I’m on a science kick lately, if you can’t tell by the last few posts. I’ve gotten my phil science batteries recharged with my current course and I feel like sharing more of what I do with the world. So today I’m going to talk about the hypothetical-deductivism model of science and the raven’s paradox. Technical words, but not that scary. What hypothetical-deductivism (from now on HD since I’m too lazy to write it out again) is, is a model for how science confirms and disconfirms hypotheses. It’s an old model, but it’s been updated to what is now called bayesianism, which I find suffers from similar problems.
So what is HD? It’s a logical approach that has two parts, confirmation and disconfirmation. Confirmation happens when we have an hypothesis that logically implies some observation. The hypothesis that all ravens are black entails that if x is a raven, then x is black. If we find something that is a raven and is black, then this confirms that all ravens are black. It can be much more interesting than this, but it’s mainly a common sensical approach to confirmation. If an hypothesis logically entails a prediction, and that prediction is correct, then the hypothesis is confirmed. Hence the name Hypothetical-Deductivism, one deduces observations from a hypothesis and if those observations are correct, confirmation happens, yay!
Disconfirmation happens in just the opposite way, that if it entails that an observation will not happen, but it does, then the theory is disconfirmed. So when Newtonian mechanics predicted that light from stars will not bend around the gravitational field of the sun (gravitational lensing), and then we observed that it did, it disconfirmed Newtonian mechanics while confirming general relativity.
It’s a straight forward approach that came out of a time when we thought that logic could solve all of our problems. It hasn’t, and it won’t. Why is this? Two reasons: white shoes and bumblebees.
The white shoes problem, usually known as the raven’s paradox, is a problem that arises from a fact in logic. It is a logical truism that if a hypothesis implies some observation, then the negation of that observation implies the negation of the hypothesis. So in the case of ravens, the HD model of confirmation, if x is a raven then x is black, is logically equivalent to if x is not black then x is not a raven. But as before we saw that if we find something that is black and a raven, then it confirms the first implication, so a white shoe that is neither black nor a raven will confirm the second implication. So white shoes confirm that all ravens are black. This is a problem, white shoes shouldn’t confirm anything along those lines.
Second is the irrelevant conjunction problem. Again, it follows from logic. You’ll have to take my word for it, but it is a logical fact that if A implies B, then (A and C) implies B. So we can take some hypothesis about bumblebees dancing to direct others toward honey and attach it to general relativity. General relativity implies that starlight will bend, and logically so will General relativity and bumblebees dancing imply that starlight will bend. The meat of this problem is that if we observe starlight bending, then we confirm both the hypothesis of General relativity, and bumblebees dancing. Hence the name, the problem of irrelevant conjunctions. We could even take this a step further and append bumble bees to the ravens implication such that white shoes confirm that all ravens are black and that bumblebees dance to show where the honey is.
Why is this interesting? Because HD is rather much like a common sense approach to science. If an observation is derived from a hypothesis, then either it is confirmed or disconfirmed by the observation. But common sense is wrong on this point. And that’s what philosophy likes to do. It likes to start from a common sense beginning, and then take it further and see how it fares. Often, it does not do so well. which is why philosophy is interesting, it questions what we take for granted as true and often finds that it doesn’t work. That doesn’t mean it has all the answers, believe me, you don’t go into philosophy for answers, but in some sense, like science, at least we know what doesn’t work.
For those familiar with bayesianism, the problem of irrelevant conjunctions plagues it as well. First is just that since an irrelevant hypothesis will not impact the probability of an observation, it too will be confirmed by observation. Or, in a more technical perspective, the HD model is a subset of bayesianism, HD is just when the likelihood of Pr(observation|hypothesis & irrelevant hypothesis)=1, which then means that the probability of Pr(hypothesis & irrelevant hypothesis | observation) = Pr(hypothesis & irrelevant hypothesis) / Pr (observation) under Bayes’ theorem. And this is always greater than than Pr(hypothesis & irrelevant hypothesis) because Pr(observation) < 1.
Philosophy, Science, Bipolar I, and Life
I’m on a science kick lately, if you can’t tell by the last few posts. I’ve gotten my phil science batteries recharged with my current course and I feel like sharing more of what I do with the world. So today I’m going to talk about the hypothetical-deductivism model of science and the raven’s paradox. Technical words, but not that scary. What hypothetical-deductivism (from now on HD since I’m too lazy to write it out again) is, is a model for how science confirms and disconfirms hypotheses. It’s an old model, but it’s been updated to what is now called bayesianism, which I find suffers from similar problems.
So what is HD? It’s a logical approach that has two parts, confirmation and disconfirmation. Confirmation happens when we have an hypothesis that logically implies some observation. The hypothesis that all ravens are black entails that if x is a raven, then x is black. If we find something that is a raven and is black, then this confirms that all ravens are black. It can be much more interesting than this, but it’s mainly a common sensical approach to confirmation. If an hypothesis logically entails a prediction, and that prediction is correct, then the hypothesis is confirmed. Hence the name Hypothetical-Deductivism, one deduces observations from a hypothesis and if those observations are correct, confirmation happens, yay!
Disconfirmation happens in just the opposite way, that if it entails that an observation will not happen, but it does, then the theory is disconfirmed. So when Newtonian mechanics predicted that light from stars will not bend around the gravitational field of the sun (gravitational lensing), and then we observed that it did, it disconfirmed Newtonian mechanics while confirming general relativity.
It’s a straight forward approach that came out of a time when we thought that logic could solve all of our problems. It hasn’t, and it won’t. Why is this? Two reasons: white shoes and bumblebees.
The white shoes problem, usually known as the raven’s paradox, is a problem that arises from a fact in logic. It is a logical truism that if a hypothesis implies some observation, then the negation of that observation implies the negation of the hypothesis. So in the case of ravens, the HD model of confirmation, if x is a raven then x is black, is logically equivalent to if x is not black then x is not a raven. But as before we saw that if we find something that is black and a raven, then it confirms the first implication, so a white shoe that is neither black nor a raven will confirm the second implication. So white shoes confirm that all ravens are black. This is a problem, white shoes shouldn’t confirm anything along those lines.
Second is the irrelevant conjunction problem. Again, it follows from logic. You’ll have to take my word for it, but it is a logical fact that if A implies B, then (A and C) implies B. So we can take some hypothesis about bumblebees dancing to direct others toward honey and attach it to general relativity. General relativity implies that starlight will bend, and logically so will General relativity and bumblebees dancing imply that starlight will bend. The meat of this problem is that if we observe starlight bending, then we confirm both the hypothesis of General relativity, and bumblebees dancing. Hence the name, the problem of irrelevant conjunctions. We could even take this a step further and append bumble bees to the ravens implication such that white shoes confirm that all ravens are black and that bumblebees dance to show where the honey is.
Why is this interesting? Because HD is rather much like a common sense approach to science. If an observation is derived from a hypothesis, then either it is confirmed or disconfirmed by the observation. But common sense is wrong on this point. And that’s what philosophy likes to do. It likes to start from a common sense beginning, and then take it further and see how it fares. Often, it does not do so well. which is why philosophy is interesting, it questions what we take for granted as true and often finds that it doesn’t work. That doesn’t mean it has all the answers, believe me, you don’t go into philosophy for answers, but in some sense, like science, at least we know what doesn’t work.
For those familiar with bayesianism, the problem of irrelevant conjunctions plagues it as well. First is just that since an irrelevant hypothesis will not impact the probability of an observation, it too will be confirmed by observation. Or, in a more technical perspective, the HD model is a subset of bayesianism, HD is just when the likelihood of Pr(observation|hypothesis & irrelevant hypothesis)=1, which then means that the probability of Pr(hypothesis & irrelevant hypothesis | observation) = Pr(hypothesis & irrelevant hypothesis) / Pr (observation) under Bayes’ theorem. And this is always greater than than Pr(hypothesis & irrelevant hypothesis) because Pr(observation) < 1.