If we could imagine that those who established the U.S. government were intelligent, educated people, we would be able to reason that they understood the language they were using. They used specific words here and non-specific words there, depending upon how they saw how things might evolve/develop. "Promote" and "general" and "welfare" are terms quite open to various views. Unless they were short sighted, blind or stupid, they fully understood this.
The constitutional convention took place in Philadelphia, and it took almost four months to write it. It took another year for nine states to ratify it, because some states opposed the Constitution for not including freedom of speech, religion, press, etc, and when Bill of Rights was added, they ratified it.
What that tells me, even the Constitution was written by very intelligent people, with great wisdom, the people running the states were not stupid neither. The Constitution was written to be understandable to pretty much anyone, and when States were ratifying it, they didn't just accept it, but put more thoughts in it. One thing is certain, regardless of the meaning of words at the time, from Founders to the States, they were all for protecting individual freedoms, and limiting the powers of central big government.
And THAT is the purpose of the Constitution.