simple scenario.

Weak Version

The weak version of the closure principle is more modest in its claim. It states that if one knows a certain fact, they can deduce its logical consequences. For example, if you know that Smith has 17 cars, you can infer that Smith has a prime number of cars, but you need not actually know it to be true. This is a more plausible claim, as it merely suggests a potential for inference rather than a necessity of knowledge in all cases.

Daily Applications and Debates

In everyday life, we often make logical inferences based on our knowledge. For instance, if someone tells you that their favorite food is pizza, you might assume that they know what cheese is, as cheese is a common ingredient in pizza. However, this inference is not universally valid. One cannot assume that the knowledge of pizza automatically implies knowledge about anchovies or rennet, which are also common pizza toppings, unless these specific toppings are mentioned.

The debate centers around the extent to which we can confidently assume certain knowledge based on a given base of information. This issue arises when there is a lack of specific knowledge about a particular aspect, even if the general knowledge is extensive. The limitations of such inferences illustrate a fundamental question in epistemology: what exactly can we know and to what extent can we rely on our assumptions?

Epistemological Closure and External World Scepticism

Epistemology, the theory of knowledge, includes various closure principles. The principle that anyone who knows if A then B and who also knows that A thereby knows that B is a common example. This can be symbolized as: if Kif A then B and KA then KB. This principle, known as closure under known implication, adds to the complexity of epistemological inquiry.

Implications of Closure

Though it may seem trivially true, the closure principle has significant implications, particularly in relation to external world scepticism. For example, according to René Descartes, we cannot be certain that we are not dreaming. However, if we know that if we are really typing, then we are not dreaming, the closure principle, combined with modus tollens, suggests that we do not know that we are typing. This argument underscores the potential threat to everyday knowledge posed by the closure principle.

Philosophical Responses and Theorists

Philosophers have responded to these challenges in various ways. Some, like Fred Dretske and Robert Nozick, argue that the premises of the argument may be true but that the argument itself is invalid because the closure principle is false. This approach seeks to preserve everyday knowledge by denying the necessity of the closure principle.

Just as the closure principle challenges our understanding of knowledge, it also highlights the importance of careful analysis in epistemology. Whether we accept the closure principle or reject it, it serves as a reminder of the complexity and nuances inherent in our comprehension of the world.

Conclusion

The closure principle in epistemology remains a topic of considerable debate. While it may seem straightforward, its implications are far-reaching, touching on the foundations of our knowledge and understanding of the external world. As scholars continue to explore these issues, our understanding of what we can know and how we acquire knowledge will undoubtedly evolve.