Supervaluational Logic A logician who applies a supervaluational approach will continue to abide by LEM, but will abandon bivalence. Under this approach, the logician accepts that the problem resolves around the incompleteness of the words used, therefore the solution is to find some way to make the meaning more precise. This is done by saying […]

# Logic

## 0147: Vagueness Part II

Classical Logic Solutions In terms of classical logic, one way to resolve the problem is to abandon the concept of bivalence. No longer must any proposition have a strictly true or false conclusion. Rather, we can say that the proposition lacks a truth-value: we have no way of saying whether the proposition is true or […]

## 0146: Vagueness Part I

Introduction The philosophical problem of vagueness usually starts with the ‘sorites paradox’ (‘sorites’ is the Greek word for ‘heap’). Consider a large heap of sand, one that is undoubtedly a ‘heap’ as it contains many grains. Then consider a second premise along the lines of: if n grains of sand is a heap, then n […]

## 0145: Reference and Naming Part IV

Criticisms of Mill’s Theory The Mill view can be questioned in a couple of ways, similar to the criticisms raised earlier in regards to Russell’s theory of descriptions. Firstly, how does Mill deal with identity, and secondly, how does Mill deal with non-existent objects? In terms of identity, consider the famous example concerning the planet […]

## 0144: Reference and Naming Part III

Criticisms of Russell’s Theory of Descriptions Russell’s theory of descriptions can be criticised on a number of grounds: Criticism 1 – Failure of Uniqueness In normal language, it is often the case that we use ‘the’ to designate a single object, when in fact the descriptor could match any number of objects. For instance, if […]

## 0143: Reference and Naming Part II

Russell’s Philosophical Puzzles Russell continues his theory of descriptions by seeing how it resolves three common philosophical puzzles. Puzzle 1 – Identity Russell starts by noting the general law of identity: if a is identical to b, whatever is true of the one is true of the other and either may be substituted for the […]

## 0142: Reference and Naming Part I

Introduction Bertrand Russell once famously made the following proposition: ‘The present King of France is bald’. Given that there is no present King of France, what truth-value do we assign to this sentence? Under classical logic, the choice will be between ‘true’ and ‘false’, so the process of analysis will go something like this. In […]

## 0141: Conditionals Part II

In support of ‘if A then B’, you could argue that because the natural language conditional is harder to satisfy then the logical construct, it means that any proposition that is logically valid is automatically true in natural language. This does not work the other way around though. If something is true in natural language, […]

## 0140: Conditionals Part I

This philosophical problem of logic considers whether the ‘if A then B’ construct is a good match for the use of the conditional in everyday language. In classical logic, as stipulated by Frege in 1879, ‘if A then B’ is considered false if A is true but B is false. In all other cases, it […]

## 0139: Modal Logic Part II

Given that sentential classical logic relies on proofs in order to verify propositions, what logical conclusions can we draw from the use of the box and diamond symbols? This question is controversial as there is no one agreed upon system. Philosophers distinguish each of the classification systems on the basis of a logic type: K-logic […]