tag:blogger.com,1999:blog-4667288583830493271.post5708855185794079408..comments2017-10-29T05:06:01.810-07:00Comments on Philosophy in Progress: Three Projects Involving Dispensing With Mathematical ObjectsSharon Berryhttp://www.blogger.com/profile/17434076853502881274noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-4667288583830493271.post-67859489393973679652016-05-03T13:06:21.232-07:002016-05-03T13:06:21.232-07:00Hey! Thanks for responding!
Okay so my current u...Hey! Thanks for responding! <br /><br />Okay so my current understanding is that there is a single goal (to remove the use of mathematical objects from scientific theories) with at least three motivations. These motivations are each to some degree associated with a method for reaching the goal. One of the motivations is that mathematical objects don't exist, so shouldn't be invoked. <br /><br />I suspect the unspoken reasoning there is that if entities that do not exist are invoked, a faulty pattern might be found, which becomes accepted because it explains some truths, but then is gradually munged in order to handle exceptions. In a phrase, flawed theories are based on flawed ontologies, such as the acceptance of the existence of aether, levity, or phlogiston. <br /><br />I'll try to tackle this more once I get corrections to my current map ;) anthonybhttps://www.blogger.com/profile/07971737958844374732noreply@blogger.comtag:blogger.com,1999:blog-4667288583830493271.post-69263514827544126502016-04-23T02:41:09.756-07:002016-04-23T02:41:09.756-07:00Does that make sense?
There are various intuitive...Does that make sense?<br /><br />There are various intuitive motivations for claiming that mathematical objects are just a figure of speech.[including motives 1 and 2 in my original post] <br /><br />But if you say this, then it seems like you should be able to back this claim up by showing that you can state your best physical theory without appealing to them.Sharon Berryhttps://www.blogger.com/profile/17434076853502881274noreply@blogger.comtag:blogger.com,1999:blog-4667288583830493271.post-43463369519632785732016-04-23T02:25:09.854-07:002016-04-23T02:25:09.854-07:00Hey! Good question, and thanks for checking out th...Hey! Good question, and thanks for checking out this blog. <br /><br />Here's an attempted explanation for why we might care about the first project (not my favorite) for a 5 year old. I'll try to remember to come back and explain the second and third similarly. <br /><br />Are there really mathematical objects like the number 3? Or are they just a figure of speech like "chips on peoples shoulders" or "the average policeman".<br /><br />It might be weird if there are mathematical objects, because they would be invisible and not located anywhere in the world. Many people find the idea of such objects strange and implausible, and believing in them can seem unscientific, like believing in gods and ghosts. [this is my attempt to charitably state motivation 1]<br /><br />So maybe mathematical objects are just a figure of speech. <br /><br />But in this case, it should be possible to say what what we believe without using that figure of speech, without mentioning [quantifying over] mathematical objects.<br /><br />However it looks very hard to do this. Specifically, it looks hard to say what we literally believe about physics without mentioning mathematical objects.<br /><br />This is Quine's Indispensibility challenge to nominalists about mathematics.<br /><br /><br /><br /><br />Sharon Berryhttps://www.blogger.com/profile/17434076853502881274noreply@blogger.comtag:blogger.com,1999:blog-4667288583830493271.post-14920482009956368332016-04-22T11:11:28.838-07:002016-04-22T11:11:28.838-07:00Could you explain as if I'm five why anyone wo...Could you explain as if I'm five why anyone would spend their time thinking about this? I don't know what any of this means but am curious. anthonybhttps://www.blogger.com/profile/07971737958844374732noreply@blogger.com