Commit 25c0151f by benkeks

Start part on potentialities and counterparts

parent 76b98e16
......@@ -665,7 +665,7 @@ lemma (in counterfactuals) counterfactual_inference_by_weakening_the_consequent:
using assms by auto
\<comment>\<open>Page 36 states that the following modus tollens for counterfactuals is valid.
The remark fails to mention that this is only the case assuming (at least weak)
The remark does not mention that this is only the case assuming (at least weak)
centering of the spheres. (The other inference patterns do not rely on this
lemma (in counterfactuals_weakly_centered) counterfactual_modus_tollens:
......@@ -674,10 +674,58 @@ lemma (in counterfactuals_weakly_centered) counterfactual_modus_tollens:
using assms counterfactual_implies_material_conditional
by (meson is_true_at.simps(3))
subsection \<open>Potentialities (\<section> 1.9)\<close>
text \<open>This section is largely concerned with the \<open>de re\<close> nature of many counterfactual
statements. This means that they are talking about \<open>the same\<close> object in different
worlds. The object name usually is fixed in the actual world.
One instance are dispositions where “a thing has disposition D iff, subjected to test
T, it would give response R” is analysed by Lewis (p. 38) as:\<close>
definition (in counterfactuals) disposed_to ::
\<open>('object \<Rightarrow> 'a formula) \<Rightarrow> ('object \<Rightarrow> 'a formula) \<Rightarrow> 'object \<Rightarrow> 'world \<Rightarrow> bool\<close>
where \<open>disposed_to test response x w \<equiv> \<lbrakk> test x \<box>\<rightarrow> response x \<rbrakk>w\<close>
locale counterparts =
counterfactuals S interpretations for
S :: \<open>'world \<Rightarrow> 'world set set\<close> and
interpretations :: \<open>'world \<Rightarrow> 'a \<Rightarrow> bool\<close> +
counterparts :: \<open>('world \<times> 'object) rel\<close>
\<comment>\<open>“anything is its own unique counterpart at its own world”\<close>
\<open>((w,n), (w,n)) \<in> counterparts\<close>
\<open>((w,n), (w,n')) \<in> counterparts \<Longrightarrow> n = n'\<close>
context counterfactuals
text \<open>“the abstract entities that exist alike from the standpoint of all world, but inhabit
none, are their own unique counterparts at all worlds”\<close>
definition abstract_entity :: \<open>'object \<Rightarrow> bool\<close>
where \<open>abstract_entity n \<equiv>
\<forall>w1. \<forall>w2. ((w1,n), (w2,n)) \<in> counterparts \<and>
(\<forall>n'. (((w1,n), (w2,n')) \<in> counterparts \<or> ((w2,n), (w1,n')) \<in> counterparts)
\<longrightarrow> n = n')\<close>
\<comment>\<open>TODO: find a way to encode the counterpart theory with Derefs without
rewriting all of the counterfactual theory\<close>
primrec is_true_at2 :: \<open>'a formula \<Rightarrow> 'world \<Rightarrow> bool\<close> (\<open>x\<lbrakk> _ \<rbrakk>_\<close> [20] 55) where
\<open>(x\<lbrakk>\<bottom>\<rbrakk>w) = False\<close> |
\<open>(x\<lbrakk>Atom a\<rbrakk>w) = interpretations w a\<close> |
\<open>(x\<lbrakk>\<phi>\<rightarrow>\<psi>\<rbrakk>w) = (\<not>(x\<lbrakk>\<phi>\<rbrakk>w) \<or> x\<lbrakk>\<psi>\<rbrakk>w)\<close>|
\<comment>\<open>Definition of counterfactuals from p. 16\<close>
\<open>(x\<lbrakk>\<phi>\<box>\<rightarrow>\<psi>\<rbrakk>w) = (
(\<forall>s \<in> S w. \<not>(\<exists>w\<phi> \<in> s. x\<lbrakk>\<phi>\<rbrakk>w\<phi>)) \<or>
(\<exists>s \<in> S w. (\<exists>w\<phi> \<in> s. x\<lbrakk>\<phi>\<rbrakk>w\<phi>) \<and> (\<forall>ws \<in> s. (x\<lbrakk>\<phi>\<rbrakk>ws) \<longrightarrow> x\<lbrakk>\<psi>\<rbrakk>ws)))\<close>
context counterfactuals
subsection \<open>Comparative Similarity\<close>
\<comment>\<open>p. 48 Section 2.3 Comparative Similarity\<close>
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