Seán Moran investigates indoor ornithology.
https://philosophynow.org/issues/138/Corvid_Captured
Corvid Captured
Re: Corvid Captured
I have always thought the main problem with the raven paradox is the presumption that the expression “All ravens are black” is interpreted in terms of the truth functional material conditional in classical logic. It is this interpretation that makes “All non-black things are non-ravens” logically equivalent to “All ravens are black”.
If there are patterns in nature, we look for explanations. In science we presume there are the natural laws that govern what patterns we observe. We might observe the pattern that all ravens are black and this pattern is well expressed by the classic logic material conditional in a universal quantifier. But if we want a hypothesis that explains this generalisation and allows us to collect evidence for it, then this hypothesis needs to be expressed in a form that allows us to articulate causal or deterministic relations between specific properties.
Imagine you observe all the toys coming out of a toy factory. All the toy ravens are black. This can be expressed by classical logic. But if you want to say that there must be some reason why all the toy ravens are black you are making another kind of claim. You could speculate that the toy makers have some rule such that if they have made a toy raven they only paint it black. Or perhaps the colour of the toy is pre-determined by the plastic used and toy makers have instructions not to make ravens from non-black plastic. These are different instructions, but they both have the same consequence - all toy ravens will be black and all non-black toys will be non-ravens. Of course there could be other ways in which a rule is realised, but what we are interested in initially is the rule itself and how that could be expressed in logic.
So if we are interested in confirming a hypothesis about the property of some object (or toy) being a raven determining the colour of that object, we would not want our hypothesis to be confirmed by something that is not a raven and which is not black because they are irrelevant. So why would we choose to interpret the conditional in this way? There are non-truth functional alternatives to the classical material conditional which dissolve the paradox, but for some reason this approach seems to be ignored in most discussions of the subject, including this article. The only article I have been able to find that proposes an alternative interpretation of the conditional to resolve the paradox is by Robert J Farrell in 1979: Material Implication, Confirmation and Counterfactuals. I can’t find any literature finding fault with this approach. Can anyone suggest any objections?
If there are patterns in nature, we look for explanations. In science we presume there are the natural laws that govern what patterns we observe. We might observe the pattern that all ravens are black and this pattern is well expressed by the classic logic material conditional in a universal quantifier. But if we want a hypothesis that explains this generalisation and allows us to collect evidence for it, then this hypothesis needs to be expressed in a form that allows us to articulate causal or deterministic relations between specific properties.
Imagine you observe all the toys coming out of a toy factory. All the toy ravens are black. This can be expressed by classical logic. But if you want to say that there must be some reason why all the toy ravens are black you are making another kind of claim. You could speculate that the toy makers have some rule such that if they have made a toy raven they only paint it black. Or perhaps the colour of the toy is pre-determined by the plastic used and toy makers have instructions not to make ravens from non-black plastic. These are different instructions, but they both have the same consequence - all toy ravens will be black and all non-black toys will be non-ravens. Of course there could be other ways in which a rule is realised, but what we are interested in initially is the rule itself and how that could be expressed in logic.
So if we are interested in confirming a hypothesis about the property of some object (or toy) being a raven determining the colour of that object, we would not want our hypothesis to be confirmed by something that is not a raven and which is not black because they are irrelevant. So why would we choose to interpret the conditional in this way? There are non-truth functional alternatives to the classical material conditional which dissolve the paradox, but for some reason this approach seems to be ignored in most discussions of the subject, including this article. The only article I have been able to find that proposes an alternative interpretation of the conditional to resolve the paradox is by Robert J Farrell in 1979: Material Implication, Confirmation and Counterfactuals. I can’t find any literature finding fault with this approach. Can anyone suggest any objections?