Thanks for the crash logs Rhiannabear.
Can you please tell me how you installed AI CC 2014 on your machine: through Adobe Creative Cloud or some other way ?
If it is not installed through Creative Cloud then please un-install it first. Then delete the "Adobe Illustrator CC 2014" folder from your "Applications" folder.
Once you complete the above steps then quit & launch Adobe Creative Cloud application & then install the Adobe Illustrator CC 2014.
Let me know if it works for you.
With Best Regards,
Raghuveer