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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72" style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal>Proving once again that, no however deep Thompson tries to go, Zingale can go deeper, much deeper. <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Ok, is mathematics (logic, etc.) a way of arriving at true propositions distinct from observation or are mathematical truths different from empirical truths? <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>I keep hearing Hywel in my ears: Mathematics is all very well but sometimes you have to know what you are doing. <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>I think I am starting to know the answer just by being badgered by you guys. I can from relativity theory predict that during a solar eclipse a distant star will pop out from behind the sun at T= xxxx =/- xxxx sec. I can observe empirically that, indeed, the star popped out within that time range. Thus I have arrived at the same proposition both by mathematical and empirical means. Is that oK. <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Nick Thompson<o:p></o:p></p><p class=MsoNormal><a href="mailto:ThompNickSon2@gmail.com">ThompNickSon2@gmail.com</a><o:p></o:p></p><p class=MsoNormal><a href="https://wordpress.clarku.edu/nthompson/">https://wordpress.clarku.edu/nthompson/</a><o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b>From:</b> Friam <friam-bounces@redfish.com> <b>On Behalf Of </b>Jon Zingale<br><b>Sent:</b> Friday, September 3, 2021 4:37 PM<br><b>To:</b> friam@redfish.com<br><b>Subject:</b> [FRIAM] Can empirical discoveries be mathematical?<o:p></o:p></p></div><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Verdana",sans-serif;color:#333333'>Beginning with Oxford,<o:p></o:p></span></p></div><blockquote style='margin-left:30.0pt;margin-right:0in'><div><p class=MsoNormal><span style='font-size:12.0pt;color:#333333'><o:p> </o:p></span></p></div><div><p class=MsoNormal><b><span style='font-size:12.0pt;font-family:"Verdana",sans-serif;color:#333333'>empirical</span></b><span style='font-size:12.0pt;font-family:"Verdana",sans-serif;color:#333333'>: </span><span style='font-size:10.5pt;font-family:"Verdana",sans-serif;color:#202124'>based on, concerned with, or verifiable by observation or experience rather than theory or pure logic.</span><span style='font-size:12.0pt;color:#333333'><o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-size:12.0pt;color:#333333'><o:p> </o:p></span></p></div></blockquote><p class=MsoNormal><span class=gmaildefault><span style='font-size:12.0pt;font-family:"Verdana",sans-serif;color:#333333'>Where then Nick goes on to argue, perhaps, that <i>experience of logic</i> is <i>experience</i> and so "experience <i>rather than</i> theory or pure logic" is meaningless. Then somewhere in hell's pub, far far away, Glen rolls his eyes and wonders whether he should write about <i>scoping</i> or simply berate Nick for navel-gazing.</span></span><o:p></o:p></p><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><span class=gmaildefault><span style='font-size:12.0pt;font-family:"Verdana",sans-serif;color:#333333'>But then, maybe this is the case for <i>logic</i> and not <i>mathematics</i>. Perhaps mathematics <i>requires</i> abstraction, representation, and objectification. It may be necessary to make bold claims like, "my love is like the integers". At some point during the process, one has to decide whether a thing <i>has</i> a front or a back or an inside to be out. Even the designation <i>married</i> comes with baggage, to be taken for granted in the objectification process.</span></span><o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><span class=gmaildefault><span style='font-size:12.0pt;font-family:"Verdana",sans-serif;color:#333333'>Ah, but if I have it correct, Nick also believes that <i>a day like no other</i> is <i>no day at all</i>. Nothing can be known about such a day. The only days are those that are like the integers (type) or days like today (class).</span></span><o:p></o:p></p></div></div></div></body></html>