This claim is highly problematic because it is not certain whether it refers to those who literate in the Latin or Ottoman script.
According to an annual book of education from 1903, 1.4 million of 19.9 million were students. Of these students 868,879, or 5% of the general population, were in elementary school. There were also students receiving education at middle schools and higher education intuitions along with unofficial schools and those who took private lessons. During this period there were hundreds of thousands of clerks working for the state. As 10% of the general population was children between the ages of five and 10, these figures indicate that one in every two children was a student at that time.
When the Republic of Turkey was formed in 1923, and taking into account the lands that the empire covered in 1903, these numbers relatively increase. Eight percent of the general population, or 981,442 of the 12,516,308 people living in the area inherited by the Republic, were elementary school students.
The figures of the new regime on literacy in the country only took elementary school students into account. According to the logic of statistics, people who were literate back then should not be under 50%, considering half of the general population had attended elementary school before. Even if a quarter of the general population attended elementary school during a period of their lives, the number of literate people should have been be around 30% of the general population. In that case, one of these two statistics does not reflect the truth.
Daily circulation of Istanbul-based newspapers was way over 100,000 between 1908 and 1914. The daily circulation of newspapers published in rural areas was also very good. In 1928, the daily circulation of Istanbul - and Ankara-based newspapers – the new regime only allowed three of the hundreds of Ottoman newspapers to continue to be published – was 19,700. This number was less than the daily circulation in the Ottoman era.
Apart from the loss of many educated people during World War I, a huge segment of society became illiterate in one day because of the alphabet reform.
How was the situation in Europe during those years?
In 1890, 17% of the general population in the Russian Empire were literate, 39% in Spain, 45% in Italy, 74% in Belgium, 78% in France, 89% in the U.S. and 92% in the U.K.
Although the Ottoman Empire was an Eastern empire, it was way ahead of Russia, and was at the same level as Spain and Italy.
Claiming the number of illiterate people in the Ottoman state tto be very high was propaganda to justify the alphabet reforms.
What is surprising is the fact those historians making this statement have not bothered to read the statistics published by the Republic of Turkey.
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