Abstract
This paper proposes an epistemic logical framework for demanding knowing why in the natural sciences. Our focus is on the phenomena and their respective causal factors revealed by experiments. Two novel modalities \(\textsf{E}(\psi ,\varphi )\) and \(\textsf {W}((\psi _1,\varphi _1)\bullet (\psi _2,\varphi _2)\bullet \cdots \bullet (\psi _n,\varphi _n))\) are introduced over models that deviate from the usual epistemic models by having both experimental evidence and the scientific theories, which is inspired by scientific practices. The modality \(\textsf{E}\) expresses scientists’ have (conclusive) experimental evidence indicating a dependence relation between the causal factor \(\psi \) and \(\varphi \). Based on the evidence, scientists often package some (perhaps seemingly unrelated) phenomena together, and the modality \(\textsf{W}\) captures scientists’ knowing why in their entirety, or having systematic knowledge-why of them, which amounts to having a unified scientific theory of all these dependences. A sound and complete axiomatization is given, followed by a decidability result. Many notions of much philosophical interest are embodied in the present framework. We also draw several comparisons and connections with some existing relevant logical work.
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Notes
In fact, John’s example is designed to talk about the relationship between knowing why and another epistemic state of understanding why. We will return to discuss briefly knowing and understanding in the final section of this paper.
Empirical evidence can be transferred by testimony. As in the case where John learns from testimony that the house burned down because of faulty wiring, which is a result reached through the firefighter’s empirical investigations.
There are several reasons to doubt that the unique causal factor will be identified. Lewis (1986) argues that what we consider to be the cause is partially a context-sensitive matter. Hitchcock (1996) discusses the contrastive feature of causal claims. Take an example from Lawler (2019b), the context-sensitivity means that in one context Julien eating his lunch quickly is the cause of his hiccups, and in another it is that a reflex of his diaphragm was stimulated. The contrastive feature means that, whether Julien eating his lunch quickly or the stimulation of his diaphragm is the cause of his hiccups seems to depend on the contrast in question. The contrast might be that Julien has the hiccups after eating rather than performing other activities, or that his diaphragm rather than the stomach and the like was stimulated. These might be of much interest, which are left for future work.
As pointed out by an anonymous reviewer, \(\mathbb {PRINCIPLE}\) may not be restricted to information from scientific theories, and a scientist could discover a new type of dependency before developing a new theory. These discussions might be of much interest, but we will keep it simple here and leave them to a future occasion.
We consciously chose the symbol
for strict implication for our scientific laws for the reason that these laws should hold universally.According to Hempel Hempel (1966), “The laws invoked in a scientific explanation will also be called covering laws for the explanandum phenomenon, and the explanatory argument will be said to subsume the explanandum under those laws." Similarly we can say a universal law in a theory is a covering law if it is applied to “cover" some evidential dependency relation.
Besides, some scholars in the literature argue that grasping independence relationship matters for explanation, to which we come in Sect. 6
The abbreviation \((\texttt{EFCON})\) is for conjunction of effect phenomena. Similarly, the abbreviation \((\texttt{CADIS})\) is for disjunction of cause phenomena.
The abbreviations \((\texttt{RECA})\) and \((\texttt{REEF})\) stand for rules of equivalence of cause phenomena and effect phenomena respectively.
A detailed comparison with conditional logic will be given later in Sect. 5
\((\texttt{4EG}) \) is an axiom constructed by modality \(\textsf{E}\) and \(\textsf{G}\), resembling the \(\texttt{4}\) axiom in standard modal logic. Similarly, this applies to the abbreviations \((\texttt{5EG}) \), \((\texttt{4WG}) \) and \((\texttt{5WG}) \). A brief comparison between this logic and modal logic is presented below.
This abbreviation represents \(\textsf{W}\) yielding \(\textsf{E}\).
The abbreviation is for background knowledge conveyed by \(\textsf{W}\). The exact meaning will be explained below.
The abbreviation \((\texttt{WSW})\) stands for weakening the effect phenomena and strengthening the cause phenomena in \(\textsf{W}\).
The abbreviation is for intersection of dependencies.
In Wang and Wang (2019), two similar global modalities are proposed and discusses capturing the physical necessity.
“For them, the world is an on-or-off matter-either something happens or it does not; and there appears to be no room in their on-or-off world for a distinction between what happens of necessity and what only happens contingently..." (see Fine (2005)).
Not all philosophers agree with our example “ice being denser than water is metaphysically possible but physically impossible". Here we follow Fine (2005) in thinking that: “surely it is conceivable, and hence metaphysically possible, that many of the natural laws that govern our universe should fail to hold" (p. 238).
Even if there is a state that a match is wet and is stroke by someone, and no transition to a match-being-ignored state, it won’t impair the observation that all transitions showed match being stroke gives rise to match being ignored. It is so because we only model positive dependence relation, which will be discussed in the following.
for strict implication for our scientific laws for the reason that these laws should hold universally.References
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Acknowledgements
The author would like to express gratitude to Yanjing Wang for his patient guidance and valuable suggestions throughout this project. Many thanks are also extended to Qiang Wang, Wenqin Zhang, and the two anonymous reviewers of this journal for their helpful and insightful comments on earlier versions of the paper. Last but not least, the support from Shanghai Pujiang Program (Grant No. 22PJC034) and Fundamental Research Funds for the Central Universities (Grant No. 2022ECNU-YYJ038) is acknowledged.
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Wei, Y. Matching Theories with Evidence: A Logic for Demanding Knowing Why. Erkenn (2024). https://doi.org/10.1007/s10670-024-00796-6
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DOI: https://doi.org/10.1007/s10670-024-00796-6