Reasoning in attitudes

Abstract

People reason not only in beliefs, but also in intentions, preferences, and other attitudes. They form preferences from existing preferences, or intentions from existing beliefs and intentions, and so on. This often involves choosing between rival conclusions. Building on Broome (Rationality through reasoning, Hoboken, Wiley. https://doi.org/10.1002/9781118609088, 2013) and Dietrich et al. (J Philos 116:585–614. https://doi.org/10.5840/jphil20191161138, 2019), we present a philosophical and formal analysis of reasoning in attitudes, with or without facing choices in reasoning. We give different accounts of choosing, in terms of a conscious activity or a partly subconscious process. Reasoning in attitudes differs fundamentally from reasoning about attitudes, a form of theoretical reasoning in which one discovers rather than forms attitudes. We show that reasoning in attitudes has standard formal properties (such as monotonicity), but is indeterministic, reflecting choice in reasoning. Like theoretical reasoning, it need not follow logical entailment, but for a more radical reason, namely indeterminism. This makes reasoning in attitudes harder to model logically than theoretical reasoning. But it can be studied abstractly, using indeterministic consequence operators.

Appendices

Appendix

A Explicit introspection

While Broomean reasoning is a process of bringing to mind premise-attitudes and then creating a new attitude, introspecting is arguably a process of bringing to mind your wondering and then creating a new meta-belief—although this belief is not derived from or based on your wondering, as introspecting is not an inferential process, unlike reasoning. Like Broomean reasoning, introspecting can in principle be done explicitly. How? By saying to yourself the marked content of your wondering and your resulting belief. Using the interrogative mood as a linguistic marker of wondering, you may introspect explicitly as follows in the fourth account of indeterministic reasoning:

$$\begin{aligned} \textit{Do I already intend to take a boat or train? I do not yet intend either.} \end{aligned}$$

You say no ‘So’, as you draw no inference, unlike in Broomean reasoning.

This suggests an objection against the fourth account: if indeterministic reasoning is indeed premised on a meta-belief whose formation by introspection requires wondering (as just claimed), then you cannot reason without wondering in the first place. In the Venice example: if reasoning to a ‘boat’ or ‘train’ intention requires finding out introspectively that you have neither intention, which requires wondering whether you do, then you cannot reason without initially wondering about this. But normally you do not initially wonder about this (why should you?). Technically, if your initial constitution C does not contain the relevant attitude of wondering, you cannot introspect, hence cannot reason.

What could help? You might be lucky and start wondering automatically when needed. But if the fourth account relied on ‘automatic wondering’, we could not uphold our claim that indeterministic reasoning on this account can be a mental activity (cf. Sect. 3.3).

Surprisingly, however, you can come to wonder about something by an act of Broomean reasoning. From what premises do you derive a wondering? Intuitively, the premises are the justifications or basis for wondering. In the Venice example, your wondering whether you already have a ‘boat’ or ‘train’ intention might be derived from your intention to visit Venice and your beliefs about possible means. Then the complete process by which you form a ‘boat’ intention (on the fourth account) is made explicit by the following inner speech:

$$\begin{aligned} \begin{array}{l} \textit{(1)}~I \textit{shall visit Venice. (2) For this I must either take a boat or take a}\\ {train. ~(3) ~Both} \textit{ means are equally good. (4) Do I already intend a means?}\\ \textit{(5) I do not intend a means. (6) So, I shall take a boat.} \end{array} \end{aligned}$$

(9)

In (1)–(3) you bring to mind attitudes; from (1)–(3) you derive the wondering (4) by reasoning; from (4) you reach (5) by introspecting; from (1)–(3) and (5) you derive (6) by reasoning.³⁰

Our claim that you can derive a wondering by reasoning is certainly debatable. The claim is perhaps easier to accept if, as suggested in Sect. 3.4, wondering whether is a derived attitude, such as intending (or desiring) to know whether. In this case, reasoning to wondering is reasoning to a particular intention or desire. In our Venice example it seems very natural that, based on your initial attitudes, you derive an intention or desire to know whether you already hold specific intentions as to how to reach Venice. This derivation goes so quickly and easily that it rarely happens explicitly.

B Correct indeterministic reasoning?

According to Broome (2013), you can reason correctly to one of several possible conclusions. That is, given suitable sets P of premise-attitudes and K of possible conclusion-attitudes, you can reason correctly from P to any attitude in K. Broome focuses on instrumental reasoning, in which K contains intentions of a means to an end; for instance, in our Venice example K contains the ‘boat’ and ‘train’ intention, and P contains the intention to visit Venice and certain beliefs (about which Broome is more sophisticated than us, as mentioned in fn. 14). We have questioned Broome’s correctness claim, suggesting that correctness requires adding a premise-attitude to P, namely the belief of not yet having any attitude from K.

We here discuss the issue. For argument’s sake, we adopt Broome’s general characterisation of correctness: reasoning from a set of premise-attitudes P to a conclusion-attitude k is correct if P is a rationally permissible basis of k, more precisely, if it is rationally permitted to (i) hold the attitudes p in P at some moments and (ii) hold the attitude k at some moment based on the former attitudes. This so-called ‘basing permission’ is diachronic: it relates your attitudes at different moments. Indeed, reasoning takes time. By the time you reach the conclusion, you may have lost some premise-attitude(s), despite the conclusion-attitude being based on the premise-attitudes. Broome does not analyse what ‘based on’ means; nor shall we.

Broome applies this correctness criterion to certain examples of reasoning with different possible conclusions, similar to the Venice example. He claims that reasoning to any possible conclusion passes the correctness test. Technically, if P and K are the relevant attitude sets, say those in the Venice example, then for any k in K the rule (P, k) passes the correctness test, i.e., in short, P is a permissible basis of k. We doubt this claim. Were it true, you could reason correctly to all attitudes in K one by one, thereby forming conflicting intentions in the Venice example. Arguably, Broome has underspecified the basis of a k in K: a permissible basis is not P, but $P\cup \{m\}$, where m is the belief of not (yet) having any attitude from K. One could replace m by other introspective beliefs.³¹ It is hard to say whether one could replace m by a non-introspective (‘first-order’) attitude.³²

After deriving the conclusion-attitude k from $P\cup \{m\}$, your introspective belief m is false. So rationality does not permit holding the conclusion-attitude and all premise-attitudes in $P\cup \{m\}$ simultaneously. Yet rationality permits holding these attitudes at different times. This is why the reasoning rule $(P\cup \{m\},k)$ can meet the correctness test.

C Full psychological models of the four accounts of choice in reasoning

The main text worked with a shorthand model of choice in reasoning, which is account-neutral thanks to focusing on the ultimate effect of reasoning on attitudes rather than the psychological process. This appendix sketches how a full psychological model might roughly look under each account. In fact, we only discuss how to model a particular instance of choice in reasoning: reasoning from a set of premise-attitudes $P\subseteq M$ to any attitude from a set of possible conclusion-attitudes $K\subseteq M$ (in our Venice example, P contains the intention to visit Venice and two beliefs, and K contains the ‘boat’ intention and the ‘train’ intention). The shorthand model represents this instance by the indeterministic rule (P, K). A full model might instead take the following form.³³

First account. Here, a full model of reasoning from P to any attitude in K has two ingredients. One is a deterministic rule $(P,k^{\vee })$ where $k^{\vee }$ is a suitable ‘broad’ or ‘disjunctive’ conclusion-attitude (in the Venice example: the ‘boat or train’ intention). The second ingredient represents the psychological process that refines your disjunctive attitude $k^{\vee }$ into an arbitrary attitude k in K (in the Venice example: into the ‘boat’ intention or ‘train’ intention). The composition of your reasoning rule $(P,k^{\vee })$ and the automatic process is effectively equivalent to the indeterministic rule (P, K) in our shorthand model.

Second account. Here, a full model of reasoning from P to any attitude in K involves, for each possible conclusion attitude $k\in K$, a rule that derives k if all attitudes in P are present and all attitudes in K are absent; denote this rule by (P, K, k). These rules are generalised deterministic rules, premised on presences and absences of attitudes.³⁴ Reasoning with the rules (P, K, k) ($k\in K$) is effectively equivalent to reasoning with the single indeterministic rule (P, K). Why? For any initial constitution C, either $K\cap C\ne \varnothing$, in which case none of these rules applies and the constitution stays C; or $K\cap C=\varnothing$, in which case any rule (P, K, k) applies and leads to the new constitution $C\cup \{k\}$, after which none of the rules applies anymore, so that the constitution stays $C\cup \{k\}$. The result is the same as for reasoning with the indeterministic rule (P, K).

Third account. Here, a full model of reasoning from P to any attitude in K involves, for each possible conclusion attitude $k\in K$, the standard deterministic rule (P, k), which forms attitude k if you have all attitudes in P. The model also contains a precondition for applying these rules: each of these rules can only be applied to constitutions not yet containing any attitude from K. This precondition operationalises the assumption that when you start reasoning from the premise-attitudes in P but already possess an attitude from K, then (on the account) your reasoning stops, caused by your having in mind or bringing to mind a preexisting attitude from K. The precondition prevents the rules from operating the usual way: they effectively operate like the generalised deterministic rules from our model of the second account (i.e., rules premised on the absence of attitudes from K). This is why reasoning in the current model is effectively equivalent to reasoning in the second model, and hence to reasoning in the shorthand model based on the indeterministic rule (P, K).

Fourth account. Here, a full model of reasoning from P to any attitude in K involves, for each possible conclusion attitude $k\in K$, the standard deterministic rule $(P\cup \{m\},k)$, which forms attitude k from the attitudes in $P\cup \{m\}$, where the additional premise-attitude m is the belief of having no attitude from K (in the Venice example: the belief of having no ‘boat’ intention and no ‘train’ intention). We must also model the mechanism that prevents repeated reasoning to different attitudes from K (we shall only model the first such mechanism envisaged by the fourth account). To do this, we prescribe that each rule $(P\cup \{m\},k)$ ($k\in K$) applies in a non-standard way to a constitution C: systematically, before application the attitude m is added to your constitution, and after application m is removed again. Interpretation: while reasoning you get aware of not having any attitude from K, i.e., form the belief m, and after reasoning you lose that belief as it has become false through forming an attitude from K. More precisely, m is only added (and later removed) if $K\cap C=\varnothing$ and $P\subseteq C$. Why only then? If $K\cap C\ne \varnothing$ then the belief m is false, while if $P\not \subseteq C$ then you do not have all attitudes in P, hence stop reasoning prematurely. In both cases, you never get to the point of forming (and later losing) the belief m. In sum, the rule $(P\cup \{m\},k)$ applies in the following non-standard way to any constitution C. If $K\cap C=\varnothing$ and $P\subseteq C$, then C is first transformed into $C\cup \{m\}$, which is then transformed by the rule into $C\cup \{m,k\}$, which is then transformed into $(C\cup \{k\})\backslash \{m\}$.³⁵ Otherwise, C is not transformed.

This model is hardly parsimonious—a drawback of modelling the full psychological process postulated by the fourth account. Reasoning on the fourth model is effectively equivalent to reasoning on the other models or the shorthand model, because the non-standard rules of the fourth model produce the same result as the non-standard rules of the second account, and hence as the indeterministic rule of the shorthand model. To be precise, this effective equivalence holds with respect to all attitudes except the introspective belief m. Indeed, reasoning in the other models never affects the presence of m, whereas reasoning in the fourth model can have a (final) effect on the presence of m.³⁶

D Proof of Theorem 1

For any constitution $C\subseteq M$, reasoning system S, and number $n\in \{0,1,...\}$, let $Cn_{S,n}(C)$ denote the set of constitutions reachable from C in n steps of S-reasoning. Now fix a reasoning system S. The corresponding operator $Cn_{S}$ is obviously inclusive and idempotent, for reasons already indicated. To show monotonicity, consider constitutions $C,D\subseteq M$ such that $C\subseteq D$, and fix a $D^{+}\in Cn_{S}(D)$. Let $S^{\prime }$ be the reasoning system arising from S by replacing each rule $(P,K)\in S$ satisfying $K\cap D^{+}\ne \varnothing$ with the rule $(P,K\cap D^{+})$. So,

$$\begin{aligned} S^{\prime }=\{(P,K)\in S:K\cap D^{+}=\varnothing \}\cup \{(P,K\cap D^{+}):(P, k)\in S:K\cap D^{+}\ne \varnothing \}. \end{aligned}$$

Claim 1

For every number of steps $n\in \{0,1,2,...\}$, each constitution $C^{+}\in Cn_{S^{\prime },n}(C)$ satisfies $C^{+}\subseteq D^{+}$ and $C^{+}\in Cn_{S,n}(C)$.

We prove this claim by an induction on n. For $n=0$, then the claim is obvious because $Cn_{S^{\prime },0}(C)=Cn_{S,0}=\{C\}$ and because $C\subseteq D\subseteq D^{+}$. Now assume $n>0$ and suppose the claim holds for smaller numbers than n. Fix any $C^{+}\in Cn_{S^{\prime },n}(C)$. Pick a $\tilde{C}\in Cn_{S^{\prime },n-1}(C)$ such that $C^{+}\in Cn_{S^{\prime },1}(\tilde{C})$. The fact that $C^{+}\in Cn_{S^{\prime },1}(\tilde{C})$ and the definition of $S^{\prime }$ imply that $C^{+}\subseteq \tilde{C}\cup D^{+}$. So, as by induction hypothesis $\tilde{C}\subseteq D^{+}$, we have $C^{+}\subseteq D^{+}$.

It remains to show that $C^{+}\in Cn_{S,n}(C)$. As $\tilde{C}\in Cn_{S,n-1}(C)$, it suffices to prove $C^{+}\in Cn_{S,1}(\tilde{C})$. As $C^{+}\in Cn_{S^{\prime },1}(\tilde{C})$, we can pick a rule $(P,K^{\prime })\in S^{\prime }$ by which $C^{+}$ arises from $\tilde{C}$. By definition of $S^{\prime }$, there exists a $K\subseteq M$ such that $(P,K)\in S$ and either [$K\cap D^{+}=\varnothing$ and $K^{\prime }=K$] or [$K\cap D^{+}\ne \varnothing$ and $K^{\prime }=K\cap D^{+}$]. The first case is impossible: it would imply that $D^{+}$ is not closed under S-reasoning, because S contains the rule (P, K) which modifies $D^{+}$ since $P\subseteq D^{+}$ (as $P\subseteq \tilde{C}$ and $\tilde{C}\subseteq D^{+}$) and since $K\cap D^{+}=\varnothing$. So the second case holds. Note that

$$\begin{aligned} \tilde{C}\cap K=\tilde{C}\cap [K^{\prime }\cup (K\backslash D^{+} )]=(\tilde{C}\cap K^{\prime })\cup (\tilde{C}\cap (K\backslash D^{+})). \end{aligned}$$

In the last expression, $\tilde{C}\cap K^{\prime }=\varnothing$ (as otherwise the rule $(P,K^{\prime })$ could not change $\tilde{C}$) and $\tilde{C} \cap (K\backslash D^{+})=\varnothing$ (as $\tilde{C}\subseteq D^{+}$ by induction hypothesis). So $\tilde{C}\cap K=\varnothing$. Since $P\subseteq \tilde{C}$ and $\tilde{C}\cap K=\varnothing$, the rule (P, K) applies to $\tilde{C}$, just as the rule $(P,K^{\prime })$. So, one can reason from $\tilde{C}$ to $C^{+}$ not just using $(P,K^{\prime })$, but also using (P, K). In other words, $C^{+}$ belongs not just to $Cn_{S^{\prime },1} (\tilde{C})$, but also to $Cn_{S,1}(\tilde{C})$. Q.e.d.

Claim 2

$Cn_{S^{\prime }}(C)\subseteq Cn_{S}(C)$.

Let $C^{+}\in Cn_{S^{\prime }}(C)$. Then $C^{+}\in Cn_{S^{\prime },n}(C)$ for some $n\in \{0,1,...\}$. So, by Claim 1, $C^{+}\in Cn_{S,n}(C)$. It remains to show that $C^{+}$ is stable under S-reasoning. To show this, consider any rule $(P,K)\in S$ such that $P\subseteq C^{+}$. We must show that $K\cap C^{+}\ne \varnothing$. Form the rule $(P,K^{\prime })\in S^{\prime }$, where $K^{\prime }$ is K if $K\cap D^{+}=\varnothing$ and is $K\cap D^{+}$ otherwise. Since $C^{+}$ is closed under $S^{\prime }$-reasoning, the rule $(P,K^{\prime })$ does not change $C^{+}$, i.e., $K^{\prime }\cap C^{+} \ne \varnothing$. So, $K\cap C^{+}\ne \varnothing$. Q.e.d.

Claim 3

Some $C^{+}\in Cn_{S}(C)$ satisfies $C^{+}\subseteq D^{+}$.

Pick a $C^{+}\in Cn_{S^{\prime }}(C)$. By Claim 2, $C^{+}\in Cn_{S}(C)$. Further, $C^{+}\in Cn_{S^{\prime },n}(C)$ for some n, and so $C^{+}\subseteq D^{+}$ by Claim 1. Q.e.d.