Getters/Setters result in more brittle code? [closed]

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A small debate flared up in a question about protected member variables regarding the use of getters/setters. There are lots of questions already over whether getters/setters are evil, however one particular argument against them, which was posed by two separate individuals with much higher reputation than myself, struck me.

One said that getters/setters made the code only 0.01% less brittle, and the other stated that adding 10 lines of code where one would do makes the code more brittle.

This goes against most of what I had previously read, been taught, thought, or experienced. Does anyone else agree/disagree with those comments?

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I know it is close to herecy, but I hate get/set methods. Loathe them. Almost never write them.

Generally, a class should either provide much more high-level operations than directly and simply reading and modifying internal state variables, or it should get the hell out of the way and act like the struct it is.

Even if I were to write one, I would almost never use it inside the class. The whole point of them is that you can change the internal representation of thing without affecting a client. Inside the class, it is the internal representation you care about! If you are tempted to do a lot of operations on the class using its own interface inside the class, you probably have a second class in there fighting to get out.