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I was writing a paper for my class about the Jewish-Islamic relationship. For that reason,I tried to read what does the Talmud as well as the Quran teach their followers about others. I was shocked when I read verses in the Talmud talking about non-Jews as animals or subhumans. Hoshen Mishpat 425 hagah 425.5 says: "It is the law to kill anyone who denies the Torah. The Christians belong to denying ones of the Torah." Is this a real verse or a fabricated one. I read many many others depicting non-Jews as animals such as in Jore dea 377,1 and Bammidber raba & Jalkut 772 and many others.I want to know your perspective about that. How do Jews perceive non-Jews.
I sense, both from your writing and the sources you cite, that the information you've found was provided by an interested party, who, for one reason or another, wishes to malign Jewish law.
The first source you quote - which is not from the Talmud but from the 16th century legal code "Shulhan Arukh", states only the first half of what you quoted (it mentions nothing about Christians or any other faith-community), only in reference to Jews! In other words, the Jewish court, in those circumstances where they had total authority over their own community, may have practiced this law. Later on in the same paragraph, the law explicitly states that it doesn't apply to non-Jews.
This example should be enough to demonstrate that if you find a line or two, quoted out of context, it is worth checking the entire source to see what it means in context, to make sure (as you judiciously asked) whether the source really says what is being claimed about it and whether, within the broader context of the law, there isn't a
statement which clarifies the meaning.
As for your second example, the line is both untrue and taken, again, out of context. That section of Yoreh Deah (again, from Shulhan Arukh) is discussing the custom of consoling mourners. The law stipulates that only blood relatives are honored with full mourning rites and anyone else, no matter how close, is not accorded the same honor. Therefore, the ruling is that even if one's servants die, he isn't to be consoled in that manner, rather, as one who has lost a valuable possession (for example, an animal). In no way does this law argue that non-Jews (who aren't mentioned there in any case) are seen as animals.
As for your question, Judaism sees all people as created "in God's Image" (Genesis , 5:1); their lives have inestimable value and we must do everything we can, given our resources and abilities, to respect and safeguard the lives of all people.