Physicists are not very precise about it, may I suggest looking into “potential outcomes” (the language some statisticians use to talk about counterfactuals):
Potential outcomes let you think about a model that contains a random variable for what happens to Fred if we give Fred aspirin, and a random variable for what happens to Fred if we give Fred placebo. Even though in reality we only gave Fred aspirin. This is “counterfactual definiteness” in statistics.
This paper uses potential outcomes to talk about outcomes of physics experiments (so there is an exact isomorphism between counterfactuals in physics and potential outcomes):
Sounds like this is perhaps related to the counterfactual-consistency statement? In its simple form, that the counterfactual or potential outcome under policy “a” equals the factual observed outcome when you in fact undertake policy “a”, or formally, Y^a = Y when A = a.
No, not quite. Counterfactual consistency is what allows you to link observed and hypothetical data (so it is also extremely important). Counterfactual definiteness is even more basic than that. It basically sets the size of your ontology by allowing you to talk about Y(a) and Y(a’) together, even if we only observe Y under one value of A.
edit: Stephen, I think I realized who you are, please accept my apologies if I seemed to be talking down to you, re: potential outcomes, that was not my intention. My prior is people do not know what potential outcomes are.
edit 2: Good talks by Richard Gill and Jamie Robins at JSM on this:
Man on the street needs to learn what counterfactual definiteness is.
Ilya, can you give me a definition of “counterfactual definiteness” please?
Physicists are not very precise about it, may I suggest looking into “potential outcomes” (the language some statisticians use to talk about counterfactuals):
https://en.wikipedia.org/wiki/Rubin_causal_model
https://en.wikipedia.org/wiki/Counterfactual_definiteness
Potential outcomes let you think about a model that contains a random variable for what happens to Fred if we give Fred aspirin, and a random variable for what happens to Fred if we give Fred placebo. Even though in reality we only gave Fred aspirin. This is “counterfactual definiteness” in statistics.
This paper uses potential outcomes to talk about outcomes of physics experiments (so there is an exact isomorphism between counterfactuals in physics and potential outcomes):
http://arxiv.org/pdf/1207.4913.pdf
Sounds like this is perhaps related to the counterfactual-consistency statement? In its simple form, that the counterfactual or potential outcome under policy “a” equals the factual observed outcome when you in fact undertake policy “a”, or formally, Y^a = Y when A = a.
Pearl has a nice (easy) discussion in the journal Epidemiology (http://www.ncbi.nlm.nih.gov/pubmed/20864888).
Is this what you are getting at, or am I missing the point?
No, not quite. Counterfactual consistency is what allows you to link observed and hypothetical data (so it is also extremely important). Counterfactual definiteness is even more basic than that. It basically sets the size of your ontology by allowing you to talk about Y(a) and Y(a’) together, even if we only observe Y under one value of A.
edit: Stephen, I think I realized who you are, please accept my apologies if I seemed to be talking down to you, re: potential outcomes, that was not my intention. My prior is people do not know what potential outcomes are.
edit 2: Good talks by Richard Gill and Jamie Robins at JSM on this:
http://www.amstat.org/meetings/jsm/2015/onlineprogram/ActivityDetails.cfm?SessionID=211222
No offense taken. I am sorry I did not get to see Gill & Robins at JSM. Jamie also talks about some of these issues online back in 2013 at https://www.youtube.com/watch?v=rjcoJ0gC_po
Well, this whole thread started because minusdash and eli_sennesh objected to the concept of accusal trade for being too metaphysical.