Our best scientific picture depicts us as sophisticated meat robots. Organized by biological evolution, physics ultimately explains the movements of our bodies and the firing of the networks in our brains.
This reductionist understanding presents us with a challenge. What do we do when mechanistic explanations seem to run in parallel with mentalistic explanations?
Suppose you are persuaded by the arguments of a (hypothetical) philosopher, Smith. When asked to explain why you are persuaded, you will talk about the logic of Smith's arguments, and the reasons why you think Smith's description of the world is better than those of his colleagues. However, if you also accept the scientific picture of our world, you implicitly claim that there is another explanation for your attitude towards Smith. Implicitly, the motions of the atoms and molecules in you, Smith and the world collectively cause you to utter the words "Smith is better than his colleagues!"
Can both explanations for your opinion of Smith be true at the same time?
Similar questions surround the concept of "intentionality." Intentionality is the aboutness of a thought. When you think about Smith's theory of mathematics, you take yourself to be thinking about mathematical objects. But, on the molecular view of the situation, it is more difficult to locate the subject of mathematics in the molecular description of your thoughts. Can the interactions of molecules ever be said to constitute thinking about mathematics?
This problem of intentionality is considered a live problem in the philosophy of mind.
Finally, if we don't see any conflict in maintaining conceptual and physical explanations of the same phenomena, then we can ask whether the two sorts of explanations are really comparable. For example, is a subconscious inference an admissible form of epistemological justification?
See Intentionality at Wikipedia and Stanford Encyclopedia of Philosophy
*To help set expectations for attendees, we, the organizers, are trying out ways of rating meetup events for technical level and contentiousness. The more stars in the rating, the more important it is to be familiar with the concepts discussed or to have read work on the topic in question before going into the meeting. The more chili peppers in the rating, the more likely it is that members will be staking out positions, stating their own arguments for conclusions, and the more comfortable we all are with criticism of those ideas. The meetup organizer will ultimately be responsible for setting the tone and keeping the the meeting on track.