Agrippa and the Greek skeptics
The following tropes for Greek skepticism are given by Sextus Empiricus, in his Outlines of Pyrrhonism. According to Sextus, they are attributed only "to the more recent skeptics" and it is by Diogenes Laertius that we attribute them to Agrippa.[1] The tropes are:
Dissent – The uncertainty of the rules of common life, and of the opinions of philosophers.
Progress ad infinitum – All proof requires some further proof, and so on to infinity.
Relation – All things are changed as their relations become changed, or, as we look upon them from different points of view.
Assumption – The truth asserted is merely a hypothesis.
Circularity – The truth asserted involves a vicious circle (see regress argument, known in scholasticism as diallelus)
The Münchhausen trilemma,
Also called Agrippa's trilemma, purports that it is impossible to prove any certain truth even in fields such as logic and mathematics. According to this argument, the proof of any theory rests either on circular reasoning, infinite regress, or unproven axioms.
Infinite regression
Overlooking for a moment the complications posed by Gettier problems, philosophy has essentially continued to operate on the principle that knowledge is justified true belief. The obvious question that this definition entails is how one can know whether one's justification is sound. One must therefore provide a justification for the justification. That justification itself requires justification, and the questioning continues interminably. The conclusion is that no one can truly have knowledge of anything, since it is, due to this infinite regression, impossible to satisfy the justification element. In practice, this has caused little concern to philosophers, since the line between a reasonably exhaustive investigation and superfluous investigation is usually clear, while others argue for coherentist systems and others still view an infinite regress as unproblematic due to recent work by Peter D. Klein. Nevertheless, the question remains theoretically interesting
The Molyneux problem
dates back to the following question posed by William Molyneux to John Locke in the 17th century: if a man born blind, and able to distinguish by touch between a cube and a globe, were made to see, could he now tell by sight which was the cube and which the globe, before he touched them? The problem raises fundamental issues in epistemology and the philosophy of mind, and was widely discussed after Locke included it in the second edition of his Essay Concerning Human Understanding.
A similar problem was also addressed earlier in the 12th century by Ibn Tufail (Abubacer), in his philosophical novel, Hayy ibn Yaqdhan (Philosophus Autodidactus). His version of the problem, however, dealt mainly with colors rather than shapes.
Modern science may now have the tools necessary to test this problem in controlled environments. The resolution of this problem is in some sense provided by the study of human subjects who gain vision after extended congenital blindness. One such subject took approximately a year to recognize most household objects purely by sight.[citation needed] This indicates that this may no longer be an unsolved problem in philosophy.
Qualia
The question hinges on whether color is a product of the mind or an inherent property of objects. While most philosophers will agree that color assignment corresponds to spectra of light frequencies, it is not at all clear whether the particular psychological phenomena of color are imposed on these visual signals by the mind, or whether such qualia are somehow naturally associated with their noumena.
Moral luck
The problem of moral luck is that some people are born into, live within, and experience circumstances that seem to change their moral culpability when all other factors remain the same.
For instance, a case of circumstantial moral luck: a poor person is born into a poor family, and has no other way to feed himself so he steals his food. Another person, born into a very wealthy family, does very little but has ample food and does not need to steal to get it. Should the poor person be more morally blameworthy than the rich person? After all, it is not his fault that he was born into such circumstances, but a matter of "luck".
A related case is resultant moral luck. For instance, two persons behave in a morally culpable way, such as driving carelessly, but end up producing unequal amounts of harm: one strikes a pedestrian and kills him, while the other does not. That one driver caused a death and the other did not is no part of the drivers' intentional actions; yet most observers would likely ascribe greater blame to the driver who killed. (Compare consequentialism.)
Moore's paradox
Although this problem has received relatively little attention, it intrigued philosopher Ludwig Wittgenstein when G. E. Moore presented it to the Moral Science Club at Cambridge.[citation needed] The statement "Albany is the capital of New York, but I don't believe it" is not necessarily false, but it seems to be unassertable. The speaker cannot simultaneously assert that Albany is the capital of New York and his disbelief in that statement. To claim that the capital of New York is Albany makes an assertion which is either true or false. Someone making this assertion implies that they believe it. When they go on to assert 'but I don't believe it', they contradict not the original assertion but the original implication.
Mathematical objects
What are numbers, sets, groups, points, etc.? Are they real objects or are they simply relationships that necessarily exist in all structures? Although many disparate views exist regarding what a mathematical object is, the discussion may be roughly partitioned into two opposing schools of thought: platonism, which asserts that mathematical objects are real, and formalism, which asserts that mathematical objects are merely formal constructions. This dispute may be better understood when considering specific examples, such as the "continuum hypothesis". The continuum hypothesis has been proven independent of the ZF axioms of set theory, so according to that system, the proposition can neither be proven true nor proven false. A formalist would therefore say that the continuum hypothesis is neither true nor false, unless you further refine the context of the question. A platonist, however, would assert that there either does or does not exist a transfinite set with a cardinality less than the continuum but greater than any countable set.[citation needed] So, regardless of whether it has been proven unprovable, the platonist would argue that an answer nonetheless does exist.
Sorites paradox
Otherwise known as the "paradox of the heap", the question regards how one defines a "thing." Is a bale of hay still a bale of hay if you remove one straw? If so, is it still a bale of hay if you remove another straw? If you continue this way, you will eventually deplete the entire bale of hay, and the question is: at what point is it no longer a bale of hay? While this may initially seem like a superficial problem, it penetrates to fundamental issues regarding how we define objects. This is similar to Theseus' paradox and the Continuum fallacy
Counterfactual conditional
A counterfactual is a statement that follows this form: "If Joseph Swan had not invented the modern incandescent light bulb, then someone else would have invented it anyway." People use counterfactuals every day; however, its analysis is not so clear
Philosophy of science[edit]
Problem of induction[edit]
Main article: Problem of induction
Intuitively, it seems to be the case that we know certain things with absolute, complete, utter, unshakable certainty. For example, if you travel to the Arctic and touch an iceberg, you know that it would feel cold. These things that we know from experience are known through induction. The problem of induction in short; (1) any inductive statement (like the sun will rise tomorrow) can only be deductively shown if one assumes that nature is uniform. (2) the only way to show that nature is uniform is by using induction. Thus induction cannot be justified deductively.
Demarcation problem[edit]
Main article: Demarcation problem
‘The problem of demarcation’ is an expression introduced by Karl Popper to refer to ‘the problem of finding a criterion which would enable us to distinguish between the empirical sciences on the one hand, and mathematics and logic as well as "metaphysical" systems on the other’. Popper attributes this problem to Kant. Although Popper mentions mathematics and logic, other writers focus on distinguishing science from metaphysics and pseudo-science.
Some, including Popper, raise the problem because of an intellectual desire to clarify this distinction. Logical positivists had, in addition, a social and intellectual agenda to discredit non-scientific disciplines.
Realism[edit]
Main article: Scientific realism
Is there a world independent of human beliefs and representations? Is such a world empirically accessible, or would such a world be forever beyond the bounds of human sense and hence unknowable? Can human activity and agency change the objective structure of the world? These questions continue to receive much attention in the philosophy of science. A clear "yes" to the first question is a hallmark of the scientific realism perspective. Philosophers such as Bas van Fraassen have important and interesting answers to the second question. In addition to the realism vs. empiricism axis of debate, there is a realism vs. social constructivism axis which heats many academic passions. With respect to the third question, Paul Boghossian's "Fear of Knowledge: Against Relativism and Constructivism". Oxford University Press. 2006. is a powerful critique of social constructivism, for instance. Ian Hacking's The Social Construction of What? (Harvard UP, 2000) constitutes a more moderate critique of constructivism, which usefully disambiguates confusing polysemy of the term "constructivism."
The following tropes for Greek skepticism are given by Sextus Empiricus, in his Outlines of Pyrrhonism. According to Sextus, they are attributed only "to the more recent skeptics" and it is by Diogenes Laertius that we attribute them to Agrippa.[1] The tropes are:
Dissent – The uncertainty of the rules of common life, and of the opinions of philosophers.
Progress ad infinitum – All proof requires some further proof, and so on to infinity.
Relation – All things are changed as their relations become changed, or, as we look upon them from different points of view.
Assumption – The truth asserted is merely a hypothesis.
Circularity – The truth asserted involves a vicious circle (see regress argument, known in scholasticism as diallelus)
The Münchhausen trilemma,
Also called Agrippa's trilemma, purports that it is impossible to prove any certain truth even in fields such as logic and mathematics. According to this argument, the proof of any theory rests either on circular reasoning, infinite regress, or unproven axioms.
Infinite regression
Overlooking for a moment the complications posed by Gettier problems, philosophy has essentially continued to operate on the principle that knowledge is justified true belief. The obvious question that this definition entails is how one can know whether one's justification is sound. One must therefore provide a justification for the justification. That justification itself requires justification, and the questioning continues interminably. The conclusion is that no one can truly have knowledge of anything, since it is, due to this infinite regression, impossible to satisfy the justification element. In practice, this has caused little concern to philosophers, since the line between a reasonably exhaustive investigation and superfluous investigation is usually clear, while others argue for coherentist systems and others still view an infinite regress as unproblematic due to recent work by Peter D. Klein. Nevertheless, the question remains theoretically interesting
The Molyneux problem
dates back to the following question posed by William Molyneux to John Locke in the 17th century: if a man born blind, and able to distinguish by touch between a cube and a globe, were made to see, could he now tell by sight which was the cube and which the globe, before he touched them? The problem raises fundamental issues in epistemology and the philosophy of mind, and was widely discussed after Locke included it in the second edition of his Essay Concerning Human Understanding.
A similar problem was also addressed earlier in the 12th century by Ibn Tufail (Abubacer), in his philosophical novel, Hayy ibn Yaqdhan (Philosophus Autodidactus). His version of the problem, however, dealt mainly with colors rather than shapes.
Modern science may now have the tools necessary to test this problem in controlled environments. The resolution of this problem is in some sense provided by the study of human subjects who gain vision after extended congenital blindness. One such subject took approximately a year to recognize most household objects purely by sight.[citation needed] This indicates that this may no longer be an unsolved problem in philosophy.
Qualia
The question hinges on whether color is a product of the mind or an inherent property of objects. While most philosophers will agree that color assignment corresponds to spectra of light frequencies, it is not at all clear whether the particular psychological phenomena of color are imposed on these visual signals by the mind, or whether such qualia are somehow naturally associated with their noumena.
Moral luck
The problem of moral luck is that some people are born into, live within, and experience circumstances that seem to change their moral culpability when all other factors remain the same.
For instance, a case of circumstantial moral luck: a poor person is born into a poor family, and has no other way to feed himself so he steals his food. Another person, born into a very wealthy family, does very little but has ample food and does not need to steal to get it. Should the poor person be more morally blameworthy than the rich person? After all, it is not his fault that he was born into such circumstances, but a matter of "luck".
A related case is resultant moral luck. For instance, two persons behave in a morally culpable way, such as driving carelessly, but end up producing unequal amounts of harm: one strikes a pedestrian and kills him, while the other does not. That one driver caused a death and the other did not is no part of the drivers' intentional actions; yet most observers would likely ascribe greater blame to the driver who killed. (Compare consequentialism.)
Moore's paradox
Although this problem has received relatively little attention, it intrigued philosopher Ludwig Wittgenstein when G. E. Moore presented it to the Moral Science Club at Cambridge.[citation needed] The statement "Albany is the capital of New York, but I don't believe it" is not necessarily false, but it seems to be unassertable. The speaker cannot simultaneously assert that Albany is the capital of New York and his disbelief in that statement. To claim that the capital of New York is Albany makes an assertion which is either true or false. Someone making this assertion implies that they believe it. When they go on to assert 'but I don't believe it', they contradict not the original assertion but the original implication.
Mathematical objects
What are numbers, sets, groups, points, etc.? Are they real objects or are they simply relationships that necessarily exist in all structures? Although many disparate views exist regarding what a mathematical object is, the discussion may be roughly partitioned into two opposing schools of thought: platonism, which asserts that mathematical objects are real, and formalism, which asserts that mathematical objects are merely formal constructions. This dispute may be better understood when considering specific examples, such as the "continuum hypothesis". The continuum hypothesis has been proven independent of the ZF axioms of set theory, so according to that system, the proposition can neither be proven true nor proven false. A formalist would therefore say that the continuum hypothesis is neither true nor false, unless you further refine the context of the question. A platonist, however, would assert that there either does or does not exist a transfinite set with a cardinality less than the continuum but greater than any countable set.[citation needed] So, regardless of whether it has been proven unprovable, the platonist would argue that an answer nonetheless does exist.
Sorites paradox
Otherwise known as the "paradox of the heap", the question regards how one defines a "thing." Is a bale of hay still a bale of hay if you remove one straw? If so, is it still a bale of hay if you remove another straw? If you continue this way, you will eventually deplete the entire bale of hay, and the question is: at what point is it no longer a bale of hay? While this may initially seem like a superficial problem, it penetrates to fundamental issues regarding how we define objects. This is similar to Theseus' paradox and the Continuum fallacy
Counterfactual conditional
A counterfactual is a statement that follows this form: "If Joseph Swan had not invented the modern incandescent light bulb, then someone else would have invented it anyway." People use counterfactuals every day; however, its analysis is not so clear
Philosophy of science[edit]
Problem of induction[edit]
Main article: Problem of induction
Intuitively, it seems to be the case that we know certain things with absolute, complete, utter, unshakable certainty. For example, if you travel to the Arctic and touch an iceberg, you know that it would feel cold. These things that we know from experience are known through induction. The problem of induction in short; (1) any inductive statement (like the sun will rise tomorrow) can only be deductively shown if one assumes that nature is uniform. (2) the only way to show that nature is uniform is by using induction. Thus induction cannot be justified deductively.
Demarcation problem[edit]
Main article: Demarcation problem
‘The problem of demarcation’ is an expression introduced by Karl Popper to refer to ‘the problem of finding a criterion which would enable us to distinguish between the empirical sciences on the one hand, and mathematics and logic as well as "metaphysical" systems on the other’. Popper attributes this problem to Kant. Although Popper mentions mathematics and logic, other writers focus on distinguishing science from metaphysics and pseudo-science.
Some, including Popper, raise the problem because of an intellectual desire to clarify this distinction. Logical positivists had, in addition, a social and intellectual agenda to discredit non-scientific disciplines.
Realism[edit]
Main article: Scientific realism
Is there a world independent of human beliefs and representations? Is such a world empirically accessible, or would such a world be forever beyond the bounds of human sense and hence unknowable? Can human activity and agency change the objective structure of the world? These questions continue to receive much attention in the philosophy of science. A clear "yes" to the first question is a hallmark of the scientific realism perspective. Philosophers such as Bas van Fraassen have important and interesting answers to the second question. In addition to the realism vs. empiricism axis of debate, there is a realism vs. social constructivism axis which heats many academic passions. With respect to the third question, Paul Boghossian's "Fear of Knowledge: Against Relativism and Constructivism". Oxford University Press. 2006. is a powerful critique of social constructivism, for instance. Ian Hacking's The Social Construction of What? (Harvard UP, 2000) constitutes a more moderate critique of constructivism, which usefully disambiguates confusing polysemy of the term "constructivism."