Why not simply use the currently displayed string as starting point?
function addition_Callback(hObject, eventdata, handles)
% get the currently displayed value and convert it to a number
current = str2double(get(handles.value, 'String'));
% current will be nan if the string is empty or not a valid number
if isnan(current)
current = 3; % start or fallback-value
end
new = 4+current;
set(handles.value,'String', new) %here value is the name of the text box