falsehoods about "corporations"
Your point is lost if you keep having to say falsehoods in order to make it.
the slogan "Corporations are not people" ----
If you want to explain your slogan "corporations are not people" you at least must give us some facts about corporations and be able to state these facts without requiring falsehoods as part of your explanation. So far no one is giving any facts to explain what this slogan means.
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. . . it [corporation] is a legal structure created by the state, with privileges . . .
No, the state did not create the corporation, but only added some change to an already-existing entity or group which then gained limited liability, which any group can gain by just incorporating.
To say the state "created" the corporation is false just as it's false to say the state "created" a labor union. Just because the unions are put under gov't power, through the labor laws, does not mean that the state
created the union. No, that entity already existed, even before applying for recognition under the labor laws. And the earlier unions (100 or so years ago) existed even before there were labor laws. These laws haven't CREATED unions, but only had gov't step in and make changes to the unions (which were already there as a problem to fix), to impose some new rules upon them. And it's the same when a business chooses to incorporate.
It's obvious that groups like labor unions and corporations and some other groups developed some problems, coming into conflict of some kind, creating conflict between differing interest groups. And even if Laissez-faire has value, there's a need for government to intervene to apply some rules, not just allow the conflicts to persist and cause chaos -- some rules are necessary in the society, when there is conflict, and the various groups have legitimate interests and cannot just be abolished or taken over by the government.
So
such groups existed first, already, before those conflicts, and only then, AFTERWARDS, did the government step and impose some new rules. So it did not create those groups. They were already there, created earlier, spontaneously by the members or in some way independently of the government.
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