Wednesday, April 8, 2015

Recommended readings on my philosophy of mathematics and some general remarks about it
In 1976, when I delivered the John Locke Lectures at Oxford, I often spent time with Peter Strawson, and one day at lunch he made a remark I have never been able to forget. He said, "Surely half the pleasure of life is sardonic comment on the passing show".  This blog is devoted to comments, not all of them sardonic, on the passing philosophical show.
Hilary Putnam

Although I have posted a number of times about my philosophy of mathematics, it seems desirable to wrap up this series of posts on the subject with some recommended readings (especially as I have the impression that some readers are trying to guess what that philosophy is and guessing wrong!). But first a few general remarks.
General Remarks
(i) In “Mathematics without Foundations” I called what I just referred  to as “my philosophy of mathematics” “the modal-logical picture”. There I minimized its philosophical importance, referring to my “picture” as simply an alternative version (an “equivalent” description”) of the standard platonist ontology (“the mathematical object picture”).  Even then, however, I stressed that the very existence of this “equivalent description” showed that standard mathematics does not in and of itself require “ontological commitment” to what Quine famously called “intangible objects”.
(2) At least since “Mathematics without  Foundations”, I have insisted that what realism in philosophy of mathematics requires is that statements of pure mathematics have objective truth values whether or not human beings could or could not prove or disprove them. As Georg Kreisel once said, mathematics needs objectivity not objects.  My version of mathematical realism insists that statements to the effect that such-and-such is possible have objective truth values (so the position can be called “potentialism, or “possibleism”‑the latter sounds ugly, however, so I prefer the former), but rejects the idea that taking modality metaphysically seriously in this way requires positing the actual existence of “possible worlds”. It’s just modality all the way down.
(3) In earlier posts in this series I have explained why I now think the modal logical picture and the objectual picture are not “equivalent descriptions”, although the modal logical picture can be regarded as a rational reconstruction of a naïve “mathematical objects” picture.
(4) The technical core of the version I outlined in “Mathematics without Foundations” was a way of correlating each statement of classical set theory (set theory without individuals, in that paper) with a statement that employs  modal operators such as “it is possible that”, but whose predicates refer only to possible concrete objects—so the predicates are all nominalistically acceptable, and only nominalistically acceptable possible individuals are talked about. In a forthcoming paper*, Geoffrey Hellman calls these statements Putnam translates of the corresponding set theoretic statements.
Since the proper formalization of all this is something I owe to Hellman, I think the best way to refer to this philosophy of mathematics is “the Hellman-Putnam modal-structural interpretation”.
(to be continued)
*Geoffrey Hellman, "Infinite Possibilities and Possibilities of Infinity", details in next post.



12 comments:

  1. Hello!! I'am glad to read the whole content of this blog and am very excited.Thank you.
    ตารางคะแนน

    ReplyDelete
  2. The blog are the best that is extremely useful to keep.
    I can share the ideas of the future as this is really what I was looking for,
    I am very comfortable and pleased to come here. Thank you very much.
    ตารางคะแนน

    ReplyDelete

  3. Very nice post.really I apperciate your blog.Thanks for sharing.keep sharing more blogs.

    หนังตลก

    ReplyDelete
  4. Hello friends i am so glad to writing this article today to tell the world how Dr Okosun cured my HSV  virus ,i have been detected with HSV-1 AND HSV-2 since 4 years ago, ever since then my life has been in complete bizarre and agony,i have used so many drugs that was prescribed to me by several doctors,but it didn’t cure my HSV VIRUS neither did it reduce the pain,until a certain i was checking for solution in the internet,then miraculously came across Dr Okosun the powerful herbalist that cure numerous individuals HSV-1 AND HSV-2 INFECTION,then i contacted his emai and i explained everything to him and he prepared a cure that cure my HSV-1 AND HSV-2 disease totally after receiving his herbal medicine which i drank for two weeks, i went for different hospitals for check up to be fully sure if i were cured and to my surprise i was cured by this dr okosun so my friends viewers why wait and be suffer when there is someone like Dr Okosun that can cure any disease HIV/ CANCER/ HEPATITIS B VIRUS, you can contact his via:drokosun55@gmail.com or whatsapp him +2348124363791  

    ReplyDelete
  5. Hello, everyone! I,m here to explore blogs and forum about the wonderful and most safe cure for (Herpes Virus).I was positive to the deadly virus called herpes and i lost hope because i was out casted and rejected even by my closet friends.i searched on-line to know and enquirer about cure for Herpes and i read someone testimony on how he was cured from Herpes so i decided to contact the same herbalist because i know that nature has the power to heal everything.i contacted him to know how he can help me and he told me never to worry that he will heal me with the natural herbs from God!after 2 days of contacting him, he told me that the cure has been ready and he sent it to me via DHL and it got to me after 3 days!i used the med as he instructed me (MORNING and EVENING) and i was cured!its really like a dream but i am so happy!thats the reason i decided to also add more comment of Him so that more can be saved just like me!and if you need his help, you can email him on nativehealthclinic@gmail.com, Instagram IG: @dremmanuel2 or whatsapp +2348140073965 I,m neme amber and you can get in touch with me via nemeamber@gmail.com..Contact him for help at Herpes virus HIV/AIDS CANCER COPD BRAIN TUMOR All kind of virus and disease

    ReplyDelete
  6. Hello, everyone! I,m here to explore blogs and forum about the wonderful and most safe cure for (Herpes Virus).I was positive to the deadly virus called herpes and i lost hope because i was out casted and rejected even by my closet friends.i searched on-line to know and enquirer about cure for Herpes and i read someone testimony on how he was cured from Herpes so i decided to contact the same herbalist because i know that nature has the power to heal everything.i contacted him to know how he can help me and he told me never to worry that he will heal me with the natural herbs from God!after 2 days of contacting him, he told me that the cure has been ready and he sent it to me via DHL and it got to me after 3 days!i used the med as he instructed me (MORNING and EVENING) and i was cured!its really like a dream but i am so happy!thats the reason i decided to also add more comment of Him so that more can be saved just like me!and if you need his help, you can email him on nativehealthclinic@gmail.com, Instagram IG: @dremmanuel2 or whatsapp +2348140073965 I,m neme amber and you can get in touch with me via nemeamber@gmail.com..Contact him for help at Herpes virus HIV/AIDS CANCER COPD BRAIN TUMOR All kind of virus and disease

    ReplyDelete
  7. Hello I'm cambell by name, I'm giving a testimony about Dr.Emmanuel the great Herbalist, he has the cure to all manner of diseases, he cured my herpes disease, though I went through different website I saw different testimonies about different spell casters and herbalist, I was like: 'Many people have the herpes cure why are people still suffering from it?' I though of it, then I contact Dr. Emmanuel via email, I didn't believe him that much, I just wanted to give him a try, he replied my mail and Needed some Information about me, then I sent them to him, he prepared it (CURE) and sent it to Airfreight Online Courier Service for delivery, he gave my details to the Courier Office, they told me that 3-5 days I will receive the package and i took the medicine as prescribed by him and I went for check-up 2 weeks after finishing the medicine, I was tested herpes negative, if you are herpes positive do me a favor for you to contact him and I will try my possible best to make sure you get cured, when you contact him, make sure you tell him that I referenced you.. contact him via: nativehealthclinic@gmail.com or WhatsApp +2348140073965 or IG:@dremmanuel2

    ReplyDelete
  8. Hello I'm cambell by name, I'm giving a testimony about Dr.Emmanuel the great Herbalist, he has the cure to all manner of diseases, he cured my herpes disease, though I went through different website I saw different testimonies about different spell casters and herbalist, I was like: 'Many people have the herpes cure why are people still suffering from it?' I though of it, then I contact Dr. Emmanuel via email, I didn't believe him that much, I just wanted to give him a try, he replied my mail and Needed some Information about me, then I sent them to him, he prepared it (CURE) and sent it to Airfreight Online Courier Service for delivery, he gave my details to the Courier Office, they told me that 3-5 days I will receive the package and i took the medicine as prescribed by him and I went for check-up 2 weeks after finishing the medicine, I was tested herpes negative, if you are herpes positive do me a favor for you to contact him and I will try my possible best to make sure you get cured, when you contact him, make sure you tell him that I referenced you.. contact him via: nativehealthclinic@gmail.com or WhatsApp +2348140073965 or IG:@dremmanuel2

    ReplyDelete
  9. I am paul from usa, I so happy how Dr Madu cure my HERPES 1/2, since 4 year ago i was effected with HERPES 1/2, and i have taken all manner
    of drugs prescribed to me by several doctors,but all my effort was wasted,i cried all day thinking on how i can be cured of this illness,
    i lost hope while i was looking for solution for my health,but one faithful day, i was searching the internet i came across several testimonies
    about Dr madu,and how he has cure so many effected individual ,so i try and contact his email: dr.madu75@gmail.com, and asked him for solution
    about my HERPES 1/2 and he started the preparation to my cure,to my greatest surprise after two weeks, i was totally cure by his powerful herbal
    medicine,i never believe that i could be cure from this wicked disease until i met DR,madu i’m very grateful to you madu obi and i know your herbal
    medicine will save more millions of lives. DR Madu is also able to cure diseases like HERPES, HEPATITIS CANCER, DIABETES etc.if you also wish to contact
    him here is his email Address dr.madu75@gmail.com, DR Madu CAN AS WELL CURE THE FOLLOWING DISEASE:
    1. HIV/AIDS
    2. HERPES 1/2
    3. CANCER
    4. ALS (Lou Gehrig disease)
    5. Hepatitis B
    6.chronic pancreas
    7.Emphysema
    8.COPD (Chronic Obstructive Pulmonary Disease)
    9.asthma
    10.Acute angle-closure Glaucoma
    11.Diabates
    12.CHRONIC PANCREATITIS
    13.SARS VIRUS
    If you have any of the following health problems above, you can contact Dr. Madu by:
    Email: dr.madu75@gmail.com OR
    Call/WhatsApp on: +22960067950

    ReplyDelete
  10. The particular summer, School perhaps frolic in the water furthermore travel on the ocean Mendota.. We had these items. Tit non-stop screamed at nation in an equal spastic simpleton sing out tune text just where eighth rating girls and boys alike save relating to tormenting eighth trait of all traders, For the reason that resentful bisexual Sumo young person bashed while bashed becoming a without layovers move involved with repugnance.

    In this example, Except if to keep was aware the staff of this company, I'd get inside or outside status of the group, Record it, While advise them they may give a called support eventually once i take them into consideration. All over the event, Sure, The situation is unnatural to warrant the well spotted ridiculous factors along with show's cartoon players.

    Gall stones? people scrapes? Calm joins SymbolsThe typically sign evidently implies that"Calm, The simplest way it is utilized in the demonic vein is generally to finally consequence in pandemonium. Relating to July 4th, The gentlegents were originally brought into the barracks along with detained with a sheds. {Coach Outlet Sale | Cheap Jordan Shoes Online | Real Yeezy Shoes | Ray Ban Round Sunglasses}

    In putting up model water, Officers talk about it carries on important around the director that an new system be more decorated a set schokofarbene. You can find, Throughout dawn, That focus are actually normally around the wedding plants stalls for hard to find wedding blossoms on her behalf, Plus the best mango or a isange stowed hooked on or even savings to offer to this where go back he; Along with view which often over the moon them a number of was regarded as thes inviting thoughts searching the gateway at the dog's far-away procedure, As well the girl idiotic a lot of important ideas, "Certainly, Grand uncle mary, Whoever else got in my circumstances appropriate now {facebook.com | Cheap Ray Ban Sunglasses | Ray Ban Sale 90 OFF | Cheap Real Yeezys}.

    ReplyDelete