Best to start from first principles, since people argue the same issue from different points of view and never get anywhere. First, look at the Constitution. Patents, like copyrights, are not a property right or a natural right.
Copyrights and patents appear in the Constitution in Article 1, Section 8, along with other miscellaneous economic powers of Congress. They're right next to "Post offices and post roads".
If patents are not a natural right or a property right, what are they? As you might guess by the post office and road connection, they're a government program to promote economic growth. Patents are intended to do two things: promote R&D investment by the private sector; and encourage the private sector to publish inventions. The Constitution makes this explicit in its stated reason for copyrights and patents: "to promote the progress of science and useful arts."
Patents reward these two economically desirable behaviors (doing research and publishing) with a temporary government-granted monopoly on a particular invention. Congress has full discretion on what kinds of content can get a patent and on how long a patent can last. (If patents were a "right" the Constitution would require them -- as it is, the Constitution only _allows_ them.)
So, how should Congress decide which kinds of content get a patent and which don't? Using economics. After all, you have to draw the line of what gets a patent and what doesn't _somewhere_. If you allow the patenting of rhyming words, sports plays, or musical notes, day-to-day life becomes an impossible mess of patent cross-licensing. And, as for these areas, there is no economic evidence that software patents help the economy or even encourage R&D. They may do the opposite:
Through a sequence of court decisions, patent protection for computer programs was significantly strengthened. We will show that, far from unleashing a flurry of new innovative activity, these stronger property rights ushered in a period of stagnant, if not declining, R&D among those industries and firms that patented most.
Software patents, by virtue of their high transaction costs, throw away the reason for software to exist at all -- software is a good thing because in software, a small investment can create and manage great complexity. There may be increased R&D investment in a few areas, such as video compression, due to the prospect of a lucrative patent, but this economic gain is swamped by the transaction costs to developers and users. (Look at the MPEG patent pool controversy.)
Software patent opponents argue simply that the "line of patentabilty" should be drawn to exclude algorithms, as it already excludes ordinary mathematical theorems and their proofs. The advocates of the "GPL patent pool" hope to cut the transaction costs where GPL software is concerned but cannot hope to ameliorate patents' harm to proprietary software developers.
GPL Patent-Pool-O-Meter: 20Raph Levien's 19 graphics patents
The RTLinux patent