To expose themselves, their underside in general, their genitalia in particular.
But if that’s true, why would a dog want to expose itself to an inanimate object?
First, let’s review the traditional/behavioral interpretation of leg-lifting. Elizabeth Marshall Thomas in “The Hidden Life of Dogs” noticed that the higher a stain appears on a post or wall, the next dog along would go to great lengths to hike its spray just a bit higher, the contortions being especially impressive if it was a small dog. She interprets this as a dog’s attempt not only to cover the preexisting mark with its own but to produce one somewhat higher in order to make itself appear larger than it really is and intimidate dogs that come along later. Supposedly this indicates that dogs can think ahead and that they’re thinking about territorial and social status. In this interpretation dogs hose upright objects because they serve as prominent venues for display.
Interestingly however, if leg lifting is fundamentally about competition, one rarely if ever sees two dogs fight it out after the so called contest. And this should strike us as odd because if it is true that a competition for rank is an organizing principle of canine social behavior, how could it be that once every dog’s cards are on the table they invariably agree on their relative status? That’s the opposite of competition. This would be like two people sitting down for a game of poker and were they somehow able to compare their respective winnings over the years; the one with the better record can just scoop up the money and walk away. It would be like two basketball teams eyeing each other during warm ups with both teams coming to a consensus as to which team is better and so no need to actually play the game. In human competition even when a winless team squares up against an undefeated team, the team with a losing record nonetheless contests every shot, rebound and pass. The game is played even when their respective standings won’t be affected by the game’s outcome because this is the essence of the competitive struggle. So in human competitive activities the struggle always follows the preliminaries with the struggle especially intense when there is some degree of question as to which is the stronger team.
So I return to the point that when dogs engage in scent marking, and remain focused on scent marking and are allowed the time and space to let things run their natural course, they rarely if ever fight. How then can the essential thrust of canine behavior be a competition for rank if they invariably end agreeing about their relative status once it’s been broadcast through a spray of urine? Why would dogs ever fight if the distinction between dogs is so unambiguous and easily revealed? Therefore it does not make sense to me that in the mind of the dog leg lifting has anything to do with a competition for rank or a delineation of territory.
In my view the biggest flaw with the traditional/behavioral theory is that it requires a dog to be able to think about such abstract concepts as territory and relative status and perceived future costs and benefits in regards to moving up or down the social ladder. And if a dog can think about all this as Stanley Coren would say they can, let’s then return to Elizabeth Thomas’ astute observation that dogs try to paint its mark higher than the mark of the previous dog that hit the post.
In my mind it actually demonstrates the opposite for if it is true that dogs can think about dominance and rank, why then would dogs only react to the stain of a bigger dog after they’ve encountered it, why not be proactive, why wouldn’t a little dog contort itself into an exaggerated position in order to leave the biggest possible stain before it encounters a bigger one? Why doesn’t a dog go for an impossible height on a blank slate? If it is true that a dog can think about a future consequence why not end all debate on the matter before it begins? This is how athletes compete. When I ran competitive long distance in college my coach taught us to always pass a competitor on a hill, the steeper the better and always pass your rival by a lot rather than by a little. Even better try to be talking casually as you pass by; now that was forward thinking.
Therefore if competition, rank and thinking don’t explain why dogs lift their legs, why would a dog want to expose itself, i.e. become sexually aroused to a fire hydrant, sign post or a tuft of grass? Answer: physical memory
In animal consciousness, there is the expression of energy and there is resistance to the expression of energy. Things that move conduct emotion, things that stand still resist the expression of emotion. Anything that resists the expression of energy triggers physical memory as it creates a feeling of resistance and this is the source of sexual energy.
When a dog encounters an inanimate object that stands out by virtue of being upright and apart from its surroundings, and the more tension that happens to be standing in the dog’s system, then the more it projects the physical memory of resistance onto such an object, and then it responds to it sexually, i.e. it exposes itself and relieves the feeling of resistance by urinating because it feels to the dog just as if it is encountering another dog. And the fact that there often is the scent of dog urine on such prominent objects greatly reinforces that emotional impression that arose from the emotional battery.
Finally, the higher the mark on the post, the more the dog must look up and therefore the deeper into the physical memory bank such an object of resistance triggers. In other words, upright objects and things overhead trigger deeper physical memories than smaller objects and lower things (sorry to add one more level of complexity, unless the physical memory of a little or lower thing is especially intense). And the deepest physical memories are from the earliest days of a dog’s “litter-hood” when its mother constantly licked its anal/genital area because infant puppies cannot urinate or defecate unless stimulated by their mother. So when dogs encounter objects of resistance, they feel sexually energized by virtue of physical memory and this energy is how they are equipped to either align with or overcome said object of resistance. They are exposing themselves due to that physical memory, and then they are then going to attempt to mount the object not because they are trying to dominate it or to copulate, but because they are trying to resist being rolled over.
So in the case of the very high stain, the dog isn’t trying to out do the previous mark: it’s acting just like a little dog trying to mount a bigger one. It’s just trying to get a leg up.