In The Modern Liberal Theory of Man, Gerald Gaus sets out a fairly rough and ready distinction between classical liberalism and modern liberalism which he, I think, correctly dates from John Stuart Mill onwards. He says that classical liberals 'share a vision of men as essentially independent, private and competitive beings who see civil association mainly as a framework for the pursuit of their own interests'. By contrast, he suggests that modern liberals are 'more apt to stress mutual dependence over independence, co-operation over competition, and mutual appreciation over private enjoyment'.
This is a prudently put distinction, one that is rather harder to refute than the more typical 'classical liberals are selfish bastards' strawmen that get put up against us in more ordinary discussion. However, I think it is wrong. Take Herbert Spencer, usually considered an archetype individualist classical liberal and a contemporary of J.S. Mill. Is he against co-operation? Not at all, he is just in favour of voluntary co-operation:
'If, instead of using the word "cooperation" in a limited sense, we use it in its widest sense, as signifying the combined activities of citizens under whatever system of regulation; then these two are definable as the system of compulsory cooperation and the system of voluntary cooperation. The typical structure of the one we see in an army formed of conscripts, in which the units in their several grades have to fulfil commands under pain of death, and receive food and clothing and pay, arbitrarily apportioned; while the typical structure of the other we see in a body of producers or distributors, who severally agree to specified payments in return for specified services, and may at will, after due notice, leave the organization if they do not like it.'
Considering the problem a little more analytically, we can see that, in fact, as Sheldon Richman has pointed out, co-operation implies competition. Trade is one kind of simple mode of co-operation. Each person gains by exchanging something they value less for something they value more. So long as both sides of the trade are satisfied, and if the trade is consensual it usually is, then that is a successful co-operative venture. A 'competitor' is simply a potential trader whom someone has decided not to co-operate with on that occasion.
Unless one were to construct a system where you somehow co-operate with absolutely everyone (in the nation, in the world?) simultaneously, there will always be successful co-operators and a few competitors who wished they had been able to co-operate. The only question is how one chooses the co-operators. Many modern liberals seem keen to restrict choice of co-operation between people, and sometimes mandate particular politically chosen co-operators. But you haven't abolished competition that way. You have simply shifted the decision making from the voluntary marketplace into the political arena. There will still be plenty of annoyed potential co-operators who didn't have the political nous to gain a license to trade, or a particular contract with the Government, for example. So I think it is for modern liberals to demonstrate that they are not anti-co-operative rather than for classical liberals to show that they are.
Co-operation isn't the only thing that classical liberal emphasise either. In fact, the ability to partake in perhaps the highest forms of sociability, friendship, was a key success of the classical liberal tradition. Do classical liberals boil down friendship as an institution into the pursuit of one's own interests? Far from it. In fact, as Allan Silver points out in his survey of Scottish Englightenment thinkers, it is the ability to engage in wider forms of commercial endeavour that allows people to pursue friendship for the sake of it.
In the past, people's personal associations were pretty much defined for them by family, church, feudal lords and other political structures. You were 'friends' with those who could protect you, serve you, or help provide for your subsistence. Once the political structures became more liberal, allowing widespread co-operation between relative strangers, one could dispense with these forced associations and actually just hang out with people you liked for the sake of it. You also have more options about who you can 'socially acceptably' fall in love with. It is no coincidence that as market economies develop, even the most primary institution of the family starts to take on more voluntary aspects.
When markets work, they allow you to get the annoying little things like food and shelter out of the way, so that you have more time to pursue more important interests. What do classical liberals hold those interest to be? With their emphasis on friendship as a principle, it seems that intimacy and sociability are classical liberalism's highest values.