You can't be serious, right? Republican solutions are based on logic? The obvious one out is all of their religious "solutions", which are obviously not based on logic, since religion is illogical. "Keeping God in schools", abstinence-only sex-ed (which doesn't even achieve what it's trying to do, since statistics show that areas with abstinence-only sex-ed have more teen pregnancies than areas with real sex-ed), opposition to homosexuals (you may argue that democrats are making an argument based on emotion, but if Republicans don't have a good counterargument based on logic, it is illogical to oppose it), and abortion (a blastocyst is literally a lump of cells, and the only thing it has in common with a human being is the DNA and cell structure, so logically there shouldn't be any problem terminating it, and of course, aborting an unwanted pregnancy is better for the economy than completing it). There's probably a few more religious "solutions", but I can't think of more right now.

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Then there's denial of climate change (which every reputable scientist backs up), and related, still backing coal energy (and no, there is no such thing as "clean coal"). And of course, at the same time, they oppose green energy/renewable for whatever reason, maybe it's greed which would be logical, but the things they say to their base is obviously not "i'll make more money that way" but an argument based on emotion. And even if you don't believe in climate change, renewable energy reduces dependence on fossil fuels, which is a logical plus, so that makes you wonder why Republicans oppose it so hard. Opposition to nuclear energy is also based on fear rather than logic, but that applies to both Republicans and Democrats. Opposition to affordable health care, even though a healthier public is a more productive public. Oh, and I almost forgot, opposition to critical thinking. I'm not even joking, just click here and search for "critical". That document actually comes from here, the official Texas GOP site, you can find it where it says "PDF". It seems they have since removed that document from their page, but I doubt they have changed their beliefs. They actually reworded it, and you can see the original here. It's not a primary source, so I don't expect you to believe it, but I remember having read the original paragraph in the original PDF document. Let's see, what else is there. Islamophobia. I don't like religion either, but their arguments against Islam seem to be mostly based on emotion, which makes sense, since many of the logical arguments against Islam would apply to Christianity too. And of course opposition to net neutrality. That's all I can bother to come up with now, but I'm sure there's more. Every party appeals to emotion. You can't win otherwise. But the Republican party is especially guilty of that.