While this may be true, it does not follow from your saying. Chaosmage is concluding p (google is more trustworthy), while CellBioGuy is concluding not-p (google is less trustworthy). If you look at the actual definitions of modus ponens and modus tollens you’ll find the following:
Modus ponens:
A → B and A,
therefore B
Modus tollens:
A → B and not-B,
therefore not-A
In other words, CellBioGuy would’ve had to conclude the negation of chaosmage’s premise (and not his conclusion) for your saying to be relevant in this situation.
There’s a double implication involved: “Google is trustworthy if and only if transhumanism is worth taking seriously.” (Or at least the probabilistic version of that.) So there’s four possible Modus Whatevers to use, and I think altogether we’ve covered three of them. The remaining possibility is “Well, I took transhumanism seriously before, but if Google supports it, then it must be nonsense.”
I think for me it’s more a combination of a touch of the first of those (low personal estimated credibility for transhumanism → lower estimated credibility of those who take it seriously), and that I tend to distrust large grand plans or narritives in general in favor of more narrowly focused objectives. Big grand plans have a way of obscuring details and sending people off track and into tangents via ideology.
Well, that saying only makes sense if it has the exact same implication in both terms (and then their respective conclusions has to be about different propositions), otherwise one is just claiming the equivalent of:
“One guy thinks A implies B, another thinks B implies A.”
And that is not a very good saying. It just sounds like something a post-modernist would say.
If you make A → B only with some probability, then B becomes probabilistically dependent on A as well; i.e. if you make logic probabilistic then this actually becomes true in a sense.
It is certainly true that if we know A implies B, then knowledge of B will also confer knowledge of A. However, this is not enough to call it a logical implication, and given that the original saying used the terms modus ponens and modus tollens, a logical implication is obviously what is meant in this setting.
To clarify, here’s what’s going on. The link between Google and transhumanism sets up the implication “If Google is trustworthy, then transhumanism should be taken seriously.”
Modus ponens: Google is trustworthy, therefore transhumanism should be taken seriously.
Modus tollens: Transhumanism should not be taken seriously, therefore Google is untrustworthy.
Interestingly, this makes me more wary of google instead.
One man’s modus ponens is another’s modus tollens. That’s all. It’s a perfectly reasonable conclusion.
While this may be true, it does not follow from your saying. Chaosmage is concluding p (google is more trustworthy), while CellBioGuy is concluding not-p (google is less trustworthy). If you look at the actual definitions of modus ponens and modus tollens you’ll find the following:
Modus ponens: A → B and A, therefore B
Modus tollens: A → B and not-B, therefore not-A
In other words, CellBioGuy would’ve had to conclude the negation of chaosmage’s premise (and not his conclusion) for your saying to be relevant in this situation.
There’s a double implication involved: “Google is trustworthy if and only if transhumanism is worth taking seriously.” (Or at least the probabilistic version of that.) So there’s four possible Modus Whatevers to use, and I think altogether we’ve covered three of them. The remaining possibility is “Well, I took transhumanism seriously before, but if Google supports it, then it must be nonsense.”
I think for me it’s more a combination of a touch of the first of those (low personal estimated credibility for transhumanism → lower estimated credibility of those who take it seriously), and that I tend to distrust large grand plans or narritives in general in favor of more narrowly focused objectives. Big grand plans have a way of obscuring details and sending people off track and into tangents via ideology.
Well, that saying only makes sense if it has the exact same implication in both terms (and then their respective conclusions has to be about different propositions), otherwise one is just claiming the equivalent of:
“One guy thinks A implies B, another thinks B implies A.”
And that is not a very good saying. It just sounds like something a post-modernist would say.
“One man’s modus ponens is another man’s modus ponens… in the other direction.”
If you make A → B only with some probability, then B becomes probabilistically dependent on A as well; i.e. if you make logic probabilistic then this actually becomes true in a sense.
It is certainly true that if we know A implies B, then knowledge of B will also confer knowledge of A. However, this is not enough to call it a logical implication, and given that the original saying used the terms modus ponens and modus tollens, a logical implication is obviously what is meant in this setting.
To clarify, here’s what’s going on. The link between Google and transhumanism sets up the implication “If Google is trustworthy, then transhumanism should be taken seriously.”
Modus ponens: Google is trustworthy, therefore transhumanism should be taken seriously.
Modus tollens: Transhumanism should not be taken seriously, therefore Google is untrustworthy.
Coudn’t agree more!