Does this example prove that an infinite causal regress is impossible? Let's suppose that a soldier wants to shoot a bullet, but in order to so he must receive an order from his superior, and his superior must himself receive the order from his superior .... if this chain goes to infinity, the first soldier will never shoot a bullet.  So does that mean that an infinite regress of causes is impossible ?
Is infinite regress of causation possible? Is infinite regress of causation necessary? For a number of reasons &mdash; including perhaps a desire to feel that we have a complete understanding of where we came from, or at least an understanding which is completely sufficient for all of our purposes &mdash; there is a strong tendency to suppose that an infinite regress of causes and effects is impossible. We see this for instance in the . Traditionally in Greco-Roman influenced philosophy, this prime mover has been identified with the notion of a creator god. A more modern formulation comes from the Big Bang theory, which (although we study the question) happened for no reason that we know of; and perhaps occurred for no reason at all. Indeed, if time is a property of the universe, a good argument can be made that .  At the same time, we have gotten a lot of leverage in science from the ideas that everything happens for a reason, i.e.&nbsp;because it is caused by something else. This is sometimes described as the . Aristotle also applies this idea, except that the first mover is made an exception, something which exists literally for no reason. Indeed, the emotionally negative way that "no reason" is used in common speech, as something groundless and irrational, indicates how widespread the feeling is that the idea of uncaused events is deeply dissatisfying.  Almost all of our modes of critical thinking are infused with both of these ideas: that we may work from first principles, a definite starting point, counting up from zero (or one, historically); but also that we may trace the causes of things to some point, and then later ask how that starting point came to be. But the two ideas are themselves in conflict.  Which is true &mdash; that infinite causal chains are impossible? Or that they are necessary? Or are they perhaps possible without being necessary?   Related questions:
Dilemma: Present Perfect Or Perfect Continuous? Let $f:\mathbb{R}\to\mathbb{R}$ continuous such that $\lim_{x\to\infty}f(x+1)-f(x)=l$.  How can I prove that $\dfrac{f(x)}x$ converges for $x\to+\infty$ ?  I am just trying to prove the convergence, not that it converges to $l$ (that part be deduced immediately by Stolz-Cesaro and the sequential characterization of limits) Probability that the bag contains all balls white given that two balls are white A bag contains $4$ balls .Two balls are drawn at random and are found to be white.  What is the probability that all the four balls in the bag are white?.  The options are $\large\frac{1}{5}\space ;\frac{2}{5} ;\frac{3}{5} ;\frac{4}{5}$  My work: It's given that two balls are white.So the rest of the balls could be    all white One of them white none of them white   So among the three above possibilities only one satisfies our conditions so the probability is $\frac{1}{3}$.But it not even the options given. What's wrong with my work? Excel multiple FIND formula How to apply layer style to one object and apply it to multiple layers Foreign key constraints failures Given the following tables:  CREATE TABLE `longdescs` (   `comment_id` int(11) NOT NULL AUTO_INCREMENT,   `bug_id` mediumint(9) NOT NULL,   `who` mediumint(9) NOT NULL,   `bug_when` datetime NOT NULL,   `work_time` decimal(7,2) NOT NULL DEFAULT '0.00',   `thetext` mediumtext NOT NULL,   `isprivate` tinyint(4) NOT NULL DEFAULT '0',   `already_wrapped` tinyint(4) NOT NULL DEFAULT '0',   `type` smallint(6) NOT NULL DEFAULT '0',   `extra_data` varchar(255) DEFAULT NULL,   PRIMARY KEY (`comment_id`),   KEY `longdescs_bug_id_idx` (`bug_id`),   KEY `longdescs_who_idx` (`who`,`bug_id`),   KEY `longdescs_bug_when_idx` (`bug_when`),   KEY `comment_id` (`comment_id`),   CONSTRAINT `fk_longdescs_bug_id_bugs_bug_id` FOREIGN KEY (`bug_id`) REFERENCES `bugs` (`bug_id`) ON DELETE CASCADE ON UPDATE CASCADE,   CONSTRAINT `fk_longdescs_who_profiles_userid` FOREIGN KEY (`who`) REFERENCES `profiles` (`userid`) ON UPDATE CASCADE ) ENGINE=InnoDB AUTO_INCREMENT=82727 DEFAULT CHARSET=utf8  CREATE TABLE `trace` (   `id` mediumint(9) NOT NULL AUTO_INCREMENT,   `comment_id` mediumint(9) NOT NULL,   `type` varchar(255) NOT NULL,   `short_hash` char(22) DEFAULT NULL,   `stack_hash` char(22) DEFAULT NULL,   `trace_text` mediumtext NOT NULL,   `quality` double NOT NULL,   PRIMARY KEY (`id`),   UNIQUE KEY `trace_comment_id_idx` (`comment_id`),   KEY `trace_short_hash_idx` (`short_hash`),   KEY `trace_stack_hash_idx` (`stack_hash`) ) ENGINE=InnoDB AUTO_INCREMENT=2 DEFAULT CHARSET=utf8  ALTER TABLE trace ADD CONSTRAINT `fk_trace_comment_id_longdescs_comment_id` FOREIGN KEY (`comment_id`) REFERENCES `longdescs`(`comment_id`) ON UPDATE CASCADE ON DELETE CASCADE; ERROR 1005 (HY000): Can't create table 'bugs4.#sql-4bb_6f1d' (errno: 150)   MariaDB [bugs4]> show warnings;  | Level  | Code | Message | | Warning |  150 | Create table 'bugs4/#sql-4bb_6f1d' with foreign key     constraint failed. There is no index in the referenced table where the referenced columns appear as the first columns.  | | Error   | 1005 | Can't create table 'bugs4.#sql-4bb_6f1d' (errno: 150)                                                                                                                       |   Any idea why I get that error? FYI I looked it up and it appears that it was a bug but not anymore. How to compute PCA scores from eigendecomposition of the covariance matrix? Given a data matrix $\mathbf X$ of $12 \times 7$ size with samples in rows and variables in columns, I have calculated centered data $\mathbf X_c$ by subtracting column means, and then computed covariance matrix as $\frac{1}{N-1} \mathbf X_c^\top \mathbf X_c$.  The dimensions of this covariance matrix are $7 \times 7$. After that I have calculated the eigenvalue decomposition, obtaining eigenvector matrix $\mathbf V$ with eigenvectors in columns.  Now I want to know about projections (i.e. principal component scores in PCA): is it $\mathbf{V}^\top \mathbf{X}_c$ or $\mathbf{X}_c \mathbf{V}$?  mean_matrix = X - repmat(mean(X),size(X,1),1); covariance = (transpose(mean_matrix) * mean_matrix)/(12-1);  [V,D] = eig(covariance); [e,i] = sort(diag(D), 'descend'); V_sorted = V(:,i); Show that $S + T$ and $aT$ are linear Let  $S:  V \to W$ and $T: V \to W$ be linear transformations. Given $a$ in $\mathbb{R}$, define functions $(S+T): V \to W$ and $(aT): V \to W$ by $(S+T)(v)=S(v) + T(v)$ and $(aT)(v)= aT(v)$ for all $v$ in $V$. Show that $S+T$ and $aT$ are linear transformations. Let $f: \mathbb N \rightarrow \mathbb N$ are increasing function such that $f\left(f(n)\right)=3n$. Find $f(2017)$ Compute $\mathbb{P}\{ W_t < 0 \, \, \text{for all} \, \, 1 < t < 2\}$ for a Brownian motion $(W_t)_{t \geq 0}$ Let $(W_t)_{t \ge 0}$ be a standard one-dimensional Brownian motion. Calculate $$\mathbb{P}\{ W_t &lt; 0 \, \, \text{for all} \, \, 1 &lt; t &lt; 2\}.$$ I can only think that this will be conditional on $W_1$. Please tell how to proceed? Illustrator: Is there an efficient and accurate way to join two circles by their tangents (and keep it editable)? It's easy to join two circles if they are the same size and horizontal/vertical, into a pill shape:    If the circles are at an add angle then it's still possible but you can no longer rely on smart guides.     You can add lines roughly where the tangents should be and then use the scissors tool on the circles, cut out the inner area and then join the two crescents into one shape.    Is there a better way to do this? Is there a way to do this that is still editable afterwards too?  There are some other questions that cover the same area as this but don't cover editability or joining circles that are not in line with each other (where smart guides can't help). How can I forward delete on iOS? Is there a way to delete text in front of the caret using the iOS software keyboard? The small wireless hardware keyboard accomplishes this with a fn+delete, so there might be a way to use multiple keys to accomplish the same task in iOS? I absolutely hate it when I watch a video on YouTube and it automatically loads another video page after it's done playing.  This is especially annoying when I'm in the middle of typing a comment as it will cause me to lose what I have typed.  I'd like the video to simply stop and for no further action to take place once it is finished playing.  Is there any way to accomplish this? "find: missing argument to `-exec'" when using "-exec rm -f {}\" Today I open my SO account like I always do. But the UI of menus has changed. I am not able to see the chat tab, the logout link or the privileges link. Are they missing or moved somewhere else?  Changed UI: How to show path-connectedness of $GL(n,\mathbb{C})$ Well, I am not getting any hint how to show $GL_n(\mathbb{C})$ is path connected. So far I have thought that let $A$ be any invertible complex matrix and $I$ be the idenity matrix, I was trying to show a path from $A$ to $I$ then define $f(t)=At+(1-t)I$  for $t\in[0,1]$ which is possible continous except where the $\operatorname{det}{f(t)}=0$ i.e. which has $n$ roots and I can choose a path in $\mathbb{C}\setminus\{t_1,\dots,t_n\}$ where $t_1,\dots,t_n$ are roots of $\operatorname{det}{f(t)}=0$, is my thinking was correct? Could anyone tell me the solution? How to yield from parallel tasks in .NET 4.5 How does "warp drive" not violate Special Relativity causality constraints? I'm talking about this nonsense:   Now, I'm aware that there are problems with the practicalities (or possibilities) of methods involving exotic matter with negative mass, and that kind of thing has been addressed here:   But in this case my question is different and more specific. Sweeping all the other problems of constructing such a beast under the rug, wouldn't this violate causality?  SR says that the simultaneity and relative ordering of events is dependent on the relative motion of the observer, but that no matter how it works out, if event A causes event B, no observer will see B first. One of the many problems with FTL travel (or signals) is that if any information is sent faster than light, there will exist an inertial frame in which the signal arrives before it is sent, a blatant violation of causality. (I think we can all agree, can we not, that the threshold should be extremely high before breaking assumptions that we're in a causal universe?)  So how is any scheme to travel faster than light, even if it may locally satisfy the equations of GR, not a blatant violation causality according to SR?  Is my understanding of GR incomplete and there's something in it that obviates the causality implications of SR? Or am I correct that FTL claims should be dismissed with extreme prejudice on this basis alone? (Pending a serious replicable experiment showing causality to be breakable.) Show that the set $\mathbb{Q}[\sqrt{2}] = \{a + b \sqrt{2} \mid a, b \in \mathbb{Q}\}$ is a field with the usual multiplication and addition. Textarea CSS issue on "needs moderator attention" To reproduce:   Click Flag (question or answer) Click other (needs moderator attention)   The textarea is too wide:  StackOverflow        AskUbuntu        StackExchange        Most probably affects other sites, but didn't check. I think it's enough. :-)  Reproducing on:   Chromium Version 40.0.2214.111 Ubuntu 15.04 (64-bit) Google Chrome Version 41.0.2272.76 (64-bit) Firefox 36.0   (I'm using Ubuntu 15.04)