Bab 3

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Bab 3

• Filsafat dan Ilmu dalam Sejarah

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Orientasi Sejarah

• Hubungan Sejarah
• Filsafat dan ilmu di dalam filsafat ilmu
  berhubungan dengan sejarah barat
• Berpusat di Eropa, terutama Eropa Barat
• Pembabakan Sejarah
• Sejarah dibagi ke dalam sejumlah babak, dari
  zaman dahulu sampai sekarang
• Pembabakan sejarah mengikuti pembabakan yang
  lazim di sejarah Eropa
• Filsafat dan Ilmu
• Di dalam sejarah ini, filsafat dan ilmu tidak
  diuraikan secara terpisah

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Pembabakan Zaman

• Zaman Kuno
• sebelum abad ke-5 sM
• Zaman Yunani Kuno
• abad ke-5 sM sampai abad ke-1 sM
• Zaman Romawi
• abad ke-1 sM sampai abad ke-5
• Zaman Gelap (Dark Ages)
• abad ke-5 sampai abad ke-10
• Zaman Pertengahan (Medieval)
• abad ke-10 sampai abad ke-15
• Zaman Kebangkitan (Rennaissance)
• abad ke-15 sampai abad ke-18
• Zaman Modern
• abad ke-18 sampai sekarang

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Zaman KunoSebelum Abad ke-5 sM

• Keteraturan Alam (Louis de Broglie)
• Gembala Chaldea di Mesopotamia memperhatikan
  gejala di langit terutama di malam hari
• Gerak benda langit teratur sehingga mereka yakin
  akan keteraturan alam
• Muncul pengetahuan astronomi termasuk kalender
  bulan dan muncul ilmu
• Mereka juga mengenal musim, sehingga satu tahun
  terdiri atas 12 bulan (tidak tepat)
• Keteraturan Alam (Dennis Gabor)
• Manusia percaya bahwa ada keteraturan pada dasar
  gelaja alam
• Keteraturan ini layak dinyatakan melalui logika
• Kepercayaan ini melahirkan ilmu

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• THE HISTORY OF SCIENCE
• On the simplest level, science is knowledge
  of the world of nature. There are many
  regularities in nature that mankind has had to
  recognize for survival since the emergence of
  Homo Sapiens as a species. The Sun and the Moon
  periodically repeat their movements. Some
  motions, like the daily motions of the Sun, are
  simple to observe others, like the annual
  motion of the Sun, are far more difficult. Both
  motions correlate with important terrestial
  events. Day and night provide the basic rhythm of
  human existence the seasons determine the
  migration of animals upon which human depended
  for millennia for survival. With the invention of
  agriculture, the seasons became even more
  crucial, for failure to recognize the proper time
  for planting could lead to starvation. Science
  defined simply as knowledge of natural processes
  is universal among mankind, and it has existed
  since the dawn of human existence.
• The mere recognition of regularities does
  not exhaust the full meaning, however. In the
  first place, regularities may be simply
  constructs of the human mind. Humans leap to
  conclusions the mind cannot tolerate chaos, so
  it constructs regularities even when none
  objectively exists. Thus, for example, one of the
  

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• astronomical laws of the Middle Ages was that
  the appearance of comets presaged a great
  upheaval, as the Norman Conquest of Britain
  followed the comet of 1066. True regularities
  must be established by detached examinations of
  data. Science, therefore, must employ a certain
  degree of skepticism to prevent premature
  generalization.
• Regularities, even when expressed
  mathematically as laws of nature, are not fully
  satisfactory to everyone. Some insist that
  genuine understanding demand explanations of the
  causes of the laws, but it is in the realm of
  causation that there is the greatest
  disagreement. Modern quantum mechanics, for
  example, has given up the quest for causation and
  today rests only on mathematical expression .
  Modern biology, on the other hand, thrives on
  causal chains that permit the understanding of
  physiological and evolutionary processes in terms
  of the physical activities of entities such as
  molecules, cells, and organism. But even if
  causation and explanation are admitted as
  necessary, there is little argument on the kinds
  of causes that are permissible, or possible in
  science. If the history of science is to make any
  sense whatsoever it is necessary to deal with the
  past on its own terms, and the fact in that for
  most of the history of science natural
  philosophers appealed to causes that

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• would be summarily rejected by modern scientists.
  Spiritual and divine forces were accepted as both
  real and necessary until the end of 18th century
  and, in areas such as biology, deep into the 19th
  century as well.
• Certain conventions governed the appeal to
  God or the gods or the spirits, it was held,
  could not be completely arbitrary in their
  actions otherwise the proper response would be
  propitiation, not rational investigation. But
  since the deity or deities were themselves
  rational, or bound by rational principles, it was
  possible for humans to uncover the rational order
  of the world. Faith in the world could actually
  stimulate original scientific work. Keplers
  laws, Newtons absolute space, and Einsteins
  rejection of the probabilistic nature of quantum
  mechanics were all based on theological, not
  scientific, assumptions. For sensitive
  interpreters of phenomena, the ultimate
  intelligibility of nature has seemed to demand
  some rational guiding spirit. A notable
  expression on this idea is Einsteins statement
  that the wonder is not that mankind comprehends
  the world, but that the world is comprehensible.
• Science, then is to be considered in this
  article as knowledge of natural regularities that
  is subjected to some degree of skeptical vigour
  and explained by rati-

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• onal causes. One final caution is necessary.
  Nature is known only through the senses, of which
  sight, touch, and hearing are the dominant ones,
  and the human notion of reality is skewed toward
  objects of these senses. The invention of such
  instruments as the telescope, the microscope, and
  the Geiger counter has brought an ever-increasing
  range of phenomena with the scope of the senses.
  Thus, scientific knowledge of the world is only
  partial, and progress of science follows the
  ability of humans to make phenomena perceivable.

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Zaman KunoSebelum Abad ke-5 sM

• Keteraturan Alam (di Mesir Kuno)
• Sungai Nil banjir setiap tahun secara teratur
  menghapus batas tanah sehingga lahir ilmu ukur
  untuk menemukan kembali batas itu
• Ilmu ukur digunakan juga untuk membuat piramida
• Secara teratur, gerak naik bintang sothis
  (sirius) sinkron dengan siklus banjir sungai Nil,
  dan berlangsung setahun sekali
• Muncul pengetahuan astronomi dan kalender
  matahari di samping kalender bulan
• Keteraturan Alam (di Yunani Kuno)
• Pengetahuan dari Mesopotamia dan Mesir Kuno masuk
  ke Yunani Kuno

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Zaman KunoSebelum Abad ke-5 sM

• Keteraturan Alam (di Romawi Kuno)
• Sebelum Romawi menjadi negara adikuasa (abad
  ke-1 sM), mereka juga menerima kalender dari
  Yunani Kuno
• Romawi menyusun kalender matahari yang
  berubah-ubah yang kemudian distandardisasi oleh
  Julius Ceaser
• Kalender inilah yang kemudian menjadi kalender
  internasional yang kita pergunakan sekarang
  (disempurnakan oleh Paus Gregorius)
• Keteraturan Alam (Kalender)
• Salah satu pengetahuan astronomi (mungkin tertua)
  yang dilahirkan oleh keteraturan alam adalah
  kalender
• Di samping astronomi, muncul pula pengetahuan
  lain yang dikenal sebagai astrologi

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• LUNAR CALENDAR
• Any dating system based on a year consisting of
  synodic monthsi.e. complete cycles of phases of
  the Moon. In every solar year (or year of the
  seasons), there are about 12.37 synodic months.
  Therefore, if a lunar-year calendar is to be kept
  in step with the seasonal year, a periodic
  intercalation (addition) of days is necessary.
• The Sumerians were probably the first to develop
  a calendar based entirely on the recurrence of
  lunar phases. Each Sumero-Babylonian month began
  on the first day of visibility of the new Moon.
  Although an intercalary month was used
  periodically, intercalations were haphazard,
  inserted when the royal astrologers realized that
  the calendar had fallen severely out of step with
  the seasons. Starting about 380 BC, however,
  fixed rules regarding intercalations were
  established, providing for the distribution of
  seven intercalary months at designated intervals
  over 19-year periods. Greek astronomers also
  devised rules for intercalations to coordinate
  the lunar and solar years. It is likely that the
  Roman republican calendar was based on the lunar
  calendar of the Greeks.

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• Lunar calendars remain in use among certain
  religious groups today. The Jewish calendar,
  which supposedly dates from 3,760 and three
  months before the Christian Era (BCE) is one
  example. The Jewish religious year begins in
  autumn and consists of 12 months alternating
  between 30 and 29 days. It allows for a periodic
  leap year and an intercalary month. Another lunar
  calendar, the Muslim, dates from the HegiraJuly
  15, AD 622, the day on which sthe prophet
  Muhammad began his migration from Mecca to
  Medina. It makes no effort to keep calendric and
  seasonal years together.
• SOLAR CALENDAR
• Any dating system based on the seasonal year of
  approximately 365¼ days, the time it takes the
  earth to revolve once around the Sun. The
  Egyptians appear to have been the first to
  develop a solar calendar, using as a fixed point
  the annual sunrise reappearance of the Dog
  StarSirius, or Sothis--in the eastern sky, which
  coincided with the annual flooding of the Nile.
  They constructed a calendar of 365 days,
  consisting of 12

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• months of 30 days each, with a 5 days added at
  the years end. The Egyptians failure to account
  for the extra fraction of a day, however, caused
  their calendar to drift gradually into error.
• Ptolemy III Euergetes of Egypt, in the Decree of
  Canopus (237 BC), introduced an extra day every
  four years to the basic 365-day calendar (this
  practice also having been introduced in the
  Seleucid calendar adopted in 312 BC). In the
  Roman Republic, Julius Ceaser in 45 BC replaced
  the confused Roman Republican calendar. Which
  probably was based on the lunar calendar of the
  Greeks, with the Julian calendar. The Julian
  calendar assigned 30 or 31 days to 11 months but
  fewer to February it allowed for a leap year
  every four years. The Julian calendar, however,
  made the solar year slightly too long by adding a
  full quarter of day annuallythe solar year
  actually runs 365.2422 days. By mid-16th century
  the extra time had resulted in an accumulated
  error of about 10 days. To correct this error,
  Pope Gregory XIII instituted the Gregorian
  calendar in 1582, dropping October 5-14 that year
  and omitting leap years when they fell on
  centurial years not divisible by 400e.g., 1700,
  1800, 1900.

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• Penanggalan Romawi mula-mula hanya 10 bulan, dari
  Martius sampai December. Oleh kaisar Romawi ke-2,
  ditambah 2 bulan pada musim dingin sehingga
  menjadi
• Martius
• Aprilis
• Maius
• Junius
• Quintilis (Julius)
• Sextilis (Augustus)
• September
• October
• November
• December
• Januarius
• Februarius
• Karena ada upacara pada bulan Januarius, maka
  kemudian awal tahun digeser ke Januarius

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• Pada tahun ke-45 sebelum Masehi, penanggalan
  Romawai cukup kacau. Julius Ceaser minta
  Sosigenes membenahi kalender.
• Dasar pembenahan adalah 365 ¼ hari setahun
  sehingga setahun 365 hari dan interkalasi 4 tahun
  sekali dengan 366 hari. Dimulai tahun 44 sebelum
  Masehi sehingga tahun 45 sM menjadi 400 hari
  lebih.
• Senat menghormati Julius Ceaser dan mengganti
  Quintilis menjadi Julius. Pada tahun 4 sM, Senat
  menghormati Augustus Ceaser dan mengganti
  Sextilis menjadi Augustus. Bulan Julius dan
  Augustus dibuat sama 31 hari.
• Ternyata setahun mengandung 365 ¼ hari kurang
  sedikit sehingga kelebihan. Pada abad ke-16
  kelebihan sampai 10 hari. Agar cocok pada tahun
  1527, 10 hari itu dihilangkan pada bulan Oktober
  (tanggal 5 lompat ke 15) dan selanjutnya setiap
  400 tahun dikurangi 3 hari pada tahun ratusan.

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• Penanggalan
• Masehi 1 1 2000
• Hijrah 24 Ramadhan 1420
• Jawa 24 Pasa 1932
• Yahudi 5761
• Koptik 1717
• Ethiopia 1993
• Persia 1379
• Hindu 5101
• Konghucu 25 11 2550
• Jepang 1 1 2660
• Romawi 2753
• Thailand 1 1 - 2543

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• TANGGAL JULIAN DI DALAM KOMPUTER
• Oleh Dali S. Naga
• Abstract. Database management systems uses
  Julian date in calculating calendar days. To
  understand Julian date, we have to trace it into
  the history of our calendar. Our calendar is
  based on the movement of the moon and the sun.
  Intercalations and cycles are needed to come back
  to the previous positions of the moon and the
  sun. One of the intercalation and system of
  cycle is Julian date. Julian date begins from 1
  January 4713, B.C.
• Di dalam komputer, seperti pada program
  manajemen basis data, tanggal yang digunakan
  adalah tanggal Julian. Apa sebenarnya tanggal
  Julian itu? Untuk itu, kita perlu menelaah
  sejarah kalender yang sekarang kita gunakan.
  Namun, sebelumnya, kita perlu membedakan dua hal
  yakni kalender dan era. Tanggal kita 2 April,
  hari Rabu, jam 12.00 adalah kalender, tetapi
  tahun kita 2003 adalah era. Gabungan mereka,
  kalender dan era Masehi menghasilkan tanggal 2
  April 2003.
• Era Masehi
• Era yang digunakan pada penanggalan kita adalah
  era Masehi, di samping era lain seperti era
  Hijrah, era Saka, dan era Konghucu. Era Masehi
  dihitung sejak kelahiran Yesus. Sekalipun
  demikian, pada waktu kelahiran Yesus, belum ada
  era Masehi. Era Masehi baru kemudian disusun dan
  diusulkan oleh seorang rahib bernama Denys le
  Petit pada tahun 532 Masehi. Pada waktu itu,
  Denys mencoba menghitung mundur untuk menemukan
  tanggal lahir Yesus. Menurut hasil hitung Denys,
  Yesus lahir pada tanggal 25 Desember, 532 tahun
  lalu. Dengan demikian, Denys menetapkan bahwa
  era Masehi dimulai pada hari Sabtu, tanggal 1
  Januari 532 tahun sebelumnya.
• Walaupun Denys le Petit telah menciptakan era
  Masehi pada tahun 532, namun era Masehi baru
  dipakai di Barat setelah tiga atau empat abad
  kemudian. Dengan demikian, era Masehi baru ada di
  dalam pemakaian pada abad ke-9 atau ke-10.
  Sebelum abad ke-9 atau ke-10, belum ada
  penggunaan era Masehi. Selanjutnya, era Masehi
  tidak mengenal tahun 0. Di dalam perhitungan
  mundur, hanya ada tahun 1 Masehi dan tahun 1
  sebelum Masehi.
• Kalender
• Kini kita beralih ke kalender. Di dalam
  kalender, kita mengenal hari. Kapan suatu hari
  dimulai? Ternyata banyak caranya. Ada orang yang
  menghitungnya sejak subuh ke subuh, ada orang
  yang menghitungnya sejak senja ke senja, ada
  orang yang menghitungnya sejak tengah hari ke
  tengah hari. Orang Romawi kuno menghitungnya dari
  tengah malam ke tengah malam. Tradisi Romawi
  inilah yang kita gunakan sekarang pada kalender
  kita yakni hari kita dimulai sejak tengah malam
  ke tengah malam berikutnya.
• Sehari dibagi menjadi 24 jam berasal dari zaman
  kuno yakni dari zaman Babylonia. Mereka
  menggunakan bilangan Sumeria yakni bilangan yang
  berbasis 60. Dari basis 60 inilah ditemukan
  bilangan 12 yang masing-masing digunakan untuk
  siang dan untuk malam sehingga sehari menjadi 2 x
  12 jam 24 jam. Hal ini pun diterima di
  mana-mana. Hari kita pada saat ini juga terdiri
  atas 2 x 12 jam 24 jam. Satu jam sebanyak 60
  menit dan satu menit sebanyak 60 detik juga
  berasal dari bilangan berbasis enam puluh
  (sexagesimal) yang digunakan oleh orang Sumeria.
• Siklus Minggu kita yang 7 hari panjangnya
  berasal dari Babylonia dan Yahudi. Di Afrika
  Barat, siklus itu adalah 4 hari di Asia Tengah
  dan juga di Jawa dikenal siklus 5 hari Mesir
  kuno mengenal siklus 10 hari dan Romawi kuno
  mengenal siklus 8 hari. Diduga bahwa siklus 7
  hari berasal dari penanggalan bulan yakni waktu
  selama seperempat bulan. Pengguaan siklus 7 hari
  di dalam kalender kita didasarkan atas dekrit
  Kaisar Constantine I dan dimulai pada tahun 321
  dengan hari Minggu sebagai hari pertama. Di dalam
  dekrit Kaisar Constantine I itu, hari Minggu
  dinyatakan sebagai hari libur. Dan libur Minggu
  itu masih terus kita gunakan sampai sekarang.
• Bulan merupakan satu bagian dari kalender.
  Perhitungan bulan dilakukan melalui fasa bulan.
  Perhitungan bulan menimbulkan masalah karena satu
  bulan terdiri atas 29 hari lebih sekian jam, pada
  hal jumlah hari di dalam bulan adalah bulat.
  Demikian pula dengan tahun. Satu tahun matahari
  terdiri atas 365 hari lebih sekian jam, pada hal
  jumlah hari di dalam setahun adalah bulat.
  Akibatnya, pada ulang bulan, kedudukan bulan
  tidak tepat sama seperti kedudukannya pada bulan
  lalu. Pada ulang tahun, kedudukan matahari tidak
  tepat sama seperti kedudukannya pada tahun lalu.
• Untuk menyelesaikan masalah sekian jam yang lebih
  pada setiap bulan dan pada setiap tahun, maka
  pada bulan dan tahun tertentu diberikan tambahan
  hari. Hal ini dikenal sebagai interkalasi.
  Interkalasi merupakan hal yang cukup rumit di
  dalam kalender. Tidak mudah untuk menemukan
  interikalasi yang menyebabkan kedudukan bulan
  atau matahari tepat kembali sama seperti pada
  waktu sebelumnya.
• Kalender Romawi
• Kita tinggalkan dulu interkalasi ini dan
  menengok ke sejarah kalender kita. Kalender kita
  berasal dari kalender Romawi kuno. Konon
  kabarnya, kalender Romawi kuno ditetapkan oleh
  raja pertamanya pada abad ke-7 atau ke-8 sebelum
  Masehi. Pada ketentuan raja Romulus ini, awal
  tahun dimulai pada bulan Martius dan diakhiri
  pada bulan December (desi 10). Panjang tahun
  adalah 10 bulan. Setiap bulan terdiri atas 30
  atau 31 hari sehingga di dalam setahun terdapat
  304 hari. Setelah itu terdapat celah musim dingin
  yang tidak ada kalendernya.
• Raja kedua Numa Pompilius membagi celah musim
  dingin itu menjadi dua bulan yakni bulan
  Januarius dan Februarius. Dua bulan tambahan
  sebanyak 50 hari ini diletakkan di akhir tahun
  sehingga di dalam setahun terdapat 354 hari.
  Kemudian pada bulan Januarius ditambahkan satu
  hari lagi sehingga di dalam setahun terdapat 355
  hari.
• Raja kelima Tarquinius Priscus (616 579 sM)
  adalah orang Etruscan. Kalender diubah menjadi
  kalender republik. Pada kalender republik ini,
  Februarius 28 hari Martius, Maius, Julius (waktu
  itu masih bernama Quintilis), dan October,
  masing-masing 31 hari serta Januarius, Aprilis,
  Junius, Augustus (waktu itu masih bernama
  Sextilis), dan December, masing-masing 29 hari.
  Di dalam setahun terdapat 355 hari. Raja ini juga
  memindahkan awal tahun ke bulan Januarius namun
  pada tahun 510 sM, melalui pengusiran orang
  Estrucan, awal tahun dikembalikan ke bulan Maret.
• Pada setiap akhir tahun, orang Romawi melakukan
  pembayaran upah. Sering upah berkenaan dengan
  pekerjaan di dalam musim yang dipengaruhi oleh
  kedudukan matahari. Namun dengan 355 hari
  setahun, kedudukan matahari bergeser dari akhir
  tahun ke akhir tahun. Karena itu orang Romawi
  menambahkan 22 dan 23 hari selang-seling pada
  setiap dua tahun, dan tambahan diselipkan di
  antara tanggal 23 dan 24 Februarius. Dengan
  demikian, setiap empat tahun terdapat 1465 hari
  atau rerata di dalam setahun terdapat 366,25
  hari.
• Julius Ceaser memanggil Sosigenes untuk membenahi
  kalender. Sosigenes menggunakan tahun dengan
  365,25 hari. Pada tahun 46 sM, Sosigenes
  menambah 67 hari ke dalam kalender sehingga pada
  tahun itu terdapat 445 hari. Mulai tahun 45 sM,
  Romawi menggunakan kalender baru yakni tahun
  dimulai pada tanggal 1 Januarius. Bulan
  Januarius, Martius, Maius, Quintilis (Juli),
  September, November terdiri atas 31 hari. Bulan
  Aprilis, Junius, Sextilis (Agustus), October, dan
  December terdiri atas 30 hari. Bulan Februarius
  terdiri atas 29 hari. Di dalam setahun terdapat
  365 hari. Dan setiap empat tahun, di antara
  tanggal 23 dan 24 Februari ditambah satu hari.

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• Tanggal Julian (tahun 1583 oleh Joseph Justus
  Scaliger)
• Menggabungkan tiga siklus interkalasi
• 19 x 15 x 28 7980 tahun
• Titik temu terakhir pada tahun 4713 sM
• Patokan tanggaln Julian 1 Januari 4713 sM sebagai
  tanggal 1 (dimulai tengah hari)
• 2 Oktober 2004 2 454 178

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Zaman KunoSebelum Abad ke-5 sM

• Keteraturan Alam (Ramuan Bahan)
• Keteraturan alam lainnya terdapat pada ramuan
  bahan (material, logam, obat)
• Mereka menjadi ilmu bahan dan farmasi
• Di samping ilmu bahan dan farmasi, terdapat pula
  ramuan bercampur kepercayaan dan mistik yang
  dikenal sebagai alkemi
• Keteraturan Alam (Pengobatan)
• Keteraturan alam juga terdapat pada pengobatan
  orang sakit
• Mereka menjadi tabib dan dukun
• Di samping itu, terdapat pula kepercayaan dan
  mistik yang dikenal sebagai tenung

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Zaman KunoSebelum Abad ke-5 sM

• Keteraturan Alam (Pertukangan)
• Keteraturan alam lainnya adalah pembuatan alat
• Mereka dikenal sebagai pertukangan
• Salah satu kegiatan arkeologi adalah mencari
  karya pertukangan pada zaman purbakala
• Tenung
• Merupakan kekuatan gaib yang dapat menyembuhkan
  atau menyakitkan orang
• Sekalipun tidak ada dasar ilmiahnya, sampai
  sekarang pun, kalangan tertentu masih percaya
  akan kekuatan tenung (guna-guna)

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Zaman KunoSebelum Abad ke-5 sM

• Astrologi
• Di samping astronomi, muncul juga pengetahuan
  lain yang dikenal sebagai astrologi
• Menurut astrologi, dunia bintang-bintang adalah
  makrokosmos dan dunia manusia adalah mikrokosmos
• Mikrokosmos adalah refleksi dari makrokosmos
  sehingga nasib manusia dapat diramal dari gejala
  bintang-bintang di langit
• Jam dan tanggal lahir menjadi patokan untuk
  ramalan nasib manusia
• Peranan Astrologi
• Peranan astrologi melampau batas zaman kuno
• Sampai sekarang pun masih muncul ramalan
  astrologi di dalam majalah

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• ASTROLOGY
• Astrology is the type of divination that
  consists in interpreting the influence of planets
  and the stars on earthly affairs in order ot
  predict the destinies of individuals, groups, or
  nations. At times regarded as science, astrology
  has exerted an extensive or a peripheral
  influence in many civilizations, both ancient and
  modern. Astrology has also been defined as a
  pseudoscience and considered to diametrically
  opposed to the theories and findings of modern
  science.
• Astrology originated in Mesopotamia, perhaps in
  the 3rd millenium BC, but attained its full
  development in the Western world much later,
  within the orbit of Greek civilization of the
  Hellenistic period. It spread to India in its
  older Mesopotamian form. Islamic culture absorbed
  it as part of the Greek heritage and in the
  Middle Ages, when Western Europe was strongly
  affected by Islamic science, European astrology
  also felt the influence of the Orient.
• The Egyptian also contributed though less

25

• directly, to the rise of astrology. They
  constructed a calendar, containing 12 months of
  30 days each with five days added at the end of
  the year, that was subsequently taken over by the
  Greeks as a standard of reference for
  astronomical observations. In order that the
  starry sky might serve them as a clock, the
  Egyptians selected a successian of 36 bright
  stars whose risings were separated from each
  other by intervals of 10 days. Each of these
  stars, called decans by Latin writers, was
  conceived of as a spirit with power over the
  period of time for which it served they later
  centered the zodiac as subdivisions of its 12
  signs.
• In pre-Imperial China, the belief in an
  intelligible cosmic order, comprehended aspects
  of which would permit influences on correlated
  incomprehended aspects, found expression in
  correlation charts that juxtaposed natural
  phenomena with the activities and the fate of
  man. The transition from the belief to a truly
  astrological belief in the direct influence of
  the stars on human affairs was slow, and numerous
  systems of observation and strains of lore
  developed. When Western astronomy and astrology
  became known in China through Arabic influence in

26

• Mongol times, their data were also integrated
  into the Chinese astrological corpus. In the
  later centuries of Imperial China it was
  universal practice to have a horoscope case for
  each newborn child and at all decisive junctures
  in life.
• Once established in the classical world, the
  astrological conception of causation invaded the
  sciences particularly medicine and allied
  disciplines. The Stoics, espousing the doctrine
  of a universal sympathy linking microcosm of
  man with the macrocosm of nature, found in
  astrology a virtual map of such a universe.
• Greek astrology was slow to be absorbed by the
  Romans, who had their own native methods of
  divination, but by the times of Augustus, the art
  had resumed its original role as a royal
  prerogative. Attempts to stress its influence on
  the populace met repeatedly with failure.
• Throughout pagan antiquity the words astronomy
  and astrology had been synonymous in the first
  Christian centuries the modern distinction
  between astronomy, the science of stars, began to
  appear. As against the omnipotence of the stars,
  Christianity

27

• taught the omnipotence of their Creator. To the
  determinism of astrology Christianity opposed the
  freedom of the will. But within these limits the
  astrological worldview was accepted. To reject it
  would have been to reject the whole heritage of
  classical culture, which had assumed an
  astrological complexion. Even at the centre of
  Christian history, Persian magi were reported to
  have followed a celestial omen to the scene of
  the Nativity.
• Although various Christian councils condemned
  astrology the belief in the worldview it implies
  was not seriously shaken. In the late European
  Middle Ages, a number of universities, among them
  Paris, Padua, Bologna, and Florence, had chairs
  of astrology. The revival of ancient studies by
  the humanists only encouraged this interest,
  which persisted into the Renaissance and even
  into the Reformation.
• It was Copernican revolution of the 16th century
  that dealt with the geocentric worldview of
  astrology its shattering blow. As a popular
  pastime or superstition, however, astrology
  continued into modern times to engage the
  attention of millions of people.

28
Zaman KunoSebelum Abad ke-5 sM

• Alkemi
• Di samping ramuan bahan secara alamiah, muncul
  kepercayaan dan mistik berkenaan dengan ramuan
  bahan itu
• Ramuan dengan kepercayaan seperti ini dikenal
  sebagai alkemi
• Alkemi bertujuan untuk membuat emas dari bahan
  murah serta membuat obat panjang umur yang
  membuat orang tidak mati
• Ada alkemi yang hanya rajin menulis melalui sandi
  rahasia serta ada alkemi yang rajin meramu bahan
• Peranan Alkemi
• Peranan alkemi melampaui batas zaman kuno
• Mereka baru hilang pada zaman modern (abad ke-18
  dan ke-19)

29
Zaman KunoSebelum Abad ke-5 sM

• Asas Determinisme Universal
• Ada keteraturan alam yang ditemukan oleh manusia
• Ada kepastian tentang keteraturan alam itu
• Mereka menjadi suatu asas yakni asas determinisme
  universal
• Asas ini dikenal sejak Zaman Kuno dan terus
  berlangsung sampai sekarrang
• Asas determinisme universal menjadi dasar untuk
  menemukan dan mengembangkan ilmu
• Asas Indeterminisme
• Dikenal sebagai uncertainty principle, ditemukan
  oleh Heisenberg pada tahun 1928
• Bertentangan dengan asas determinisme universal,
  tetapi hanya berlaku di fisika partikel subatomik
  dan dalam ukuran yang sangat kecil

30
Zaman Yunani Kuno5 sM sampai 1 sM

• Kebudayaan Yunani
• Zaman ini merupakan zaman emas Yunani Kuno
• Budaya berkembang ke arah kecendekiaan
• Sekalipun Yunani Kuno mengenal dewa dan dewi,
  pemikiran mereka tidak melibatkan dewa dewi itu
• Di zaman itu lahir filsafat dan demokrasi dan
  sangat berpengaruh terhadap kebudayaan barat
  sampai sekarang
• Babakan
• Zaman pra-Sokrates
• Zaman Sokrates
• Zaman pasca-Sokrates

31
Zaman Yunani Kuno5 sM sampai 1 sM

• Zaman Pra-Sokrates
• Ada tiga pemikiran besar pada zaman itu yang
  dibicarakan di sini
• Unsur dasar pembentuk alam dan bentuk alam
• Alam tunggal dan alam jamak
• Realitas bilangan
• Zaman Sokrates (Sokrates, Plato, Aristoteles)
• Dialog
• Metafisika dan epistemologi
• Logika
• Etika dan estetika
• Zaman Pasca-Sokrates
• Stoik, Epikurus, Cynics, dan Skeptik

32

• Greece
• Greece, officially called Hellenic Republic
  (Greek ???????? ??µ???at?a Eliniki Dhimokratia),
  is a country in the southeast of Europe on the
  southern tip of the Balkan peninsula.
• The historical name of Greece in Greek is ?????
  Ellas. This name is also written Hellas in
  English, following the ancient Greek
  pronunciation. More commonly, it is called ????da
  Elladha in modern Greek. The mythical ancestor of
  the Greek is the eponymous Hellen.
• The name of Greece in European languages
  (English Greece, French Grèce, Portuguese
  Grécia, Spanish and Italian Grecia, German
  Griechenland, Russian ??????, etc) comes from a
  different root G?a???? Graik?s (via Latin
  Graecus) which according to Aristotle was an
  ancient name of the Greeks. On the other hand,
  the name of Greece in some Middle Eastern and
  Eastern languages (Turkish Yunanistan, Arabic
  (tulisan Arab Yunan), Hebrew (tulisan Hebrew),
  ancient Persian Yauná, Indian Pali Yona, Malay
  and Indonesian Yunani) derives from the Greek
  toponym ????a Ionia. Norwegian is one of the few
  languages apart from Greek in which the name
  Hellas predominates.

33

• THE HELLENISTIC WORLD
• The history of the Greek-speaking world in
  antiquity may be divided into three periods that
  of the free City States, which was brought to an
  end by Philip and Alexander that of the
  Macedonian domination, of which the last remnant
  was extinguished by the Roman annexation of Egypt
  after the death of Cleopatra and finally that of
  the Roman Empire. Of these three periods, the
  first is characterized by freedom and disorder,
  and the second by subjection and disorder, the
  third by subjection and order.
• The second of these periods is known as the
  Hellenistic age. In science and mathematics, the
  work done during this period is the best ever
  achieved by the Greeks. In philosophy, it
  includes the foundation of the Epicurean and
  Stoic schools, and also of scepticism as a
  definitely formulated doctrine it is therefore
  still important philosophically, though less so
  than the period of Plato and Aristotle. After the
  third century BC, there is nothing really new in
  Greek philosophy until the Neoplatonists in the
  third century AD. But meanwhile the Roman world
  was being prepared for the victory of
  Christianity. ...
• After Alexanders death, there was an
  attempt to preserve the unity of his empire. But
  of his two sons,

34

• one was an infant and the other was not yet born.
  Each had supporters, but in the resultant civil
  war both were thrust aside. In the end, his
  empire was divided between the families of three
  generals, of whom, roughly speaking one obtained
  the European, one the African, and one the
  Asiatic parts of Alexanders possessions. The
  European part fell ultimately to Antigonuss
  descendants Ptolemy, who obtained Egypt, made
  Alexandria his capital Seleucus, who obtained
  Asia after many wars, was too busy with campaigns
  to have a fixed capital, but at later times
  Antioch was the chief city of his dynasty.
• From the point of view of Hellenistic
  culture, the most brilliant success of the third
  century BC was the city of Alexandria. Egypt was
  less exposed to war than the European and Asiatic
  parts of the Macedonian domain, and Alexandria
  was in extraordinarily favoured position for
  commerce. The Ptolemies were patrons of learning,
  and attracted to their capital many of the best
  men of the age. Mathematics became, and remained
  until the fall of Rome, mainly Alexandrian
  from Bertrand Russell, History of Western
  Philosophy

35
Zaman Yunani KunoPra-Sokrates Unsur Alam

• Unsur Dasar Alam
• Menurut Thales dari Miletus ( 624 sM - 546 sM)
  adalah air
• Menurut Anaximenes ( 570 sM - 500 sM) adalah
  udara
• Menurut Xenophanes ( 570 sM - 480 sM) adalah
  tanah
• Menurut Heraklitus ( 540 sM - 475 sM) adalah
  api
• Menurut Empedokles ( 490 sM - 430 sM) adalah
  kombinasi dari air, udara, tanah, dan api
• Sifat Dasar Unsur
• panas dan dingin
• kering dan basah

36

• THALES OF MILETUS
• Thales of Miletus (fl. 6th century BC),
  philosopher remembered for his cosmology based on
  water as the essence of all matter. According to
  the Greek thinker Apollodorus, he was born in
  624 the Greek historian Diogenes Laeritus placed
  his death in the 58th Olympiad (548-545) at the
  age of 78.
• No writings by Thales survive, and no
  contemporary sources exist thus, his achievement
  are difficult to assess. Inclusion of his name
  in the canon of legendary Seven Wise Men led to
  his idealization, and numerous acts and sayings,
  many of them no doubt spurious, were attributed
  to him. According to Herodotus, Thales was a
  practical statesman who advocated the federation
  of Ionian cities of the Aegian region. The Greek
  scholar Callimachus recorded a traditional belief
  that Thales advised navigators to steer by the
  Little Bear (Ursa Minor) rather than by the Great
  Bear (Ursa Major), both prominent constellation
  in the north.

37

• He is also said to have used his knowledge of
  geometry to measure the Egyptian pyramids and to
  calculate the distance from the shore of ships at
  sea. Although such stories are probably
  apocryphal, they illustrate Thales reputation.
  The Greek writer Xenophanes claimed that Thales
  predicted the solar eclipse that stopped the
  battle between the Lydian Alyattes and the Median
  Cyaxares, evidently on May 48, 585. Modern
  scholars believe, however, that he could not
  possibly have had the knowledge to predict
  accurately either the locality or the character
  of an eclipse. Thus, his feat was apparently
  isolated and only approximate Herodotus spoke of
  his foretelling the year only. That the eclipse
  was nearly total and occurred during a crucial
  battle probably contributed considerably to his
  exaggerated reputation as an astronomer.
• In geometry Thales has been credited with the
  discovery of five theorems (1) that a circle is
  bisected by its diameter, (2) that angles at the
  base of a triangle having two sides of equal
  length are equal, (3) the opposite angles of
  intersecting straight lines are equal, (4) that
  the angle inscribed in a semicircle is a right
  angle, and (5) that a triangle is determined if
  its base and the angles relative to the base are
  given. His mathematical achievements are
  difficult o assess, however, because of the
  ancient practice of crediting particular
  discoveries to men with a general reputation for
  wisdom.

38

• The claim that Thales was the founder of a
  European philosophy rests primarily on Aristotle,
  who wrote that Thales was the first to suggest a
  single material substratum for the
  universenamely, water, or moisture. Even though
  Thales as philosopher renounced mythology, his
  choice of water as the fundamental building block
  of matter had its precedent in tradition. A
  likely consideration in this choice was the
  seeming motion that water exhibits, as seen in
  its ability to become vapour for what changes or
  moves itself was thought by the Greeks to be
  close to life itself. To Thales the entire
  universe is a living organism, nourished by
  exhalations from water.
• Thales significance lies in his choice of water
  as the essential substance than in his attempt to
  explain nature by the simplification of phenomena
  and in his search for causes within nature itself
  rather than in the caprices of anthropomorphic
  gods. Like his successors Anaximander and
  Anaximenes, Thales is important in bridging the
  worlds of myth and reason.

39
Zaman Yunani KunoPra-Sokrates Unsur Alam

• Letak Unsur
• Tanah
• di tengah alam, benda jatuh karena kembali ke
  letak asal
• Air
• di tepi tanah, air keluar dari tanah melalui
  mata air karena kembali ke letak asal
• udara
• di tepi air, udara di dalam air bergelembung
  naik karena kembali ke letak asal
• api
• di tepi udara, dalam bentuk kilat di langit
• Unsur kelima (quintessential)
• unsur pembentuk benda langit, unsur sempurna

40
Zaman Yunani KunoPra-Sokrates Unsur Alam

• Sifat Unsur
• tanah kering dingin
• air basah dingin
• udara basah panas
• api kering panas
• Benda
• Benda merupakan kombinasi dari keempat unsur
  beserta sifat mereka
• Asumsi
• Unsur alam beserta sifatnya ini dijadikan asumsi
  di dalam pengetahuan kemudian

41
Zaman Yunani KunoPra-Sokrates Unsur Alam
42
Zaman Yunani KunoPra-Sokrates Unsur Alam

• Bentuk Alam
• Menurut Anaximander ( 610 sM - 546 sM) dari
  Miletus langit berentuk bola serta permukaan bumi
  melengkung dan berbentuk silinder dengan sumbu
  timur-barat
• Menurut Anaximenes dari Miletus, bumi berbentuk
  meja bundar (cakram)
• Menurut Pythagoras, bumi berbentuk bola
• Alam
• alam terdiri atas substansi dan bentuk
• Peta Zaman Kuno
• Timur (orient) terletak di atas
• Membaca peta, perlu mencari letak timur dulu
• Pencarian letak timur (orient) adalah orientasi

43
Zaman Yunani KunoPra-Sokrates Wujud Alam

• Paham Alam Tunggal (Monisme)
• Realitas alam adalah tunggal walaupun tampak
  jamak
• Tidak ada celah
• Tidak terbagi
• Tiada gerakan (statis)
• Penganut perguruan Elea yang dipimpin oleh
  Parmenides

44
Zaman Yunani KunoPra-Sokrates Wujud Alam

• Paham Alam Jamak (Pluralisme)
• Realitas alam adalah jamah (banyak)
• Ada celah
• Terbagi
• Ada gerakan (dinamis)
• Penganut Heraklitus dan Empedokles

45
Zaman Yunani KunoPra-Sokrates Wujud Alam

• Perguruan Elea
• Dipimpin oleh Parmenides
• Pengikut terkenal adalah Zeno dari Elea
• Menganut alam tunggal (monisme)
• Heraklitus
• Mengagumi api yang bergerak dan air yang
  mengalir
• Ucapan terkenal panta rhei semua mengalir
• Menganut alam jamak
• Empedokles
• Substansi alam terus bergerak, berpadu melalui
  kasih, dan bercerai melalui benci, berulang-ulang
  terjadi secara periodik
• Menganut alam jamak

46

• PARMENIDES
• Parmenides (b. c. 515 BC), Greek philosopher of
  Elea in southern Italy who founded Eleaticism,
  one of the leading per-Socratic schools of Greek
  thought. His general teaching has been diligently
  reconstructed from the few surviving fragments of
  his principal work, a lengthy three-part verse
  composition titled On Nature.
• Parmenides held that the multiplicity of
  existing things, their changing forms and motion,
  are but an appearance of a single eternal reality
  (Being), thus giving rise to the Parmenidian
  principle that all is one. From this concept of
  Being, he went on to say that all claims of
  change or or bob-Being are illogical. Because he
  introduced the method of basing claims about
  appearances on a logical concept of Being, he is
  considered one of the founders of metaphysics.
• Platos dialogue the Parmenides deals with his
  thought. An English translation of his work was
  edited by L. Taran (1965).

47
Zaman Yunani KunoPra-Sokrates Wujud Alam

• Paradoks Zeno
• Zeno dari Elea (penganut paham alam tunggal)
  membantah paham alam jamak melalui empat paradoks
• Paradoks dikotomi
• Paradoks Achilles
• Paradoks panah
• Paradoks stadion
• Cara
• Menggunakan paham alam jamak (terbagi) dan
  menunjukkan ketidaklogisan

48
Zaman Yunani KunoPra-Sokrates Wujud Alam

• Paradoks Dikotomi
• Dari titik A bergerak menuju ke titik B
• Kalau jarak ini terbagi (paham jamak) maka jalan
  itu dibagi dua
• Setelah tiba di tengah jalan, sisa jalan dibagi
  dua lagi
• Setelah mencapai titik tengahnya, sisa jalan
  dibagi dua lagi
• Demikian seterusnya, sehingga kita tidak mungkin
  tiba di B

A
B
49
Zaman Yunani KunoPra-Sokrates Wujud Alam

• Paradoks Achilles
• Achilles adalah dewa Yunani yang larinya
  tercepat kura-kura adalah hewan yang jalannya
  paling lambat
• Achilles ingin menyusul kura-kura yang sudah
  lebih dahulu berjalan
• Setiap kali Achilles tiba ke tempat kura-kura,
  sang kura-kura sudah maju sedikit
• Demikian seterusnya, sehingga Achilles tidak
  mungkin melewati kura-kura
• Bahkan menurut paradoks dikotomi, Achilles tidak
  mungkin mencapai tempat kura-kura

Achilles
Kura-kura
50
Zaman Yunani KunoPra-Sokrates Wujud Alam

• Teori Atom
• Leucippus dan Democritos muncul dengan teori atom
  ( a tomos tidak terpenggal)
• Menurut mereka segala sesuatu memiliki bagian
  terkecil berupa atom
• Segala sesuatu itu meliputi benda dan bukan benda
  (berbeda dengan atom unsur di kimia)
• Benda kayu, batu, air bukan benda api, jiwa,
  perasaan, pikiran
• Ada atom kasar seperti atom api ada atom halus
  (eidola) seperti atom jiwa (psyche)
• Pemenggalan sesuatu akan terhenti pada atom
• Tampaknya teori atom ini dapat menjawab paradoks
  Zeno

51
Zaman Yunani KunoPra-Sokrates Bilangan

• Perguruan Pythagoras
• Kita mengenal dalil Pythagoras di geometri
  (sebelum Pythagoras, dalil ini sudah dikenal)
• Sebenarnya, banyak hal yang dikemukakan oleh
  Perguruan Pythagoras, dan kesemuanya berkenaan
  dengan bilangan
• Paham Pythagoras
• Segala sesuatu duduk di atas bilangan dan dapat
  dinyatakan dalam bilangan
• Perguruan Pythagoras menemukan berbagai sifat
  bilangan
• Tugas ahli filsafat, menurut perguruan
  Pythagoras, adalah mencari bilangan itu

52

• PYTHAGOREAN PHILOSOPHY
• Although much of the tradition about Pythagorean
  philosophy is confused because of dissensions
  within the school and on account of intermixture
  of later speculation with earlier doctrine, yet
  some of the chief principles are quite clear.
  Pythagorass discoveries in musical theory, such
  as that the basic musical harmonies depend on
  very simple numerical ratios between the
  dimensions of the instruments (such as strings,
  pipes, disks) producing them, let him interpret
  the world as a whole through numbers. The
  discovery was the basis for the Pythagorean
  theory of numbers, of which the systematic study
  induced the intense Pythagorean devotion to
  mathematics and the subsequent development of
  this science by Greek scientists. Pythagoras
  taught that number is the fundamental part of the
  worlds framework. According to his theory that
  the dominant note of the universe are proportion,
  order, and harmony. All three are expressible by
  numerical relations. Pythagoreans thus considered
  that the universes essential character is
  number, but they went beyond this by asserting
  that the world is made of numbersa doctrine that
  is the core of Pythagorean

53

• philosophy. In preaching this principle the
  Pythagoreans both propounded several semi
  mystical speculations and discovered more
  scientific truths.
• On the speculative side occurs the celebrated
  Pythagorean table of opposites, derived from
  their proposition that the universe is composed
  of pairs of contradictories. The pairs are 10 in
  number (1) limited and unlimited (2) odd and
  even (3) one and many (4) right and left (5)
  masculine and feminine (6) rest and motion (7)
  straight and crooked (8) light and darkness (9)
  good and evil (10) square and oblong. Though
  this theory may not be so fantastic as it
  appears, the Pythagorean development of numbers
  was quite arbitrary in the following proposition.
  The number 1 is the point, 2 is the line, 3 is
  the plane, 4 is the solid, 5 is physical
  qualities, 6 is animation, 7 is intelligence and
  health, 8 is love, friendship, wisdom.
  Identification of different numbers with
  different things exemplifies no principle. The
  Pythagoreans themselves disagreed on what number
  should be assigned to what things. Thus, since
  justice is that which returns equal for equal,
  the only numbers which do this are square
  numbers thus 4 equals 2 into 2 and so returns
  equal for

54

• for equal thus 4 must be justice. But since 9 is
  equally square of 3, 9 also can represent
  justice. Such speculation seems sterile, save to
  numerologists.
• Among the Pythagorean achievements in science
  were
• (1) The Pythagorean theorem, reliably reported
  to have been discovered by Pythagoras, to whose
  speculation was owed also, quite probably, most
  of the first book of Euclids Stoicheaia
  (Elements) on geometry.
• (2) By 500 BC the earth sphericity was
  proclaimed by Pythagoreans, who were among the
  first, if not the first, to teach it.
• (3) Hippasus (fl. 450 BC) discovered
  incommensurability and elaborated a theory of
  proportions applicable to incommensurables.
• (4) By 400 BC the Pythagoreans taught the theory
  that the earth, sun, and moon, planets, and fixed
  stars revolve around a central firea denial of
  the earlier and later geocentric view of the
  universe and an anticipation of Nicolaus
  Copernicus heliocentric hypothesis announced in
  1543. From this theory they

55

• developed the doctrine of the music of the
  spheres, which lasted into modern times.
• (5) Archytas of Tarentum (fl. 360 BC)
  developed a very advanced theory of acoustics and
  founded mechanics.
• (6) At an undetermined date Pythagoreans
  developed the theory of mathematical means and
  they also invented the theory of polygonal
  numbers.
• Pythagorean ethics consisted in ascetics
  practice. Happiness was the perfection of the
  souls virtue, which was a kind of harmony. The
  process of purification of the soul was
  accomplished by metemorsychosis, the
  transmigration of the soul, a theory imported by
  Pythagoreans from the Orient and one of their
  most characteristic dogmas.

56
Zaman Yunani KunoPra-Sokrates Bilangan

• Harmoni
• Pythagoras menemukan bahwa nada dapat dinyatakan
  dengan rasio panjang kawat yang menghasilkan
  nada (1 ¾ 2/3 ½ ) atau (12 9 8 6)
• oktaf (diaspason) 12 6 fourth (diatessaron) 8
  6 fifth (diapente) 12 8
• Rasio ini dinamakan harmoni
• Menurut mereka, jarak benda langit ke bumi juga
  memiliki rasio harmonis (music of the sphere)
• Menurut mereka, tubuh manusia sehat memiliki tone
  yang harmonis sakit berarti tone tidak harmonis
  lagi, diobati dengan tonikum

57
Zaman Yunani KunoPra-Sokrates Bilangan

• Arti Bilangan
• 1 titik penalaran
• 2 garis pendapat
• 3 bidang
• 4 bentuk ruang keadilan
• 5 kualitas fisik perkawinan
• 6 animasi semangat
• 7 inteligensi kesehatan
• 8 cinta persahabatan kearifan
• 9 keadilan
• Genap Ganjil
• Bilangan genap (artios) tidak disukai karena
  mudah terbagi/pecah
• Bilangan ganjil (perissos) disukai karena tidak
  mudah terbagi/pecah

58
Zaman Yunani KunoPra-Sokrates Bilangan

• Bilangan 10
• Bilangan 10 adalah ideal karena 1 2 3 4
  10
• Ada 10 pasang lawanan
• terbatas lawan tak terbatas
• ganjil lawan genap
• satu lawan banyak
• kanan lawan kiri
• lelaki lawan perempuan
• diam lawan gerak
• lurus lawan bengkok
• terang lawan gelap
• baik lawan jahat
• bujur sangkar lawan lonjong

59
Zaman Yunani KunoPra-Sokrates Bilangan

• Bilangan dan Gambar
• Bilangan bulat bilangan segi tiga
• Bilangan ganjil bilangan bujur sangkar
• Bilangan genap bilangan persegi panjang
• Bilangan segi lima
• Bilangan kubik
• Number and Figure
• Di dalam bahasa Inggris figure dapat diartikan
  number atau bilangan rupanya dari sini
• Bilangan Irasional
• Bilangan ?2, ?3 membingungkan perguruan ini
  karena tidak dapat dinyatakan sebagai rasio dua
  bilangan bulat

60
Zaman Yunani KunoPra-Sokrates Bilangan
61

• THE SQUARE ROOT OF TWO
• The square root of 2, which was the first
  irrational to be discovered, was known to the
  early Pythagoreans, and ingenious methods of
  approximating to its value was discovered. The
  best was as follows Form two columns of numbers,
  which we will call the as and the bs each
  starts with 1. The next a, at each stage, is
  formed by adding the last a and b already
  obtained the next b is formed by adding twice
  the previous a to the previous b. The first 6
  pairs so obtained are (1,1), (2,3), (5,7),
  (12,17), (29,41), (70,99). In each pair, 2a2?b2
  is 1 or ?1. Thus b/a is nearly the square root of
  two, and at each fresh step it gets nearer. For
  instance, the reader may satisfy himself that the
  square of 99/70 is very nearly equal to 2. from
  Bertrand Russell, History of Western Philosophy
• (a, b), (a, b),
• a a b
• b 2a b ? b/a

62
Zaman Yunani KunoPra-Sokrates Bilangan

• Sifat Bilangan
• Bilangan sempurna
• jumlah faktor bilangan
• mis. 1 2 3 6
• 1 2 4 7 14 28
• Bilangan berkekurangan
• jumlah faktor lt bilangan
• mis. 1 2 4 lt 8
• Bilangan berlimpahan
• jumlah faktor gt bilangan
• mis. 1 2 3 4 6 gt 12
• Bilangan bersahabat
• jumlah faktor bilangan bilangan sahabatnya
• mis. 1245101120224455110284
• 12471142220

63
Zaman Yunani KunoPra-Sokrates Protagoras

• Protagoras (c. 500 sM)
• Menyatakan dirinya sebagai sophist
• Tidak mendirikan perguruan, menerima bayaran dari
  jasa mengajar
• Ukuran
• Menurut Protagoras, manusia adalah ukuran dari
  semua benda, tentang benda yang ada dan tentang
  benda yang tidak ada
• Akibatnya, menurut orang yang satu, benda adalah
  seperti ini, tetapi menurut orang yang lain, bisa
  lain lagi
• Baik dan benar
• Sesuatu bisa lebih baik tetapi belum tentu lebih
  benar

64
Zaman Yunani KunoSokrates

• Perguruan
• Sokrates adalah guru dari Plato
• Plato adalah guru dari Aristoteles
• Sokrates, Plato, Aristoteles adalah tiga ahli
  filsafat yang terkenal dari zaman Yunani Kuno
• Setelah Aristoteles, Yunani ditaklukkan oleh
  Alexander, dan mengalami kemunduran
• Kegiatan Sokrates ( 470 sM - 399 sM)
• Memiliki perguruan
• Tidak menulis buku karyanya terdapat di dalam
  tulisan Plato
• Ikut dalam politik sehingga dihukum mati pada
  tahun 399 sM
• Merintis metoda dialog
• Filsafat moral dan hipotesis

65
Zaman Yunani KunoPlato

• Perguruan
• Memberi pelajaran di taman Akademon di pinggir
  kota Athena
• Dikenal sebagai Perguruan Akademia (asal usul
  dari kata akademik) dari 387 sM sampai 529
• Perguruan Akademia
• Akademia tua oleh Plato (387 sM), diteruskan
  oleh pengikutnya (dan kemanakan) Speusippus,
  Xenokrates dari Khalkedon, Polemon dari Athena,
  Krates
• Akademia pertengahan diteruskan oleh Arkesilaus
  (316 - 241 sM)
• Akademia baru oleh Kameades (214?sM - 129 sM)
• Dibubarkan oleh Kaisar Justinian pada tahun 529

66
Zaman Yunani KunoPlato

• Kegiatan Plato ( 427 sM - 347 sM)
• Meninggalkan banyak karya paling terkenal adalah
  Dialogue
• Merintis teori bentuk (form, ide) yakni bentuk
  umum (universal) dari sesuatu seperti kursi,
  biru, buku, pohon
• Diduga bahwa bentuk umum ini ada di dalam ide,
  maka dikenal juga sebagai ide
• Berkarya juga di bidang epistemologi, logika,
  etika, hukum, metoda dialektika (dialog)
• Paham tentang Pengetahuan
• Menganut paham tunggal dari Parmenides, terutama
  tentang ketidakubahan pengetahuan
• Benda berubah tetapi bentuk tidak berubah
  pengetahuan harus melalui bentuk atau ide yang
  tidak berubah

67
Zaman Yunani KunoAristoteles

• Perguruan
• Memberi pelajaran sambil berjalan-jalan
  (peripatetik) di taman Lyceum
• Dikenal sebagai Perguruan Lyceum
• Karena mengajar sambil berjalan-jalan, anggota
  perguruan ini dikenal sebagai Peripatetik
• Pernah memberi pelajaran kepada anak Raja yang
  kemudian menjadi Alexander Agung
• Kegiatan Aristoteles (384 sM - 322 sM)
• Meninggalkan banyak sekali karya
• Merintis logika, terutama silogisme
• Merintis kategori substansi, kuantitas,
  kualitas, relasi, tempat, waktu, posisi, status,
  aksi, kepasifan (terkena aksi)
• Terkenal dengan metoda induksi dan deduksi, serta
  teleologi

68
Zaman Yunani KunoAristoteles

• Kegiatan Ilmiah
• Sebagai anak dokter, ia banyak menelaah alam
  terutama biologi dan psikologi
• Tidak sepaham dengan Plato tentang bentuk (ide)
  Plato bentuk sebelum materi, Aristotles bentuk di
  dalam materi
• Bidang Karya Aristoteles
• Dari karya yang masih dapat ditemukan, karya
  Aristoteles dapat dikelompokkan ke dalam beberapa
  bidang
• Filsafat teoretik atau spekulatif (teologi,
  fisik, metafisika, biopsikologi)
• Filsafat Praktis (etika dan ilmu politik)
• Filsafat Produktif (retorika, estetika, kritik
  sastra)

69
Zaman Yunani KunoAristoteles

• Karya Aristoteles
• Logika di dalam Organon
• kategori, tentang interpretasi, prior analytics
• posterior analytics, topik, sophistical
  refutations
• Filsafat Alam
• tentang langit (meteorologi)
• fisika (materi dan bentuk atau form)
• tentang unsur (tanah, air, udara, api)
• astronomi, geografi, kimia, biologi
• Psikologi
• raga dan jiwa (materi dan bentuk)
• pikiran
• Metafisika
• Etika dan Politik
• Seni dan Retorika

70

• CATEGORY
• Category, in logic, a term used to denote
  the several most general or highest types of
  thought forms of entities, or to denote any
  distinction such that, if a form or entity
  belonging to one category is substituted into a
  statement in place of one belonging to another a
  nonsensical assertion must result.
• The term was used by Aristotle to denote a
  predicate type i.e., the many things that may be
  said (or predicated) of a given subject fall into
  classessuch as quantities, substances,
  relations, and stateswhich Aristotle called
  categories. To the Greeks, the clarification of
  predicate categories helped resolve qu