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<p class="MsoNormal" style="text-align:right" align="right">06.08.2016<o:p></o:p></p>
<p class="MsoNormal"
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-align:justify;line-height:normal"><span
style="font-size:12.0pt;
font-family:"Times New
Roman","serif";mso-fareast-font-family:"Times
New Roman";
mso-fareast-language:TR">Sayın Ercan,<o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-align:justify;line-height:normal"><span
style="font-size:12.0pt;
font-family:"Times New
Roman","serif";mso-fareast-font-family:"Times
New Roman";
mso-fareast-language:TR">Makelenizi okudum.<i> İlginç, güzel,
iyi</i> gibi
sıfatlarla nitelemek yaptığınız değerli çalışmaya haksızlık,
belki saygısızlık
olacaktır. Çalışmanızı zor bir uğraşının verdiği değerli bir
ürün olarak
görüyorum.<o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-align:justify;line-height:normal"><i><span
style="font-size:12.0pt;
font-family:"Times New
Roman","serif";mso-fareast-font-family:"Times
New Roman";
mso-fareast-language:TR"><a class="moz-txt-link-abbreviated" href="mailto:turkmath@listweb.bilkent.edu.tr">turkmath@listweb.bilkent.edu.tr</a></span></i><span
style="font-size:12.0pt;font-family:"Times New
Roman","serif";mso-fareast-font-family:
"Times New Roman";mso-fareast-language:TR">
üyelerine açmanız iyi olur
sanıyorum. Bu adımı başlatmak için size yanıtımı <i
style="mso-bidi-font-style:
normal">turkmath</i> ile veriyorm. Bazı matematikçiler,
matematiğin yalnızca,
yazı tahtalarına sığmayan denklemleri çözmeye yarayan bir araç
olmadığının
farkına varmalıdır.<o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
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style="font-size:12.0pt;
font-family:"Times New
Roman","serif";mso-fareast-font-family:"Times
New Roman";
mso-fareast-language:TR">Matematik, insan aklının yarattığı en
büyük değerdir.
Her bilim dalı değişiyor. Ama matematiğin ortaya koyduğu
sonuçlar, ona temel
olan aksiyomlar değişmeden değiştirilemiyor. Tales teoremi
ortaya konduğu
günkü kadar tazedir ve öyle kalacaktır.<o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-align:justify;line-height:normal"><span
style="font-size:12.0pt;
font-family:"Times New
Roman","serif";mso-fareast-font-family:"Times
New Roman";
mso-fareast-language:TR">Geçen yüzyılın başında, matematiğin
(aritmetiğin)
temellerini sağlam kurma yönünde ciddi çalışmalar oldu. Sizin
de belirttiğiniz
gibi Frege ve Hilbert'in uğraşıları, sonu hayal kırıklığına
dönen önemli
öncülerdir. Sonunda hüsrana uğramaları o düşüncelerin değerini
yoketmez. Akıl
oyunları tiyatrosundayız. O tiyatroda farklı oyunların
sergilenmesi
doğaldır.<o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-align:justify;line-height:normal"><span
style="font-size:12.0pt;
font-family:"Times New
Roman","serif";mso-fareast-font-family:"Times
New Roman";
mso-fareast-language:TR">Matematiğe temel kurmaya
çalışıyorsanız, kurduğunuz
sistem Hilbert'in sisteminin akibetine uğramayacak mı? Bu
soru burada
anlamsızdır. Çünkü ZF sistemi için söyledikleriniz soruya
yanıt veriyor. <o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-align:justify;line-height:normal"><span
style="font-size:12.0pt;
font-family:"Times New
Roman","serif";mso-fareast-font-family:"Times
New Roman";
mso-fareast-language:TR">Hilbert sizin tümce dediğiniz
formülleri kurarken,
matematiği konuşulan dilden ayırdı. Sözler yerine semboller
kullandı. Matematiğin
sembollerle kurulan bir dil olduğunu sanıyordu. Gödel ortaya
çıkana kadar ünlü
matematikçiler Hilbert’e boyun eğdi. Buna Poincare gibi bir
dahi de dahildir. <o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-align:justify;line-height:normal"><span
style="font-size:12.0pt;
font-family:"Times New
Roman","serif";mso-fareast-font-family:"Times
New Roman";
mso-fareast-language:TR">Belki sorun araç olarak kullandığımız
iki değerli
mantık sistemindedir. Ünlü matematikçilerin ciddiye almadığı
Fuzzy mantığı ile
uğraşanlar bunu başarabilirler mi? Göreceğiz. İkili mantık
sistemine dayalı
matematiği bir düşünce aracı olarak ele alırsak, acaba önümüze
çıkan engelleri
aşmak için kullandığımız araç (iki-değerli mantığa dayalı
matematik) yeterli
mi? Balta ile mobilya yapılamaz. Estetik katmak istiyorsanız,
balta yerine daha
gelişkin araçlara gerekseme doğar.<o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;
text-align:justify;line-height:normal"><span
style="font-size:12.0pt;
font-family:"Times New
Roman","serif";mso-fareast-font-family:"Times
New Roman";
mso-fareast-language:TR">Çalışmanızın çoğu yerinde hem söz hem
sembol kullanılıyor.
Yanlış olduğunu söylemiyorum. Konuştuğumuz dilin kavramları
yerine sembolleri
koyuyorsak, ikisi bir arada niye duruyor? Birisi yeterli olmaz
mı? Tabii, öğretimde bu gereklidir. Gene çok
önemli değil ama 9.1 Teorem sonunda {</span><span
style="font-size:12.0pt;
font-family:Symbol;mso-ascii-font-family:CMMI12;mso-hansi-font-family:CMMI12;
mso-bidi-font-family:CMMI12;mso-char-type:symbol;mso-symbol-font-family:Symbol"><span
style="mso-char-type:symbol;mso-symbol-font-family:Symbol">boş
küme</span></span><span
style="font-size:12.0pt;font-family:"Times New
Roman","serif";mso-fareast-font-family:
"Times New Roman";mso-fareast-language:TR">} = {0}
bağıntısını veriyorsunuz. 0’ın
rolüne bağlı olarak bu eşitlik kabul görmeyebilir. <o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-margin-top-alt:auto;margin-right:3.6pt;
mso-margin-bottom-alt:auto;text-align:justify;line-height:normal;tab-stops:
450.0pt"><span style="font-size:12.0pt;font-family:"Times
New Roman","serif";
mso-fareast-font-family:"Times New
Roman";mso-fareast-language:TR">Bu tür
çalışmaların yaygınlaşmasını diliyor ve sizi kutluyorum. Bu
arada, benim
Matematikçiler Derneğinin 05-07 Mayıs 2004 tarihinde Milli
Kütüphane’de
yaptığı toplantıya sunduğum çağrılı konuşmayı ekliyorum. Aynı
konuya farklı
bakış açıları var.<o:p></o:p></span></p>
<p class="MsoNormal">Saygı ve sevgilerle,<o:p></o:p></p>
<p class="MsoNormal">T.Karaçay<o:p></o:p></p>
</p>
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