No: computers can't have free will
Machines only do what they have been designed to do and can't make voluntary, unconstrained decisions that are independent of the influence of deterministic factors. Hence, they lack free will and, therefore, can't think.

2

This view has been held by many since the conception of computing machines. Probably the first published claim of this sort is by Lady Lovelace, who is cited by Alan Turing, 1950, p. 449 and Douglas Hartree in their discussion of this issue in the 1950s. The source of the Lady Lovelace objection is provided in the source book page for box 17, "Computers only exhibit the free will of their programmers."

References

Turing, A. M. 1950. Computing machinery and intelligence. Mind, Vol. LIX, No. 236, Oct. 1950, pp. 433-460.

Hartree, Douglas. 1949.Calculating Instruments and Machines, New York.

Free will: The ability to make voluntary unconstrained decisions. Freely made decisions are independent of the influence of such deterministic factors as genetics (nature) and conditioning (nurture).

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Artificial Intelligence »Artificial Intelligence
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Can computers think? [1] »Can computers think? [1]
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No: computers can't have free will
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Computers can't do otherwise »Computers can't do otherwise
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Computers don't choose their own rules »Computers don't choose their own rules
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Free will has infititude beyond deterministic limits »Free will has infititude beyond deterministic limits
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A determined machine can still have free will »A determined machine can still have free will
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Computers only exhibit the free will of programmers »Computers only exhibit the free will of programmers
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Free will derives from multi-level structure »Free will derives from multi-level structure
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Free will is a decision-making process »Free will is a decision-making process
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Humans also lack free will »Humans also lack free will
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Random selection produces free will »Random selection produces free will
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No: computers can't be creative »No: computers can't be creative
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