Richard Stallman is a phenomenon; a man whose views are so compartmentalised into right and wrong that it's hard to avoid the suspicion that he's cheerfully parodying himself. His fundamentalist ethos is that free software is good and everything else is bad.
And free software is, at heart, whatever Stallman or his creation the Free Software Foundation (FSF) says it is. And it is free if it meets four critera:
users are free to use the program for any purpose;
they are free to examine the software to see how it works;
they are free to distribute the program to others;
they are free to improve the program.
It doesn't exclude the sale of free software -- the old mantra "think free speech, not free beer" makes this explicit -- but does impose the requirement that programs derived from free software must themselves be free, if the programmer chooses to pass them on.
Open source software is less easy to categorise because it is used in many different ways. At its simplest, it just means software with public source code -- you can look and learn, but not necessarily do much with the information. The Open Source Initiative, which exists to make open source software more acceptable to commercial enterprises, has a much more complex definition largely congruent with that of the Free Software Foundation. It guarantees the right of programmers and users to inspect, modify, pass on and make free use of software so licensed. Other kinds of open source software are considerably more restrictive, and the term open source itself can be used primarily as a marketing device. Caveat emptor.
The much-publicised differences between OSI and FSF boil down to philosophical objections by Stallman to the idea that proprietary software should have anything to do with free software, and his ethos that free software should be a tool of social change. There is little practical difference between the two organisations' views.
As is often the case with two very similar ideas with only a sliver of dogma between them, the arguments run deep. Massive edifices are built out of rhetoric, the significance of which is lost on bystanders. This also tends to obscure the real and significant differences between open source software that is free to use, and open software that is called thus by companies keen to wear the clothes but not to walk the walk.
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