It might seem logical, but it isn't true.
The Luddites were people who were frightened of the introduction of machinery, and used to go around attacking factories, thinking there would be no more jobs.
In reality, whenever automation provides benefits through lower prices, what this does is reduce the amount of hours labor a person needs to spend in order to fulfill that need. If you have a cow, it will take a person a couple of hours to obtain a gallon of milk, and then you have to house, feed and look after the cow. Instead, with automated and factory-produced milk, the average person spends a fraction of that time - maybe 10 minutes - to earn the money to purchase that milk at a convenient location.
And so it goes with everything - whenever a product is automated and the jobs (hours) required to produce that thing is reduced, then the cost of the product falls. The consumer then has a surplus of cash, which is really just a surplus of their time spent, to either keep for themselves, or spend on something else.
As human needs and wants are essentially unlimited (most of us want to go to the moon if it was possible) then, for each good that falls in price, demand will shift to other goods. As automation lowers the cost of each additional good, a person is able to consume more of that good or more additional goods.
Now, you might say that 'consumption' is bad - but consuming a good might also mean consuming a service, like a movie, a local band, or an art gallery, which is still consumption, but not in the 'using up resources' manner (although nearly every consumption save for walking to a tai-chi class on the local beach uses up some kind of resources)
This curve of increasing standard of living is intrinsically linked to increases in productivity, which roughly means the amount of goods + services produced for the given input of working hours.
Thus increasing amounts of automation will never, ever reduce the supply of jobs, because each automated thing that frees up human time for something else, in itself creates activity which generally means creating more jobs.
You don't get an iPhone 5 to buy unless farmers can milk a herd of 150 cows singlehandedly. And so we'll never have tourist trips to the moon unless there is increasing automation amongst industries that are currently labour-intensive. This has been going on for a millenia, and there is no tipping-point or transition point, as it is a very smooth curve. Yes, it can be disruptive for small pockets of workers who become no longer required - there are no more pools of typists - but at the macro level the transition is relatively smooth.
