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Department of Logic, Institute of Philosophy, Jagiellonian University in Kraków, Poland
Department of Logic, Institute of Philosophy, Jagiellonian University in Kraków, Poland
Paradoxes are mental constructs which, despite their (seemingly impeccable) logical form, lead to conclusions that are intellectually or formally unacceptable. Some of these conclusions are internally inconsistent; others are manifestly incompatible with propositions commonly regarded as indubitable. There are also cases whose paradoxical nature results from reasoning that is itself logically dubious. The latter may be called paradoxes of one’s own making—logical puzzles that arise by design rather than by necessity.
Paradoxes are mental constructs which, despite their (seemingly impeccable) logical form, lead to conclusions that are intellectually or formally unacceptable. Some of these conclusions are internally inconsistent; others are manifestly incompatible with propositions commonly regarded as indubitable. There are also cases whose paradoxical nature results from reasoning that is itself logically dubious. The latter may be called paradoxes of one’s own making—logical puzzles that arise by design rather than by necessity.
The first part of the tutorial will be devoted to such pseudo-paradoxes. The second will address the vast and logically irresolvable problem of vagueness. The third will turn to the logical problem par excellence—the Liar Antinomy.
The first part of the tutorial will be devoted to such pseudo-paradoxes. The second will address the vast and logically irresolvable problem of vagueness. The third will turn to the logical problem par excellence—the Liar Antinomy.
1. Paradoxes of One’s Own Making
1. Paradoxes of One’s Own Making
Among the “made-to-order” logical problems, the principal class consists of those arising from ambiguity or equivocation. These problems are of little intrinsic importance and are rarely treated with seriousness. They typically function as amusing logical anecdotes rather than as genuine challenges to reasoning. Most are simple equivocations.
Among the “made-to-order” logical problems, the principal class consists of those arising from ambiguity or equivocation. These problems are of little intrinsic importance and are rarely treated with seriousness. They typically function as amusing logical anecdotes rather than as genuine challenges to reasoning. Most are simple equivocations.
Unfortunately, some of paradoxes of “one’s own making” have been granted undue philosophical significance and have evolved into prominent problems influencing the development of certain philosophical debates. Notable among these are Fitch’s Paradox of Knowability and Newcomb’s Problem, both of which will be examined in detail.
Unfortunately, some of paradoxes of “one’s own making” have been granted undue philosophical significance and have evolved into prominent problems influencing the development of certain philosophical debates. Notable among these are Fitch’s Paradox of Knowability and Newcomb’s Problem, both of which will be examined in detail.
2. Paradoxes of Vagueness and State Change
2. Paradoxes of Vagueness and State Change
There also exist logical problems that are not so easily dismissed. Perhaps the most serious among them is vagueness, along with its conceptual twin—the problem of state change. Attempts to resolve these difficulties tend to be less intuitive than the paradoxes themselves. Our discussion will focus on the interpretation of vague terms, balancing the requirement of logical rigor with the observation that, in everyday reasoning, vagueness seldom troubles us: we manage to live with it without falling into contradiction.
There also exist logical problems that are not so easily dismissed. Perhaps the most serious among them is vagueness, along with its conceptual twin—the problem of state change. Attempts to resolve these difficulties tend to be less intuitive than the paradoxes themselves. Our discussion will focus on the interpretation of vague terms, balancing the requirement of logical rigor with the observation that, in everyday reasoning, vagueness seldom troubles us: we manage to live with it without falling into contradiction.
3. The Liar Antinomy
3. The Liar Antinomy
The Liar Antinomy stands as one of the grand problems of logic—the very monarch among paradoxes of thought. Although its origins trace back to antiquity, it underwent a remarkable revival at the turn of the nineteenth and twentieth centuries. Numerous sophisticated solutions have since been proposed, many drawing upon significant mathematical theorems. Yet one must ask: is the Liar truly a mathematical problem? What, in fact, constitutes its essence? The adequacy of any proposed resolution may well depend on how this question is answered.
The Liar Antinomy stands as one of the grand problems of logic—the very monarch among paradoxes of thought. Although its origins trace back to antiquity, it underwent a remarkable revival at the turn of the nineteenth and twentieth centuries. Numerous sophisticated solutions have since been proposed, many drawing upon significant mathematical theorems. Yet one must ask: is the Liar truly a mathematical problem? What, in fact, constitutes its essence? The adequacy of any proposed resolution may well depend on how this question is answered.
References
References
[2] P. Łukowski, A “distributive” or a “collective” approach to sentences?, Logic and Logical Philosophy Vol.28, No.2 (2019), pp.331-354
[2] P. Łukowski, A “distributive” or a “collective” approach to sentences?, Logic and Logical Philosophy Vol.28, No.2 (2019), pp.331-354
[3] P. Łukowski, Formalizing the conditionals of Diodorus Cronus and Chrysippus: logic and potential applications in human thinking, Synthese , Vol.206, article 28 (2025)
[3] P. Łukowski, Formalizing the conditionals of Diodorus Cronus and Chrysippus: logic and potential applications in human thinking, Synthese , Vol.206, article 28 (2025)
and many others…
and many others…
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