On a Mac, try this:
Go to /System/Library/Java/JavaVirtualMachines in the Finder (you can type Command+Shift+G and paste the path in directly)
Delete everything in this folder
Open the Minecraft launcher
A system window will pop-up prompting you to install Java
Follow the instructions to install Java
Re-open the Minecraft launcher
Should work now
On a Mac, try this:
Go to /System/Library/Java/JavaVirtualMachines in the Finder (you can type Command+Shift+G and paste the path in directly)
Delete everything in this folder
Open the Minecraft launcher
A system window will pop-up prompting you to install Java
Follow the instructions to install Java
Re-open the Minecraft launcher
Should work now