BREAKING: How do we know about 7 + 5?

TUESDAY, DECEMBER 4, 2018

Goldstein got it right:
In this morning's report, we reminisced about our introduction to the problems, or perhaps to the alleged problems, of academic philosophy.

Eventually, the later Wittgenstein would suggest that most of these apparent problems are simply the product of conceptual confusion—even that there may be no such discipline as "philosophy" at all.

Setting that aside for another day, let's return to the particular "problem" we cited this morning:
How can we know that 7 + 5 = 12?
In late September, back before the Kavanaugh hearings dragged us back in, we posted Rebecca Goldstein's answer to that question. Quick background:

When Jim Holt wrote his New Yorker essay about "the greatest logician since Aristotle," he was reviewing Goldstein's 2005 book, Incompleteness: The Proof and Paradox of Kurt Godel. This morning, we posted the passage by Holt which we love—the passage in which Holt describes Godel's love of "Platonism," along with his concern about the mysteries of 2 + 2.

We had read Goldstein's book in real time. When we did, we were surprised to think that a ranking philosophy professor could take many of the approaches she took some 52 years after the publication of Wittgenstein's Philosophical Investigations.

That said, Goldstein addressed the question about 2 + 2 (and 7 + 5) early on in her book. As we noted in late September, her presentation went exactly like this, and we thought it was largely spot on:
GOLDSTEIN (page 17): The rigor and certainty of the mathematician is arrived at a priori, meaning that the mathematician neither resorts to any observations in arriving at his or her mathematical insights nor do these mathematical insights, in and of themselves, entail observations, so that nothing we experience can undermine the grounds we have for knowing them. No experience would count as grounds for revising, for example, that 5 + 7 = 12. Were we to add up 5 things and 7 things, and get 13 things, we would recount. Should we still, after repeated recountings, get 13 things we would assume that one of the 12 things had split or that we were seeing double or dreaming or even going mad. The truth is that 5 + 7 = 12 is used to evaluate counting experiences, not the other way around.
We think that's basically right. Back in that late September post, we simplified this eternal question by discussing the logic of 1 + 1 = 2. Same basic idea!

How was this matter presented to us college freshmen back in the fall of 1965? We'd love to see film of those unloved lectures. We have no idea what was said.

One other philosophical problem: We're fairly sure that Professor Nozick exposed us to six "problems in philosophy."

We can't recall what most of those alleged problems were. One, though, involved "free will."

How do you solve the philosophical problem of free will? First, you'd have to see the specific way the problem was being presented.

Having said that, one beginning approach to the philosophical problem of free will goes something like this, and no, we aren't joking:
Free will? People in prison don't have it.
Our nation was heading toward Vietnam. As a point of curiosity, what were the nation's many logicians discussing and doing that year?

Going back to Godel and those he followed, were the world's greatest logicians doing things which actually mattered? Moving ahead to the later Wittgenstein, did their ruminations about the timeless existence of circles and numbers even make any real sense?

We pitiful freshmen were skeptics that year. Did we pitiful scrubs get it right?

15 comments:

  1. "we would assume that one of the 12 things had split"

    Hmm, why should one of them split? Can't you imagine that 5 things together with 7 things, morph, by the virtue of being combined, into 13 things?

    ReplyDelete
  2. I am very much pleased to read this post. I enjoyed every little bit part of it. It contains truly information. thanks for sharing publicly.

    Brand Development Company | Travel Technology Software | Software Development Solutions | Website Design Company in India | Mobile App Development Solution

    ReplyDelete
    Replies
    1. HOW I GOT CURE TO MY HERPES WITH THE HELP OF DR EBAKO NATURAL HERBS CURE WHATSAPP HIM ON +1 (213) 861-9461


      I can’t believe this. A great testimony that i must share to all HERPES 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 sites of how DR EBAKO prepare herbal 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 HERPES DRUGS 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: doctorebakospellhome@gmail.com his WHATSAPP number is +1 (213) 861-9461
      https://drebakocurehome.blogspot.com/
      http://drebakocurehome.over-blog.com
      he can also cure you from
      HPV
      HIV
      HIV2
      Hepatitis B
      Diabetes
      etc














































































      HOW I GOT CURE TO MY HERPES WITH THE HELP OF DR EBAKO NATURAL HERBS CURE WHATSAPP HIM ON +1 (213) 861-9461


      I can’t believe this. A great testimony that i must share to all HERPES 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 sites of how DR EBAKO prepare herbal 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 HERPES DRUGS 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: doctorebakospellhome@gmail.com his WHATSAPP number is +1 (213) 861-9461
      https://drebakocurehome.blogspot.com/
      http://drebakocurehome.over-blog.com
      he can also cure you from
      HPV
      HIV
      HIV2
      Hepatitis B
      Diabetes
      etc ......



















      Delete
  3. I think Christopher Hitchens said it best:


    “Of course we have free will because we have no choice but to have it.”

    — Christopher Hitchens

    ReplyDelete
  4. I have been casting spells for many years and I have helped many people, I might be able to help you too. I am honest, and I genuinely care for all the clients who choose me to cast a spell for them.


    If you have any questions about Love, Money, curse, protection, bad luck, divorce, court cases, or about me please call or email me. I really want you to feel comfortable before moving forward with any spells, or other services. I will take the time to explain things to you and provide you with honest advice, to what is best for your situation. I will not pressure you into having a spell cast, I will leave that decision up to you, and when or if you decide to move forward, I might be able to help you.
    I will respect your Privacy. I will not seek to obtain any of your personal information beyond what you might voluntarily offer and all information you might give me including emails, phone numbers and photos will remain private and confidential.
    I perform my Rituals only at night between the hours of 0.00 - 0.59 (South African time) lasting 1 hour but of course, this depends on the nature of the ritual, some rituals might take hours and can also become necessary to be performed at specials places like; flowing streams, cemeteries and other places dictated by the gods.
    I do not want anyone to be under any illusions about my spells and its numerous rituals. Real and effective Voodoo is no child's play, it is expensive because, after the rituals, I will have to destroy all the materials involved by fire and the ashes scattered over a flowing stream or river.
    You will get what you seek.But please understand this might take a lot of time and that individual results may vary. contact +27663492930, greatogudugu@gmail.com

    Herbal cure for Following DISEASES,this is not scam is 100% Real.

    -HPV
    -DIABETES
    -PENIS ENLARGEMENT AND WEAK ERECTION
    -VIRGINA PROBLEM
    -WHOOPING COUGH
    - HEPATITIS B
    -FORDYCE SPOT
    -COLD SORE
    -ALS
    -LOWER RESPIRATORY INFECTION
    -LOW SPERM COUNT
    -MRSA(METHICILLIN-RESISTANT STAPHYLOCOCCUS AUREUS
    -ZIKA VIRUS
    -HIV
    -STROKE
    -IMPOTENCE
    -PILE
    -HYPERTENSION
    -LOW SPERM COUNT
    -MENOPAUSE DISEASE
    -ASTHMA
    -CANCER
    -BARENESS/INFERTILITY
    -PCOS
    -SHINGLES
    -VIRAL HEPATITIS/HEPATITIS B
    -FIBROID
    -ASTHMA
    -SICKLE CELL
    -TINNITUS
    -BARENESS/INFERTILITY
    -DIARRHEA and so on...

    ReplyDelete
  5. I really liked your article. I have learned a lot from this article on this site. I will be very grateful for this information. I have come to know a lot more from your article about this site. I want you to write more articles on the same topic.

    Thank you! I look forward to reading more news from you.

    Maldives Tour Packages | Dubai Tour Packages | Singapore Packages | Bangkok Packages | Bali Packages | Indonesia Tour Package

    ReplyDelete
  6. LOTTO, lottery,jackpot.
    Hello all my viewers, I am very happy for sharing this great testimonies,The best thing that has ever happened in my life is how I win the lottery euro million mega jackpot. I am a Woman who believe that one day I will win the lottery. finally my dreams came through when I email believelovespelltemple@gmail.com and tell him I need the lottery numbers. I have spend so much money on ticket just to make sure I win. But I never know that winning was so easy until the day I meant the spell caster online which so many people has talked about that he is very great in casting lottery spell, . so I decide to give it a try.I contacted this great Dr Believe and he did a spell and he gave me the winning lottery numbers. But believe me when the draws were out I was among winners. I win 30,000 million Dollar. Dr Believe truly you are the best, all thanks to you forever

    ReplyDelete
  7. Hi I’m for the first time here. I found this blog and I find It truly helpful & it helped me out much.
    I am hoping to give something back and aid others such as you helped me.
    Dreamy Places To Propose | Domestic & International Holiday Packages | Trending Tours Packages | GET ADDICTED TO TRAVEL | Travel Gateway | TRAVEL SAFARI |

    ReplyDelete
  8. Your content is very informative for us ... so thanks a lot

    Travel Technology Company in India |

    ReplyDelete
  9. this blog is brilliant thanks for posting this informative blog

    Psychiatrist in Chennai

    ReplyDelete