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Fig.4 The general structure of total interpretation As noted above, both the interpretans and the interpretandum are explanations; each consists of an explanans, explanation process, and explanandum. A case of total inter- pretation is one in which the interpretans is totally different from the interpretandum. In other words, one in which the explanans, explanation process, and explanandum contained in the former differ in some way from the explanans, explanation process,

Figure 4 The general structure of total interpretation As noted above, both the interpretans and the interpretandum are explanations; each consists of an explanans, explanation process, and explanandum. A case of total inter- pretation is one in which the interpretans is totally different from the interpretandum. In other words, one in which the explanans, explanation process, and explanandum contained in the former differ in some way from the explanans, explanation process,

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While the DN model is good for illustrating the explanation of phenomena which result from deterministic laws, it does not capture the characteristics of probabilis- tic events. In response to this, Hempel (1965) introduced Inductive Statistical (IS) explanation. IS explanation involves the inference of an individual event from a sta- tistical law and empirical information about the event (see Fig. 2). For example, the increased probability of having breast cancer given a mutated BRCA/ gene in con- junction with a particular patient having a mutated BRCA/ gene explains the patient having breast cancer. Here, the relation between the explanandum and the explanans is inductive because all that can be inferred from the information given is there being a higher or lower probability that the patient has breast cancer. If the probability of having breast cancer given that the patient has a mutated BRCA/ gene were lower then even if the patient has breast cancer, this information cannot be used to explain
While the DN model is good for illustrating the explanation of phenomena which result from deterministic laws, it does not capture the characteristics of probabilis- tic events. In response to this, Hempel (1965) introduced Inductive Statistical (IS) explanation. IS explanation involves the inference of an individual event from a sta- tistical law and empirical information about the event (see Fig. 2). For example, the increased probability of having breast cancer given a mutated BRCA/ gene in con- junction with a particular patient having a mutated BRCA/ gene explains the patient having breast cancer. Here, the relation between the explanandum and the explanans is inductive because all that can be inferred from the information given is there being a higher or lower probability that the patient has breast cancer. If the probability of having breast cancer given that the patient has a mutated BRCA/ gene were lower then even if the patient has breast cancer, this information cannot be used to explain
when ANNs are recurrent, the pathways can always be unrolled and mechanistically depicted. depicted. There are several criticisms of the accounts of explanation described above (see Salmon 1989; Skillings 2015; Godfrey-Smith 2016). While we do not have the space to engage with all of these, there are two that may have implications for the arguments that follow, and are thus worth addressing. First, it may be argued that some of the typically cited challenges facing DN, IS, and CM explanations, such as explanatory asymmetry and explanatory irrelevance, are the result of disregard for, or inadequate treatment of the role of causation in explanation (Woodward 2003). Woodward’s (2003) causal-interventionist account of explanation, according to which successfu explanations exhibit patterns of counterfactual dependence, may help deal with these issues, particularly when it comes to the problem of explanatory relevance. Since we argue in Section 3 that ANNs are explainable using the traditional models described above, it may be argued that our account of interpretability could inherit some o these issues. We agree that the causal-interventionist account may be useful for solv ing some questions about explainability, understandability, and interpretability in A (Paez 2019). Indeed, we describe interpretability processes in Section 4.3 some o which result in understandable explanations which include counterfactual informa- tion, however, the causal-interventionist account includes pragmatic elements that we maintain should not count against a phenomenon’s explainability, namely that an explanation should be “deeper or more satisfying” (Woodward 2003: 190) than those provided by DN, IS, or CM explanations. Of course, we agree that some expla- nations can be more preferable than others given some explanatory virtue, such as simplicity, but we disagree that such virtues should be considered when evaluating the explainability of a phenomenon. Second, proponents of the ontic conception of explanation, according to which
when ANNs are recurrent, the pathways can always be unrolled and mechanistically depicted. depicted. There are several criticisms of the accounts of explanation described above (see Salmon 1989; Skillings 2015; Godfrey-Smith 2016). While we do not have the space to engage with all of these, there are two that may have implications for the arguments that follow, and are thus worth addressing. First, it may be argued that some of the typically cited challenges facing DN, IS, and CM explanations, such as explanatory asymmetry and explanatory irrelevance, are the result of disregard for, or inadequate treatment of the role of causation in explanation (Woodward 2003). Woodward’s (2003) causal-interventionist account of explanation, according to which successfu explanations exhibit patterns of counterfactual dependence, may help deal with these issues, particularly when it comes to the problem of explanatory relevance. Since we argue in Section 3 that ANNs are explainable using the traditional models described above, it may be argued that our account of interpretability could inherit some o these issues. We agree that the causal-interventionist account may be useful for solv ing some questions about explainability, understandability, and interpretability in A (Paez 2019). Indeed, we describe interpretability processes in Section 4.3 some o which result in understandable explanations which include counterfactual informa- tion, however, the causal-interventionist account includes pragmatic elements that we maintain should not count against a phenomenon’s explainability, namely that an explanation should be “deeper or more satisfying” (Woodward 2003: 190) than those provided by DN, IS, or CM explanations. Of course, we agree that some expla- nations can be more preferable than others given some explanatory virtue, such as simplicity, but we disagree that such virtues should be considered when evaluating the explainability of a phenomenon. Second, proponents of the ontic conception of explanation, according to which
Fig.5 A partial interpretation wherein the explanandum remains the same in both the interpretans and interpretandum
Fig.5 A partial interpretation wherein the explanandum remains the same in both the interpretans and interpretandum
Fig. 6 A partial interpretation wherein the process of interpretation used results in a new process of explanation for an explanans and explanandum understanding whatever about x. Another way to put the problem of relating different explananda in a total inter- pretation is by asking what sorts of relationships between phenomena are relevant to scientific explanation: Similar phenomena can sometimes figure in explanations with the same overall structure. For example, explanations of tissue classifications based on radiological whiteness can inform explanations of classifications based on tissue density. Provided we have some justification for substituting radiological whiteness for tissue density, explanations on the basis of radiological whiteness can be totally interpreted by those referring to tissue density instead. The hope being that tissue den- sity provides some understanding that radiological whiteness does not. Of course, the similarity of two phenomena does not imply that there should be any understanding gained about one via explanation of the other—understanding is too psychologi- cally contingent for this—but such relationships are, methodologically, good places to begin the search for understanding. In the context of formal explanations. where our concern is not phenomena
Fig. 6 A partial interpretation wherein the process of interpretation used results in a new process of explanation for an explanans and explanandum understanding whatever about x. Another way to put the problem of relating different explananda in a total inter- pretation is by asking what sorts of relationships between phenomena are relevant to scientific explanation: Similar phenomena can sometimes figure in explanations with the same overall structure. For example, explanations of tissue classifications based on radiological whiteness can inform explanations of classifications based on tissue density. Provided we have some justification for substituting radiological whiteness for tissue density, explanations on the basis of radiological whiteness can be totally interpreted by those referring to tissue density instead. The hope being that tissue den- sity provides some understanding that radiological whiteness does not. Of course, the similarity of two phenomena does not imply that there should be any understanding gained about one via explanation of the other—understanding is too psychologi- cally contingent for this—but such relationships are, methodologically, good places to begin the search for understanding. In the context of formal explanations. where our concern is not phenomena
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Philosophy of SciencePhilosophy of MedicinePhilosophy of Artificial Intelligence
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