EMOTIONAL ERROR

In Section 2.2 I noted that when philosophers distinguish emotions from feelings, the feelings they usually have in mind are the sensations of body states that typically accompany some strong emotions: muscular tightness in face and neck and arms, goose pimples, abdominal perturbations, and so on. I agreed that such feelings are not emotions, and was led into the exposition of my basic account of emotions by identifying a kind of feeling that is very far from being a bodily sensation, namely feelings of triumph, of awkwardness, of having been ripped off, and so on. These feelings of states or qualities of the self I called feelings of construed condition. This observation gave us the concept of a kind of feeling that is, for ordinary purposes, indistinguishable from emotion. It is this concept of a feeling of an emotion – and not that of a sensation that may or may not accompany an emotion – that justifies the interchangeability in many ordinary language contexts of “emotion” and “feeling.”

Robert Kraut once tried out the thesis that emotions are feelings in a certain kind of context: “Just as a piece of wood, when caught up in the appropriate conventions, qualifies as a pawn, a certain feeling, when occupying a specifiable position relative to the causal order and the order of social practices and communal norms, qualifies as an emotion.

WHAT THIS BOOK IS ABOUT

Anthony Trollope comments about an unsavory character who looms large in his novel The Prime Minister (Chapter 58):

Without directly mentioning any of Lopez's actions, Trollope here unmistakably sketches a man of momentous moral defects, just by indicating his patterns of emotional responsiveness – that he is more ashamed of being rejected by a classy female adventurer than of being the object of public moral opprobrium, but not at all ashamed of his shameful deeds. His lack of appreciation for good and bad action, suggests Trollope, is due to his emotional unresponsiveness to actions in moral terms (notice how Trollope mixes descriptions of Lopez's emotional dispositions with cognitive ascriptions like “no inner appreciation,” “not the faintest notion,” “a very keen conception”).

Language

In this chapter we will consider the ways in which the notions of possibility and necessity, and related notions, are expressed in ordinary language. Ordinary usage will indicate the concepts used, and the interrelations between them. There are also sentences of English that pose considerable difficulties for translation to logics that use possible worlds semantics. At the same time, possible worlds can, in some cases, illuminate the meaning of the propositions expressed by such sentences. Above all, reasoning and arguments involving the notions of possibility and necessity are usually expressed in ordinary language.

We begin with the distinction, in ordinary language, between “possible for” and “possible that”. We then move on to consider some difficult cases. We consider whether the idea of possible worlds is effective in explaining the interrelationships between the concepts that surround possibility, correct reasoning and the validity of argument in ordinary discourse.

“Possible for” and “possible that”

“What's possible?” “What's impossible?” These questions are asked in context. In government the questioner might want to know what is economically possible. In business the questioner might want to know what is financially possible. In academia the questioner might want to know what is politically possible in the academic institution, or what is possible given the regulations for the degree. In physics the questioner might want to know what is physically possible. In chemistry the questioner might want to know what is chemically possible.

Predicate logic

We begin with the extension of propositional logic to predicate logic and then to modal predicate logic. We look first, from a logical perspective, at what happens when we translate from ordinary language to predicate logic without modal operators. We focus on a very small fragment of both ordinary language and predicate logic: a fragment large enough to show the impact of possible worlds semantics on a range of topics and problems. We then turn to what happens when possible worlds semantics is added to predicate logic.

The first thing about translating from ordinary language to predicate logic is that there is far more to consider than when translating to propositional logic. Predicate logic forces us to understand what is said in ordinary language in a way that does not always accord with our simplistic intuitions. Our intuitions have to be informed and changed. We have to look for features, expressions and underlying meanings in natural language that match the structures and meanings in predicate logic. Here we see clearly that ordinary language and predicate logic are quite different languages. Fortunately, we do not have to begin with complex sentences to see what is important.

Basic logical features

Consider the simple sentences:

Kermit is a frog.

Kermit is green.

These sentences contain a singular term and two general terms. The singular term is “Kermit”. It is a naming term that we take to refer to just one entity.

Introduction

There is an interpretation of quantum physics that is known as the many worlds interpretation. The interpretation is not, by any means, a majority view, but it is much discussed, and is much beloved by authors of fiction, especially the authors of science fiction. In this chapter we will look at the many worlds interpretation from the perspective of possible worlds.

Our considerations will be much assisted if we begin by looking at time from a possible worlds perspective. There are logics for time that have been developed on the basis of standard modal logics with possible world semantics. These logics provide an interesting background for the discussion of the many worlds interpretation of quantum physics, as we shall see.

Possible worlds and time

States of the universe at any point in history can be seen as possible worlds. Such states are sometimes called “time-slices”, but we will call them “instant states”. The state of the universe at one particular instant state, say right now, could be seen as possible world n. World n is the possible world in which it is true that you are reading this book, the Earth is orbiting the Sun, and the Sun is in the Milky Way galaxy. The state at the next instant can be seen as possible world k, the next after that as possible world l. Earlier instant states are before the later instant states; later instant states are after the earlier ones.

Knowledge and belief

One of the common uses of modal logic, apart from use in the discussion of logical possibility and necessity, is to provide a logic for knowledge and a logic for belief. These logics have practical applications in artificial intelligence, especially in knowledge representation.

Logics for knowledge are epistemic logics, and logics for belief are doxastic logics. Nevertheless, the term “epistemic logic” is often taken to encompass both epistemic and doxastic logics. One of the first twentieth-century suggestions for a logic for knowledge came from Lemmon in his paper, “Is There Only One Correct System of Modal Logic?” We have already noted that Lemmon was one of the great axiomatizers of modal logic, and he presented his epistemic logic in terms of the axiomatic system S0.5 (“S nought point 5”).

The first comprehensive text in epistemic and doxastic logic, Knowledge and Belief, was published by Hintikka in 1962. This work has become a classic. Hintikka made no explicit use of possible worlds as such in the text. He used model sets instead of possible worlds. Model sets are consistent sets of sentences. He set out consistency conditions for these sets of sentences, conditions such as:

(A. ˜) If p ∈ λ and “˜ p” ∈ λ, then λ is inconsistent.

(A. &) If λ is consistent and if “p & q” ∈ λ then λ + {p, q} is consistent.

What might have been

Possible worlds – the very phrase can set the speculative imagination alight. Leibniz suggested that this world was the best of all possible worlds. The suggestion has enraged some, bewildered many, satisfied some and set others to pondering. What is this idea of possible worlds?

Many works of narrative fiction, such as novels, films and even television programmes, describe possible worlds. Such worlds usually have some sort of internal consistency, or some sort of internal logic, even when they are quite unrealistic. Although realism is not always important, it can be. This is particularly so with the genre of historical novels and films. Works such as Pride and Prejudice and No Barrier are highly realistic and depend on a setting that is historically accurate. By contrast, some novels, and the films derived from them, such as The Lord of the Rings and Harry Potter and the Philosopher's Stone are works of sheer fantasy. Their setting is quite unlike the real world in crucial ways. They are valued just because they are not realistic. But there is an internal logic to the possible worlds described in these works.

In the television series Sliders there is explicit use of the idea of possible worlds. The series is built on the idea of possible worlds parallel to ours, worlds to which the heroes can “slide”. The heroes have their adventures in these possible worlds, in a different one each episode.

Singular terms and identity

We begin with the addition of singular terms to predicate logic. Consider again the following two sentences:

Kermit is a frog.

Kermit is green.

“Kermit” is a proper name. Proper names are singular terms, not general terms. They are terms that, in everyday discourse, refer to one and only one individual, one and only one entity in the domain. Proper names like “Emma”, “Socrates”, “Pickwick”, “Pegasus” and “Excalibur” are singular terms. If I say “Emma is a student,” then I am not taken to be talking about all the people who are named “Emma”, but only about one individual named “Emma”. This is so even though we know that there are many individuals called “Emma”. Similarly when I say, “Excalibur was cast into the lake,” I am taken to be talking about just one sword: the sword named “Excalibur”.

There are other words and phrases that we normally take to be singular terms as well. Some of these are singular pronouns like “I” and “she”. Some are descriptive singular terms like “the King of France”, “the Lord Mayor of Brisbane” and “the fountain of youth”. The definite article, “the”, in English usually gives indication of a descriptive singular term.

Individual constants and proper names

It is not unusual to translate all singular terms in English to individual constants in predicate logic. If this is done then the descriptive content of some singular terms is lost.

This volume is an exploration of the ways in which the notion of possible worlds has been used in recent philosophy and logic. There is a bias towards looking at the topics from a philosophical logic perspective. Although this book is intended for the wider audience, it is written with an eye to making the topics readily available to senior undergraduates and postgraduates. I begin with the ways in which possible worlds have been used as a framework for considering problems in logic and argument analysis. There are chapters that introduce the absolutely minimal amount of logic required for a logical perspective on possible worlds. These are followed by chapters with possible worlds and modal logic based discussions of questions of meaning, epistemic possibility, temporal logic, metaphysics and impossibility. The focus has been on underlying assumptions and doctrines, rather than on the consequential problems that come out of alleged solutions. It is quite surprising to find in some areas that, although the writers base their work on modal logic, very little use is actually made of possible worlds. Again and again I have come back to the questions of existence, quantification and impossibility. The text is deliberately, and perhaps rashly, provocative. I hope it will provide a good stepping-off point for vigorous discussion.

Introduction

If possibilities are real, what follows? Lots of things. But, if we use possible worlds to explain the nature of possibility, does the reality of possibilities mean that possible worlds must be real?

Some argue for a “yes” answer. Famously, David Lewis was the chief of those in the twentieth century arguing for a “yes” answer. Perforce, we will spend a great deal of time in this chapter considering Lewis's ideas, but not in the detail they deserve. Lewis takes the possible worlds account of possibility and necessity, and some other modal notions such as ought, with utmost seriousness. An analogy has been drawn between his approach to possible worlds and Gallileo's ideas about the heliocentric solar system.

At the time of Gallileo there were two astronomical pictures of the solar system: Gallileo's picture and Ptolemy's picture. Ptolemy's picture had the Earth at the centre of the solar system, and everything orbited about the Earth. The vast majority of astronomers accepted the Ptolemaic account. The Ptolemaic picture was more in accord with everyday intuition, common sense and observation. There is an excellent picture-book account of Ptolemy's account that shows how closely it follows observation. It was not a “silly” account.

Gallileo's picture, by contrast, had the Sun at the centre of the solar system, and the planets, including Earth, orbited the Sun. His motto was, “The earth moves”. This solar-centric account is quite contrary to everyday, and every night, common-sense observation.

A budget of heresy

I have declared or argued for several quite heretical things. First, I declared in favour of the status of first-order modal logic as an artificial language. I then gave examples that show that the language of classical logic is unreliable for the evaluation of many arguments couched in ordinary language. It was urged that more attention should be paid to the logic–language relationship. Modal logic is more reliable for some argument evaluation than non-modal logic. But we saw that there is much beyond the scope of present modal logic – the present logic of boxes and diamonds.

I argued for a renewed look at the whole question of existential import for both quantifiers and names. An appeal was made to ordinary intuitions and sensible talk of the properties of nonexistent entities. McGinn effectively denies Parmenides' law as he writes:

Modal logics

In this chapter we will consider the way in which possible worlds came to the aid of logicians working with modal logic. Modal logic is generally seen as the logic of possibility and necessity. Possible worlds have made formal modal logic quite clear and precise. In order to see possible worlds and modal logic in clearer perspective we will consider a little of the historical context.

Modern formal logic began with Frege's first-order logic. First-order logic is now seen in philosophy, mathematics, linguistics and computer science as the stepping-off point for virtually all work in logic. First-order logic includes classical propositional logic, which we looked at in Chapter 1, together with predicate logic. We have already said that we take first-order logic to be an artificial language that gives a precise and unambiguous account of logical concepts that are very like, but not exactly the same as, the logical concepts expressed in ordinary language.

We have seen that some of the logical concepts expressed in ordinary language are negation (standardly expressed with “not”), conjunction (“and”), disjunction (“or”) and implication (“if … then …”). We now turn to possibility and necessity. I have introduced special font expressions for the propositional logic operators used to translate these ordinary language logical operations: not for negation, and for conjunction, or for disjunction and imp for implication. Standard modal logic adds to these the diamond, ◊, for possibility and the box, □, for necessity.