Sunday, April 1, 2018

The Access Problem for Holes

[Hello to anyone out there!

Project: exposure therapy for my fear of posting sloppy/confusing stuff to this blog continues. So uh... sorry. I hope to return to regularly posting polished content soon.]

One of the least popular aspects of my philosophy of mathematics  is what I call Moderate Quantifier Variance. So I thought I'd explain one reason why I'm such a big fan of this view (and why I think you should be too) which has nothing to do with philosophy of mathematics.


The Access Problem for Holes

Consider our knowledge of holes. As discussed in D and S Lewis' On Holes, it's appealing take holes to be distinct from things like the air inside them, portions of the matter that `hosts' (e.g. portions of cheese with some diameter aronud a hole in Swiss cheese).



We seem to know how deeply a piece of cheese must be indented in order for there to count as being a hole in that piece of cheese. But (to a crazy philosopher, for a second) this knowledge can seem rather mysterious. For our senses tell us how the cheese is distributed through space. But how do we know where to draw the line: re how shallow a hole can be? No sensory experience seems to point out a single metaphysically special place to draw the line. So how can one explain the match between human beliefs about how shallow a hole can be and objective matters of facts?

It's appealing to say: there's no mystery about human accuracy here because if we had used `hole' differently (by taking the minimum hole angle to be larger or smaller) then the meanings of our words would have been different so these alternative hole-identifying practices would have yeilded true utterances. But since variant practices of "hole" individuation can require change in sentences whcih don't even use the word hole  (e.g. a purely logical sentence like the Fregean paraphrase for `there are >3000 things' can go from true to false). So it seems plausible that allowing such changes in meaning requires allowing variant meanings for logical vocabulary like ``there is'' as well as in the meaning of  ``hole''.

So I think a great way to solve this `access problem for holes'' is to accept

Moderate Quantifier Variance: there are multiple existential quantifier like meanings which the words `there is' can take on in different ideolects, (say English_1910, English_2010 etc.), though within any particular ideolect `there is' is univocal.

  • These meanings are `quantifier like' in the sense that they obey the all instances of standard first order logical inferential rules/axioms for `exists' (within the language they belong to). 
  • If there is a single maximally natural quantifier sense (as e.g. Sider thinks there is corresponding to our talk about `what there is' takes on when doing ontology), these variant quantifier senses need not be mere quantifier restrictions of this fundamental sense. 
I like to use Moderate Quantifier Variance to explain/vindicate the freedom mathematicians take themselves to have to introduce new logically coherent structures for study, by saying that when mathematicians consistently extend the axioms of pure mathematics by adding axioms describing some new mathematical structures like the complex numbers, their words can both give meaning to expressions like `complex number' and also change the meaning of `there is', so that these axioms express truths.

But whatever you say about math, I think moderate quantifier variance is already useful for understanding our knowledge of swiss cheese!

14 comments:

  1. I can’t believe this. A great testimony that i must share to all HERPES SIMPLEX VIRUS patient in the world i never believed that their could be any complete cure for Herpes or any cure for herpes,i saw people’s testimony on blog sites of how dr Ero prepare herbal medicine that cure and brought them back to life again. i had to try it too and you can,t believe that in just few weeks i started using it all my pains stop gradually and i had to leave without the pills the doctor gave to me. Right now i can tell you that few months now i have not had any pain,delay in treatment leads to death. Here is his email:(wealthylovespell@gmail.com) whatsapp him with +2348105150446 visit blog http://wealthyspellhome.over-blog.com

    ReplyDelete
  2. This is a testimony that I will tell everyone to hear. i have been married for 4 years and on the fifth year of my marriage, another woman had a spell to take my lover away from me and my husband left me and the kids and we have suffered for 2 years until i meant a post where this man Dr.Wealthy have helped someone and i decided to give him a try to help me bring my love Husband home and believe me i just send my picture to him and that of my husband and after 48 hours as he have told me, i saw a car drove into the house and behold it was my husband and he have come to me and the kids and that is why i am happy to make everyone of you in similar issues to meet with this man and have your lover back to your self His email: wealthylovespell@gmail.com or you can also contact him or whatsapp him on this +2348105150446.....  thank so much Dr.Wealthy. ...

    ReplyDelete

  3. Your blog is very informative, finally, I found exactly what I want. Paypal is an excellent service for online payments but lots of its users confront issues while they access Paypal. If you want to resolve your problems then must visit Paypal contact.

    ReplyDelete
  4. Your blog is very informative, finally, I found exactly what I want. Paypal is an excellent service for online payments but lots of its users confront issues while they access Paypal. If you want to resolve your problems then must visit Paypal ondersteuning nederland

    ReplyDelete
  5. Your blog is very informative and interesting to read, finally, I found exactly what I searching for. There are lots of users of Macfee antivirus in the world because of its features and easy interface. If you want to explore more interesting facts about Mcafee antivirus or want to resolve your technical issues then must visit Mcafee ondersteuning Nederland.

    ReplyDelete
  6. This comment has been removed by the author.

    ReplyDelete

  7. Hi, Thank you for sharing such a good and valuable information,It is very important for me. Gmail is the worldwide used email service but sometimes user faces some problems in it. If you want to get some information about the Gmail then you can visit Gmail tuki suomi.

    ReplyDelete

  8. Your blog is very informative and interesting to read, finally, I found exactly what I searching for. There are lots of users of Macfee antivirus in the world because of its features and easy interface. If you want to explore more interesting facts about Mcafee antivirus or want to resolve your technical issues then must visit Mcafee bellen Nederland.

    ReplyDelete
  9. Hi thankyou for this great helpful information.this information is really useful at today's time.you had easily explained whole information in a short note. Now i would like to share some information about PayPal.So If you are a Paypal user and you are facing any problem regarding to PayPal. No need to worry just simply visit on our site- paypal contact belgie

    ReplyDelete
  10. Hi your post is really appreciatable.I really thankful for this post. Here i would llike to share some information about facebook. As we know that facebook is a social trap where we connect with people in all over world. So if you are using facebook and face any technical issue that time so just visit our website. We can resolve the smallest problem on same time. For further information please visit on our website- facebook bellen belgie

    ReplyDelete
  11. Hi your post is very nice and i am greatful to you for sharing this post with us.here i want to share some information about Norton Antivirus.As we all know how much Norton Antivirus is usefull for our laptops and mobiles.so whenever you have any query regarding Norton or need any assistance how to run or any information that time please visit over this site-Bellen norton Ondersteuning

    ReplyDelete
  12. Hi this post is very nice.finally i got all those information whatever i really wanted to know. Thankyou for sharing this usefull information. Here I want to share the information about Dell support. As we all have been digitalied and we do multiple works together so if you face any problem or need any assist about Dell klentenservice so pleae visit over this site:- dell ondersteuning bellen

    ReplyDelete
  13. Thanks for sharing such an Amazing information, I Couldn't leave without reading your blog. I have read another good blog, I think you have read it too. click here bellen netflix ondersteuning

    ReplyDelete
  14. Thanks for sharing such an Amazing information. I have read another good blog, I think you have read it too. click here PortoBlend

    ReplyDelete