I care if something is true or not and matches reality. Ti has no agenda, nor does Te. It is only people who have agendas, not elements.
As far as what Ti and Te are and how people use them: Take any large system of data, and Ti is your own understanding and interpretation, your consistent system and the connections you make between the items in the data set. Do they all fit? How do they relate to each other, and does it make sense? Is anything out of place? These are concrete connections (in contrast to Fi connections,) Te on the other hand is the general consensus and conclusions, the established facts based on the data. Rules that you memorize and apply are Te, not Ti, because remember Ti is your own understanding of something. Te sees how the data functions, what it does. Ti sees how it is related to other parts and interconnected.
So, for the logic test Aylen posted - all the questions asking how A is related to B is related to C - those questions can be solved through application of Ti. Also, analogies, solving algebraic-type equations, etc all lend themselves to be solved by using Ti. It's all seeing how something is connected to something else, how they all fit together. Whether you include the real, physical world and the properties of that world in your data set as points of reference for making connections and sense of things may be related more to Se vs Ne, or maybe not, but you can certainly include the real world and still use Ti.



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